Getting Started

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Here we document how to do some basic stuff, including learning and inference in kernel parameters, with Stheno.jl. To do this, we make use of a variety of packages from the Julia ecosystem:

AdvancedHMC.jl to perform Bayesian inference in our model parameters,
Optim.jl for point-estimates of our model parameters,
ParameterHandling.jl to make it easy to work with our model's parameters, and to ensure that it plays nicely with Optim and AdvancedHMC,
Zygote.jl to compute gradients.

This guide assumes that you know roughly what's going on conceptually with GPs. If you're new to Gaussian processes, an excellent introduction can be found in either this video lecture or this one.

Exact Inference in a GP in 2 Minutes

This is only a slightly more interesting version of the first example on the README. It's slightly more interesting in that we give the kernels some learnable parameters.

Import the packages we'll need for this bit of the demo.

using AbstractGPs
using LinearAlgebra
using Stheno
using Plots

Short length-scale and small variance.

l1 = 0.4
s1 = 0.2

0.2

Long length-scale and larger variance.

l2 = 5.0
s2 = 1.0

1.0

Specify a GaussianProcessProbabilisticProgramme object, which is itself a GP built from other GPs.

f = @gppp let
    f1 = s1 * stretch(GP(Matern52Kernel()), 1 / l1)
    f2 = s2 * stretch(GP(SEKernel()), 1 / l2)
    f3 = f1 + f2
end;

Generate a sample from f3, one of the processes in f, at some random input locations. Add some iid observation noise, with zero-mean and variance 0.02.

const x = GPPPInput(:f3, collect(range(-5.0, 5.0; length=100)));
σ²_n = 0.02;
fx = f(x, σ²_n);
const y = rand(fx);

Compute the log marginal likelihood of this observation, just because we can.

logpdf(fx, y)

26.167045566275164

fx should be thought of as "f at x", and is just as a multivariate Normal distribution, with zero mean and covariance matrix

heatmap(cov(f, x) + σ²_n * I)

As such samples can be drawn from it, and the log probability any particular value under it can be computed, in the same way that you would an MvNormal from Distributions.jl.

We can visualise x and y with Plots.jl

plt = plot();
scatter!(plt, x.x, y; color=:red, label="");
display(plt)

It's straightforward to compute the posterior over f:

f_posterior = posterior(fx, y);

f_posterior is another GP, the posterior over f given noisy observations y at inputs x.

The plotting recipes from AbstractGPs.jl can be utilised to easily print whichever component of the GPPP is needed.

x_plot = range(-7.0, 7.0; length=1000);
xp = GPPPInput(:f3, x_plot);
plot!(
    plt, x_plot, f_posterior(xp);
    ribbon_scale=3, label="", color=:blue, fillalpha=0.2, linewidth=2,
)
plot!(
    plt, x_plot, rand(f_posterior(xp, 1e-9), 10);
    samples=10, markersize=1, alpha=0.3, label="", color=:blue,
);
plt

So you've built a simple GP probabilistic programme, performed inference in it, and looked at the posterior. We've only looked at one component of it though – we could look at others. Consider f2:

xp2 = GPPPInput(:f2, x_plot);
plot!(
    plt, x_plot, f_posterior(xp2);
    ribbon_scale=3, label="", color=:red, fillalpha=0.2, linewidth=2,
);
plot!(
    plt, x_plot, rand(f_posterior(xp2, 1e-9), 10);
    alpha=0.3, label="", color=:red,
);
plt

Fit a GP with NelderMead in 2 Minutes

Stheno.jl is slightly unusual in that it declines to provide a fit or train function. Why is this? In short, because there's really no need – the ecosystem now contains everything that is needed to easily do this yourself. By declining to insist on an interface, Stheno.jl is able to interact with a wide array of tools, that you can use in whichever way you please.

Optim requires that you provide an objective function with a single Vector{<:Real} parameter for most of its optimisers. We'll use ParameterHandling.jl to build one of these in a way that doesn't involve manually writing code to convert between a structured, human-readable, representation of our parameters (in a NamedTuple) and a Vector{Float64}.

First, we'll put the model from before into a function:

function build_model(θ::NamedTuple)
    return @gppp let
        f1 = θ.s1 * stretch(GP(SEKernel()), 1 / θ.l1)
        f2 = θ.s2 * stretch(GP(SEKernel()), 1 / θ.l2)
        f3 = f1 + f2
    end
end

build_model (generic function with 1 method)

We've assumed that the parameters will be provided as a NamedTuple, so let's build one and check that the model can be constructed:

using ParameterHandling

θ = (
    # Short length-scale and small variance.
    l1 = positive(0.4),
    s1 = positive(0.2),

    # Long length-scale and larger variance.
    l2 = positive(5.0),
    s2 = positive(1.0),

    # Observation noise variance -- we'll be learning this as well. Constrained to be
    # at least 1e-3.
    s_noise = positive(0.1, exp, 1e-3),
)

(l1 = ParameterHandling.Positive{Float64, typeof(exp), Float64}(-0.9162907691270586, exp, 1.4901161193847656e-8), s1 = ParameterHandling.Positive{Float64, typeof(exp), Float64}(-1.6094379869399091, exp, 1.4901161193847656e-8), l2 = ParameterHandling.Positive{Float64, typeof(exp), Float64}(1.6094379094538682, exp, 1.4901161193847656e-8), s2 = ParameterHandling.Positive{Float64, typeof(exp), Float64}(-1.490116130486996e-8, exp, 1.4901161193847656e-8), s_noise = ParameterHandling.Positive{Float64, typeof(exp), Float64}(-2.312635428847547, exp, 0.001))

We've used ParameterHandling.jls positive constraint to ensure that all of the parameters remain positive during optimisation. Note that there's no magic here, and Optim knows nothing about positive. Rather, ParameterHandling knows how to make sure that Optim will optimise the log of the parameters which we want to be positive.

We can make this happen with the following:

using ParameterHandling
using ParameterHandling: value, flatten

θ_flat_init, unflatten = flatten(θ);

Concrete types used for clarity only.

unpack = value ∘ unflatten;

We can now easily define a function which accepts the flat form of the parameters, and return the negative log marginal likelihood (nlml) of the parameters θ:

function nlml(θ::NamedTuple)
    f = build_model(θ)
    return -logpdf(f(x, θ.s_noise + 1e-6), y)
end

nlml (generic function with 1 method)

We can use any gradient-free optimisation technique from Optim.jl to find the parameters whose negative log marginal likelihood is locally minimal:

using Optim
results = Optim.optimize(
    nlml ∘ unpack,
    θ_flat_init + randn(length(θ_flat_init)),
    NelderMead(),
)
θ_opt = unpack(results.minimizer);

Note that we just added some noise to the initial values to make the optimisation more interesting.

We can now use this to construct the posterior GP and look at the posterior in comparison to the true posterior with the known hyperparameters

f_opt = build_model(θ_opt);
f_posterior_opt = posterior(f_opt(x, θ_opt.s_noise), y);
ms_opt = marginals(f_posterior_opt(xp));
plot!(
    plt, x_plot, mean.(ms_opt);
    ribbon=3std.(ms_opt), label="", color=:green, fillalpha=0.2, linewidth=2,
);
plot!(
    plt, x_plot, rand(f_posterior_opt(xp, 1e-9), 10);
    alpha=0.3, label="", color=:green,
);
plt

Of course, the exact posterior has not been recovered because the exact hyperparameters cannot be expected to be recovered given a finite amount of data over a finite width window.

Fit a GP with BFGS in 2 minutes

The BFGS algorithm is generally the preferred choice when optimising the hyperparameters of fairly simple GPs. It requires access to the gradient of our nlml function, which can be straightforwardly obtained via reverse-mode algorithmic differentiation, which is provided by Zygote.jl:

using Zygote: gradient

This will probably take a while to get going as Zygote needs to compile.

results = Optim.optimize(
    nlml ∘ unpack,
    θ->gradient(nlml ∘ unpack, θ)[1],
    θ_flat_init + 0.1 * randn(length(θ_flat_init)),
    BFGS(),
    Optim.Options(
        show_trace=true,
    );
    inplace=false,
)
θ_bfgs = unpack(results.minimizer);

Iter     Function value   Gradient norm 
     0     1.170108e+01     3.410076e+01
 * time: 0.023088932037353516
     1    -2.084716e+01     1.402413e+01
 * time: 0.9327669143676758
     2    -2.185325e+01     1.285075e+01
 * time: 0.9400568008422852
     3    -2.573729e+01     5.798843e+00
 * time: 0.9474749565124512
     4    -2.702040e+01     3.970563e+00
 * time: 0.9580848217010498
     5    -2.720792e+01     2.862285e+00
 * time: 0.9857938289642334
     6    -2.738694e+01     1.133410e+00
 * time: 0.9927189350128174
     7    -2.741634e+01     1.605934e-01
 * time: 0.9992489814758301
     8    -2.741766e+01     6.390593e-02
 * time: 1.0058479309082031
     9    -2.741777e+01     2.254641e-03
 * time: 1.0312438011169434
    10    -2.741777e+01     4.129739e-04
 * time: 1.0419678688049316
    11    -2.741777e+01     7.111930e-06
 * time: 1.0487689971923828
    12    -2.741777e+01     2.759712e-07
 * time: 1.0638668537139893
    13    -2.741777e+01     1.214082e-09
 * time: 1.070429801940918

Once more visualising the results:

f_bfgs = build_model(θ_bfgs);
f_posterior_bfgs = posterior(f_bfgs(x, θ_bfgs.s_noise), y);
ms_bfgs = marginals(f_posterior_bfgs(xp));
plot!(
    plt, x_plot, mean.(ms_bfgs);
    ribbon=3std.(ms_bfgs), label="", color=:orange, fillalpha=0.2, linewidth=2,
);
plot!(
    plt, x_plot, rand(f_posterior_bfgs(xp, 1e-9), 10);
    alpha=0.3, label="", color=:orange,
);
plt

Notice that the two optimisers produce (almost) indistinguishable results.

Inference with NUTS in 2 minutes

AdvancedHMC.jl provides a state-of-the-art implementation of the No-U-Turns sampler, which we can use to perform approximate Bayesian inference in the hyperparameters of the GP. This is slightly longer than the previous examples, but it's all set up associated with AdvancedHMC, which is literally a copy-paste from that package's README:

using AdvancedHMC, Zygote

Define the log marginal joint density function and its gradient

ℓπ(θ_flat) = -nlml(unpack(θ_flat)) - 0.5 * sum(abs2, θ_flat)
function ∂ℓπ∂θ(θ_flat)
    lml, back = Zygote.pullback(ℓπ, θ_flat)
    ∂θ_flat = first(back(1.0))
    return lml, ∂θ_flat
end

∂ℓπ∂θ (generic function with 1 method)

Sampling parameter settings

n_samples, n_adapts = 500, 20

(500, 20)

Perturb the initialisation a little bit.

θ0_flat = θ_flat_init + 0.1 * randn(length(θ_flat_init))

5-element Vector{Float64}:
 -0.8540144085871901
 -1.671441179423649
  1.593404571893314
  0.07201657737340676
 -2.325955496061365

Define metric space, Hamiltonian, sampling method and adaptor

metric = DiagEuclideanMetric(5)
h = Hamiltonian(metric, ℓπ, ∂ℓπ∂θ)
int = Leapfrog(find_good_eps(h, θ0_flat))
prop = NUTS{MultinomialTS, GeneralisedNoUTurn}(int)
adaptor = StanHMCAdaptor(n_adapts, Preconditioner(metric), NesterovDualAveraging(0.8, int.ϵ))

StanHMCAdaptor(
    pc=WelfordVar,
    ssa=NesterovDualAveraging(γ=0.05, t_0=10.0, κ=0.75, δ=0.8, state.ϵ=0.8),
    init_buffer=75, term_buffer=50, window_size=25,
    state=window(76, -30), window_splits()
)

Perform inference.

samples, stats = sample(h, prop, θ0_flat, n_samples, adaptor, n_adapts; progress=true)

([[-0.8540144085871901, -1.671441179423649, 1.593404571893314, 0.07201657737340676, -2.325955496061365], [-0.8540144085871901, -1.671441179423649, 1.593404571893314, 0.07201657737340676, -2.325955496061365], [-0.37788121144782594, -1.565625884157911, 1.4257008338680641, -0.22549746440521273, -4.2385540149601475], [-0.8320667537703447, -1.7806616757741918, 1.5395578661269969, -0.44556976631848155, -3.399410513522236], [-1.2184903057973488, -1.7621943783457488, 1.4559712273184893, -1.403669552800396, -4.064923561401586], [-0.50003683692132, -1.5758763875661168, 0.07954884160999194, -0.458737149287061, -3.869051241048587], [-0.09516390505924988, -0.4852304142916978, -0.01411826482747744, -0.48393691595840294, -3.6472529861459257], [-0.25865226425035154, -0.483063507400526, -0.1906932965554575, -0.5566631876312145, -3.7073658746829414], [-1.4951882866213664, -1.987781163793732, 1.5357691332613612, -0.8533711223234419, -3.825091314678223], [-1.0004963405323806, -1.4719442210641307, 1.3567375044706853, -0.3841723315976137, -3.975480045505678], [-1.1156626649705972, -1.6244333721993782, 1.5321011936938098, -0.46183903878526744, -4.0201956739597], [-1.4044412222501457, -1.973306934970894, 1.5567651074524833, -0.35882364364036407, -4.11410273373961], [-0.7351696884384905, -1.2080837701493083, 1.0018813525297399, -0.45425924787457345, -3.583345383978572], [-0.693169326229582, -1.7310618907920021, 1.4488487380620765, -1.0451344504984708, -3.951491114737527], [-0.7935787822752399, -1.4473338460079057, 0.7632569452998645, -0.9853485286326106, -3.6633228800952065], [-1.3306013410145612, -1.6346385753864798, 1.8760908621453967, 0.034739947228634514, -3.9879929249837627], [-1.153849651936063, -1.433409357397685, 1.8601535905706585, -0.09097623024659801, -4.0657084019423655], [-1.0390884590702916, -1.6703255430859565, 1.183065536840299, -0.34209664856680366, -3.894583898270839], [-1.0390884590702916, -1.6703255430859565, 1.183065536840299, -0.34209664856680366, -3.894583898270839], [-0.9194958622669693, -1.2745091760334053, 1.0490033414744848, -0.5319079172519026, -3.8342749497291715], [-1.2610188424883573, -1.927348752454338, 1.7870940514458111, -0.9912733607577972, -3.922204612938939], [-1.3080197547266708, -1.6407768081966867, 1.4523137545516196, -0.6308293760752659, -4.149126335338955], [-0.9485027160845777, -1.201451784284443, 1.3019938642361535, -0.9346179102006444, -3.8669966734479733], [-0.8618119664732838, -1.5402260806215107, 1.546009846363032, -0.07771622878707185, -3.7958113213278], [-1.1991134647058868, -1.5548896406699297, 1.8316000300977278, -0.2623248699482653, -3.942492581455487], [-0.9996455287058672, -1.5597481994273485, 0.9953744825202263, -0.46477381535375817, -3.7351292445903783], [-1.428931441581258, -1.7661975151994342, 1.457084954201301, -0.7253220285471488, -4.007845082536074], [-0.6506894420168967, -1.2769185774945717, 1.25985693124919, 0.25845665105994414, -3.8866126423789074], [-0.5147460889670399, -1.1649517167348267, 1.3988266991876754, 0.4188360534566946, -4.15343451062087], [-0.7786459150110885, -1.5485986607556559, 1.1602575778593878, -0.8865694772116949, -3.3154837236356247], [-0.5991773605160572, -1.7513113329210184, 1.0226976189044008, -0.7724455510410889, -3.3823570124133613], [-1.0280318193372762, -1.086219845408079, 1.1729357378429865, -0.6611326501055322, -4.0319386312973515], [-0.9522107516521283, -1.5808029391014375, 1.3846599000776276, -0.5819642812467638, -3.7299142898264557], [-1.3681349788478223, -1.8670625567655366, 1.6551894743592117, -0.18529127690735056, -4.145653217633238], [-0.49233591302866847, -1.2708509439798659, 0.10894131327449266, -0.8567457995746054, -3.7870420692343005], [-0.8680092248320873, -1.3619261823037119, 0.9608147562389249, -0.35051608121282485, -3.7658640213027508], [-1.0836620285656813, -1.612595297131731, 0.3943778977594187, -0.47724596779428047, -4.058544357368397], [-1.0063173597306898, -1.5702688749490052, 1.8730104823775549, -0.9034393776664096, -4.00298527720487], [-0.31815793720636587, -1.1504683607439115, 1.5648266907097892, -0.6760694092166262, -3.258346820928002], [-1.1710647805522147, -1.3425026712149206, 1.5575336799759028, -0.3201304031803452, -4.17582941386129], [-0.9896519498147669, -1.7989833552735928, 0.8703815758378468, -0.8577345523228419, -3.7587793441982855], [-0.9273230779216671, -1.6629758496823794, 0.6083797831111388, 0.11466661107443488, -3.7042820282730173], [-1.1898254820566962, -1.6263753093976896, 1.8600653109642211, -0.97243808922474, -4.072829090946446], [-0.6996289033680517, -1.133848318136997, 1.541172338595726, -0.8793223130251069, -3.738644428296399], [-0.9905217648568252, -1.8152264710605022, 0.490502611825119, -1.015365334373073, -3.8928465329736532], [-1.0488222305416826, -1.5200474466693756, 1.6207089188747288, -0.30765136524325964, -3.728104522396042], [-1.0414162572751606, -1.5278856421034197, 1.1235520359861986, -0.9204946669496561, -3.917083150905882], [-1.0207659252067236, -1.5415187074611576, 1.5857752127748963, -0.3225135051447946, -3.994821245990608], [-1.4175850007487476, -1.6861618081573213, 1.8234767817845479, -0.4475457073135002, -3.928289861595007], [-1.006914989426204, -1.7538549201192046, 0.77590438552983, -0.43851029696545163, -3.8982285588529977], [-1.0590803737183585, -1.6461236766486587, 1.4611481351695965, -0.6494762558984235, -3.7197762394597973], [-0.8910590765682089, -1.2857425534554698, 1.5656642258201303, -0.21110028318046628, -3.924730409921791], [-1.4140944215483298, -1.983442894164883, 0.9116811797670764, -0.7152753006728936, -3.8618158043477733], [-1.2250872624709985, -1.4373021502947885, 1.0108595555069597, -0.7345992454457376, -3.7577518369358938], [-0.7278629642502907, -1.6767553178559276, 1.5042525782176115, -1.2898029281869428, -3.8768119924627777], [-1.0449755213489949, -1.0920073019899, 1.3021006274040732, -1.3552109062616366, -3.7666946712465097], [-1.2857726442590898, -2.240356982567733, 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0.18215471636218186, -3.6898670838047325], [-0.7345773504547977, -1.414375854871148, 1.7635719330876236, -0.45900155094391715, -4.0884530224168705], [-1.125557135190241, -1.9950358287000085, 0.6288049664683343, -0.7224987536394079, -3.9047601089626394], [-1.597735014702634, -1.7368592110751309, 1.0674578107591133, -0.649922818897479, -3.797727206305709], [-0.8816149945710919, -1.2983412705172466, 1.7075060245913, -0.5606725038655899, -3.448936336023402], [-1.3664812447238037, -1.664148213083287, 0.6468281772330136, -0.6900214933051851, -3.6778329799573877], [-0.9675784870150896, -1.801307261817187, 1.0820754920425457, -0.7720218975605878, -3.798993288887293], [-1.0262723384522343, -1.189885828681241, 1.2565906216059273, 0.5645962915318659, -3.7822275460360846], [-0.5709359282449546, -1.6274400678515941, 1.5716907246473375, 0.5863259500296253, -3.8608993494395083], [-1.3092978377478166, -1.7367904346592224, 1.4084934806701328, -1.1669397458737478, -4.38430687324242], [-1.3823764482454506, -1.550147489190739, 1.3992893389396988, -0.9136765595648184, -3.737301913532066], [-0.8208210166330427, -1.7734659195786473, 1.4046937310448688, -0.17322500348564907, -3.9889271330684344], [-1.0669325291555571, -1.295265538782186, 0.7454238553322264, -1.4381265965065086, -4.39164079656055], [-0.8965819332158627, -1.500425205278955, 1.1660165895273247, -1.4848330325145165, -3.6520273940966375], [-1.0782275087642683, -1.9143223046698568, 0.8876965639127516, -0.42572824761841765, -3.5323409794422735], [-1.2520049162043023, -1.722952874625037, 0.8532534907140981, -0.4656370660156171, -3.871835164674867], [-0.7223739558192417, -1.0609707069627752, 0.17805030671255856, -1.36493378958798, -3.813454361390979], [-0.9999166687676178, -1.581235555563521, 1.979869052808994, 0.7984559687877922, -3.823899136952413], [-0.921197090955432, -1.4742265892096555, 2.06117476328665, 0.2263599136143689, -3.9365383300116776], [-1.1569601322528842, -1.8073968640979807, 0.9550545156423251, -0.9965512881514029, -4.065452684630446], [-0.5115927789079247, -0.9402795685382869, 1.4687869759104042, -1.0383931999612788, -3.6989014709521006], [-0.9753457084062328, -1.5630690721120062, 1.0250467743943181, 0.023632725374117272, -3.6574736146129507], [-0.8721081943415949, -1.57935872676282, 1.810417452156335, -0.1341273913456158, -4.0119942280517416], [-1.1836791387801007, -1.1453794422630736, 1.6782964892924583, -0.34102442332044686, -4.06807924920482], [-0.9211201207283278, -2.0102676988720805, 2.0010318684569652, 0.14176951981697766, -3.891563328804593], [-1.050409759589945, -1.457626941663004, 1.6509800461952682, 0.5600922677870678, -4.015617204823946], [-0.9863622326525116, -1.8769552496023387, 1.2433664910647546, -1.165279264278902, -3.7473592069855712], [-1.0610141059910339, -1.502028793485609, 1.2114023335441255, -0.1386200675816752, -4.135236687894155], [-1.0885413562161703, -1.5962907504465422, 1.6237995823351814, -0.1024950598648456, -3.575368297708671], [-0.7723055338723117, -1.2961603750689277, 1.3067343239075921, -0.8397049480686191, -4.060569249829922]], NamedTuple[(n_steps = 1, is_accept = true, acceptance_rate = 0.0, log_density = -11.658445188088342, hamiltonian_energy = 15.173588876745226, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 18577.22944522172, tree_depth = 0, numerical_error = true, step_size = 0.8, nom_step_size = 0.8, is_adapt = true), (n_steps = 1, is_accept = true, acceptance_rate = 0.0, log_density = -11.658445188088342, hamiltonian_energy = 13.512658388222231, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 895845.4681648945, tree_depth = 0, numerical_error = true, step_size = 1.8680518327273068, nom_step_size = 1.8680518327273068, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 6.198361387578917, hamiltonian_energy = 8.46980494480131, hamiltonian_energy_error = -4.136300312801362, max_hamiltonian_energy_error = -4.136300312801362, tree_depth = 2, numerical_error = false, step_size = 0.18418867766839725, nom_step_size = 0.18418867766839725, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9437312947112206, log_density = 12.582185606931981, hamiltonian_energy = -2.9647693998996196, hamiltonian_energy_error = -2.1274607598717683, max_hamiltonian_energy_error = -2.514638735599087, tree_depth = 2, numerical_error = false, step_size = 0.19183312443074416, nom_step_size = 0.19183312443074416, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.8416865336974224, log_density = 13.06944411768601, hamiltonian_energy = -8.780776141828564, hamiltonian_energy_error = -0.6803044143394565, max_hamiltonian_energy_error = 1.0664388396511661, tree_depth = 2, numerical_error = false, step_size = 0.2209325967007916, nom_step_size = 0.2209325967007916, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.8822886724698505, log_density = 11.184740871757832, hamiltonian_energy = -10.578939669598476, hamiltonian_energy_error = 0.33568595516014454, max_hamiltonian_energy_error = 0.33568595516014454, tree_depth = 3, numerical_error = false, step_size = 0.214007790966611, nom_step_size = 0.214007790966611, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.20201771758818934, log_density = 10.772180593875273, hamiltonian_energy = -8.490243814925865, hamiltonian_energy_error = -0.18695394184125824, max_hamiltonian_energy_error = 78.51222609307129, tree_depth = 4, numerical_error = false, step_size = 0.24970249288702256, nom_step_size = 0.24970249288702256, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9995677020862591, log_density = 11.245584941852407, hamiltonian_energy = -10.445597671587986, hamiltonian_energy_error = -0.0023277655024163124, max_hamiltonian_energy_error = -0.022872082278563965, tree_depth = 4, numerical_error = false, step_size = 0.03665157236119139, nom_step_size = 0.03665157236119139, is_adapt = true), (n_steps = 31, is_accept = true, acceptance_rate = 0.9847536208008456, log_density = 13.036970677850762, hamiltonian_energy = -9.40410847927143, hamiltonian_energy_error = 0.006793073722725751, max_hamiltonian_energy_error = 0.060745965997792695, tree_depth = 5, numerical_error = false, step_size = 0.06514694623089154, nom_step_size = 0.06514694623089154, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 15.638202911810312, hamiltonian_energy = -12.640829462310412, hamiltonian_energy_error = -0.18515522941825502, max_hamiltonian_energy_error = -0.18515522941825502, tree_depth = 3, numerical_error = false, step_size = 0.11407023095024822, nom_step_size = 0.11407023095024822, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9715400376084344, log_density = 15.701821848790704, hamiltonian_energy = -14.968514706293433, hamiltonian_energy_error = -0.02845940222142218, max_hamiltonian_energy_error = 0.10490554282936237, tree_depth = 3, numerical_error = false, step_size = 0.21344317468480165, nom_step_size = 0.21344317468480165, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 0.051197164930052885, log_density = 13.311332443823849, hamiltonian_energy = -12.429014260354066, hamiltonian_energy_error = 1.981379192233284, max_hamiltonian_energy_error = 16.83772746322007, tree_depth = 2, numerical_error = false, step_size = 0.36845679664147213, nom_step_size = 0.36845679664147213, is_adapt = true), (n_steps = 31, is_accept = true, acceptance_rate = 0.9987561754964004, log_density = 13.703420693033788, hamiltonian_energy = -11.63313272512382, hamiltonian_energy_error = 0.007599402492807883, max_hamiltonian_energy_error = -0.008106701334732236, tree_depth = 5, numerical_error = false, step_size = 0.035179722059006734, nom_step_size = 0.035179722059006734, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9950040931860507, log_density = 13.190300821476708, hamiltonian_energy = -11.517872387297036, hamiltonian_energy_error = 0.016898134802298515, max_hamiltonian_energy_error = -0.06123408010504505, tree_depth = 4, numerical_error = false, step_size = 0.06719588138033394, nom_step_size = 0.06719588138033394, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9223868405235425, log_density = 14.920347291381933, hamiltonian_energy = -10.591863989232092, hamiltonian_energy_error = -0.14276560236332436, max_hamiltonian_energy_error = -0.40395358009258864, tree_depth = 4, numerical_error = false, step_size = 0.12670814312326076, nom_step_size = 0.12670814312326076, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.8969355491881521, log_density = 14.107979928030877, hamiltonian_energy = -11.59521160630402, hamiltonian_energy_error = -0.15388840360383682, max_hamiltonian_energy_error = 0.34502235571028983, tree_depth = 3, numerical_error = false, step_size = 0.19003851446685296, nom_step_size = 0.19003851446685296, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 0.684859699848118, log_density = 14.151002234802162, hamiltonian_energy = -13.229894362037584, hamiltonian_energy_error = 0.16095405520009898, max_hamiltonian_energy_error = 0.701408481073603, tree_depth = 2, numerical_error = false, step_size = 0.2628012540467184, nom_step_size = 0.2628012540467184, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9286787717242267, log_density = 15.8027489073489, hamiltonian_energy = -12.797194910313596, hamiltonian_energy_error = -0.19493668759964322, max_hamiltonian_energy_error = -0.19493668759964322, tree_depth = 2, numerical_error = false, step_size = 0.18961973169002772, nom_step_size = 0.18961973169002772, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.04923690900603607, log_density = 15.8027489073489, hamiltonian_energy = -14.377630305699716, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 132.23378869380815, tree_depth = 3, numerical_error = false, step_size = 0.2883020511218599, nom_step_size = 0.2883020511218599, is_adapt = true), (n_steps = 63, is_accept = true, acceptance_rate = 0.998030583987367, log_density = 15.067132966125008, hamiltonian_energy = -14.476934925125313, hamiltonian_energy_error = 0.00364086217914128, max_hamiltonian_energy_error = 0.00364086217914128, tree_depth = 5, numerical_error = false, step_size = 0.03099362542095587, nom_step_size = 0.03099362542095587, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9727949092042467, log_density = 12.405168007581352, hamiltonian_energy = -11.663067595688377, hamiltonian_energy_error = 0.10696660435041494, max_hamiltonian_energy_error = 0.10696660435041494, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9226209663708796, log_density = 14.967857109774975, hamiltonian_energy = -10.016956295084189, hamiltonian_energy_error = -0.14371355967263, max_hamiltonian_energy_error = 0.2863445906308044, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9709570008198046, log_density = 14.640099994295852, hamiltonian_energy = -13.598746086162887, hamiltonian_energy_error = 0.05323562514939795, max_hamiltonian_energy_error = 0.07339631696739879, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9731596183862763, log_density = 14.92707328586678, hamiltonian_energy = -12.13629500009386, hamiltonian_energy_error = -0.06256490109401369, max_hamiltonian_energy_error = 0.07947894772326336, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9789391757051722, log_density = 14.908401913134709, hamiltonian_energy = -13.697756172624679, hamiltonian_energy_error = -0.033761829687341205, max_hamiltonian_energy_error = 0.060323296181254094, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9951136767467351, log_density = 15.496027278936628, hamiltonian_energy = -14.191775535045743, hamiltonian_energy_error = 0.011222896944092398, max_hamiltonian_energy_error = -0.025396804471801815, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9781399467757568, log_density = 14.949019247296231, hamiltonian_energy = -13.653932371390114, hamiltonian_energy_error = -0.0558012737128184, max_hamiltonian_energy_error = 0.060259841598492514, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.946937384130477, log_density = 12.968095332335052, hamiltonian_energy = -12.068955181863508, hamiltonian_energy_error = 0.0767442683909092, max_hamiltonian_energy_error = 0.10914765785953406, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7858003203496657, log_density = 9.555926791571984, hamiltonian_energy = -6.5547906507459155, hamiltonian_energy_error = 0.3960604138739061, max_hamiltonian_energy_error = 0.5093332025526713, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 12.12466233197487, hamiltonian_energy = -7.966158528842552, hamiltonian_energy_error = -0.08532535277315123, max_hamiltonian_energy_error = -0.42803795952066626, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9655196045579352, log_density = 12.388419868164931, hamiltonian_energy = -8.903562718163206, hamiltonian_energy_error = -0.18211853283423096, max_hamiltonian_energy_error = -0.2861105346673458, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.975865613647337, log_density = 13.357469636772276, hamiltonian_energy = -11.170045428059984, hamiltonian_energy_error = -0.040287922875082316, max_hamiltonian_energy_error = -0.28742368873042423, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9981112622935439, log_density = 15.673316753453268, hamiltonian_energy = -11.800901592140928, hamiltonian_energy_error = -0.1870890169327808, max_hamiltonian_energy_error = -0.1870890169327808, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9125874297175466, log_density = 13.647054182996776, hamiltonian_energy = -12.69656719346627, hamiltonian_energy_error = 0.10647759815856439, max_hamiltonian_energy_error = 0.13051152257887466, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9986198503512885, log_density = 13.407138212821394, hamiltonian_energy = -11.983157064467186, hamiltonian_energy_error = -0.1107812954830294, max_hamiltonian_energy_error = -0.11984367040856014, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9737142128175427, log_density = 14.831505550336173, hamiltonian_energy = -11.809453550973219, hamiltonian_energy_error = 0.026529433684176595, max_hamiltonian_energy_error = 0.11086449615314287, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9538467859202401, log_density = 13.754705143804248, hamiltonian_energy = -11.756093103136696, hamiltonian_energy_error = -0.013819683969474639, max_hamiltonian_energy_error = 0.13920395966914434, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 14.009459562431525, hamiltonian_energy = -13.076999752312254, hamiltonian_energy_error = -0.0031207029040096756, max_hamiltonian_energy_error = -0.09361867963498938, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7848688025196512, log_density = 10.204791932196425, hamiltonian_energy = -7.375679529604783, hamiltonian_energy_error = 0.2425679240047689, max_hamiltonian_energy_error = 0.4689863574479123, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9966417525736467, log_density = 13.614428201530794, hamiltonian_energy = -9.52691039674783, hamiltonian_energy_error = -0.1362609710003575, max_hamiltonian_energy_error = -0.5364663211167517, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9989207811367699, log_density = 15.428541907015878, hamiltonian_energy = -13.266749426683788, hamiltonian_energy_error = -0.1273255044019983, max_hamiltonian_energy_error = -0.20822844947033659, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8737414923538871, log_density = 11.701177571469522, hamiltonian_energy = -9.28804666588993, hamiltonian_energy_error = 0.11992551779408345, max_hamiltonian_energy_error = 0.29213778213001973, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9992522048906263, log_density = 13.4543381539293, hamiltonian_energy = -10.884691437408758, hamiltonian_energy_error = -0.023600091783672283, max_hamiltonian_energy_error = -0.14044464407243495, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9979411769438622, log_density = 13.97060789599831, hamiltonian_energy = -11.919368218114172, hamiltonian_energy_error = 0.014516619505581474, max_hamiltonian_energy_error = -0.07272468743923532, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9747595384048637, log_density = 14.389653039438988, hamiltonian_energy = -11.869802205430547, hamiltonian_energy_error = 0.004565043025918314, max_hamiltonian_energy_error = -0.19372021299863107, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9969389474216707, log_density = 15.113070262670472, hamiltonian_energy = -13.349358284665707, hamiltonian_energy_error = -0.05462693370539107, max_hamiltonian_energy_error = -0.12308831373237972, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9954193985466129, log_density = 16.139730714331368, hamiltonian_energy = -14.40200634914796, hamiltonian_energy_error = -0.0806359241063106, max_hamiltonian_energy_error = -0.0806359241063106, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9142148499538489, log_density = 15.45987314514163, hamiltonian_energy = -13.51101761180464, hamiltonian_energy_error = 0.03431875497053838, max_hamiltonian_energy_error = 0.17278714359427916, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8347768810732432, log_density = 13.992420006433449, hamiltonian_energy = -12.310109032476975, hamiltonian_energy_error = 0.1353721234555234, max_hamiltonian_energy_error = 0.2724601900709622, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9914785572308656, log_density = 14.834013202594226, hamiltonian_energy = -12.193092834499563, hamiltonian_energy_error = -0.006953318495142469, max_hamiltonian_energy_error = 0.05089960878413713, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9751160862640895, log_density = 15.58846555738453, hamiltonian_energy = -13.461257418563363, hamiltonian_energy_error = -0.037754540619467036, max_hamiltonian_energy_error = 0.10743541629209652, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9734742636403809, log_density = 14.60426696416479, hamiltonian_energy = -13.547697534256548, hamiltonian_energy_error = 0.004716468662509854, max_hamiltonian_energy_error = 0.07707308111890221, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9942786268095568, log_density = 14.462179777191057, hamiltonian_energy = -13.149537335933038, hamiltonian_energy_error = 0.02340478776167032, max_hamiltonian_energy_error = -0.06432645339961418, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8725890861955218, log_density = 14.798950237839193, hamiltonian_energy = -11.939107751555735, hamiltonian_energy_error = 0.20042797528295075, max_hamiltonian_energy_error = 0.6165847136942428, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9290014866219728, log_density = 13.079260660231437, hamiltonian_energy = -11.33989667486404, hamiltonian_energy_error = -0.019473442112548867, max_hamiltonian_energy_error = -0.2688252066976933, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.949247114566026, log_density = 12.018882604816646, hamiltonian_energy = -10.455279819985746, hamiltonian_energy_error = 0.11773984407783367, max_hamiltonian_energy_error = -0.16914127523705424, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9839111051633799, log_density = 10.3961075670898, hamiltonian_energy = -8.24844807187715, hamiltonian_energy_error = 0.04149557777056678, max_hamiltonian_energy_error = -0.8011970085961604, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9954598043365998, log_density = 13.827575171270103, hamiltonian_energy = -10.528172448673638, hamiltonian_energy_error = -0.9691803938401744, max_hamiltonian_energy_error = -1.1342694322707079, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.3322943189595493, log_density = 14.224329530918958, hamiltonian_energy = -10.358934927591704, hamiltonian_energy_error = 1.1492562366342334, max_hamiltonian_energy_error = 1.5878257828099098, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9816368627838037, log_density = 14.078404564454104, hamiltonian_energy = -12.620705311532456, hamiltonian_energy_error = -0.08822374061026395, max_hamiltonian_energy_error = -0.14911715341951215, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9991104234279096, log_density = 15.310588795997973, hamiltonian_energy = -12.891916850393578, hamiltonian_energy_error = -0.07338164473881648, max_hamiltonian_energy_error = -0.1321058490680489, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.944724834529559, log_density = 14.853930805336969, hamiltonian_energy = -14.19120139149387, hamiltonian_energy_error = 0.11193500384778332, max_hamiltonian_energy_error = 0.13488823295643826, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9766852134288514, log_density = 13.843011233897855, hamiltonian_energy = -12.30212872697814, hamiltonian_energy_error = -0.15703308757195167, max_hamiltonian_energy_error = 0.16774294639052378, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9863174550111301, log_density = 12.242293663166324, hamiltonian_energy = -11.381680266279822, hamiltonian_energy_error = 0.030144258322227557, max_hamiltonian_energy_error = 0.08611713776624264, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8467916669379124, log_density = 13.28286494209715, hamiltonian_energy = -8.29130206687011, hamiltonian_energy_error = 0.15376955290870775, max_hamiltonian_energy_error = 0.36206878146038335, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8327072305354967, log_density = 12.959468724177906, hamiltonian_energy = -10.18861913616592, hamiltonian_energy_error = 0.15702781224084283, max_hamiltonian_energy_error = 0.4548128516141521, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9871993559881787, log_density = 14.665532494265836, hamiltonian_energy = -11.147409186188401, hamiltonian_energy_error = -0.2290018251298651, max_hamiltonian_energy_error = -0.27887878903719887, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9495399346848024, log_density = 13.127948172265848, hamiltonian_energy = -11.740095802387684, hamiltonian_energy_error = 0.01740022928659002, max_hamiltonian_energy_error = 0.19925554729727502, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9644573179570912, log_density = 13.480140788729086, hamiltonian_energy = -11.045496353759265, hamiltonian_energy_error = -0.16934344556001157, max_hamiltonian_energy_error = -0.37339455290698, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9006804759825465, log_density = 13.893342793298622, hamiltonian_energy = -11.122139503518364, hamiltonian_energy_error = 0.12194249084963005, max_hamiltonian_energy_error = 0.2201159664223038, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9575047959518703, log_density = 13.104695178924672, hamiltonian_energy = -12.233374031688337, hamiltonian_energy_error = -0.4407805987813571, max_hamiltonian_energy_error = -0.4407805987813571, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9930930206133067, log_density = 11.62793851058587, hamiltonian_energy = -10.97772052840328, hamiltonian_energy_error = 0.004394313602977817, max_hamiltonian_energy_error = -0.05376989026427559, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.987611237677106, log_density = 10.778394662768894, hamiltonian_energy = -9.137039580422035, hamiltonian_energy_error = 0.013827795812300536, max_hamiltonian_energy_error = -0.12542150552369158, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9320987533550957, log_density = 9.66418031595255, hamiltonian_energy = -8.505446553320482, hamiltonian_energy_error = -0.013933708039871817, max_hamiltonian_energy_error = 0.34494150342903396, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.9952638904799281, log_density = 12.912360166099267, hamiltonian_energy = -7.494061692482895, hamiltonian_energy_error = -0.07347083761172879, max_hamiltonian_energy_error = -0.18361857958022654, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.999826708975504, log_density = 14.663950400339907, hamiltonian_energy = -11.682873269344752, hamiltonian_energy_error = -0.020242738559140605, max_hamiltonian_energy_error = -0.10386358011040464, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9856318269530703, log_density = 14.746099121469028, hamiltonian_energy = -13.816558839745214, hamiltonian_energy_error = 0.021282160295328367, max_hamiltonian_energy_error = -0.10951625653987662, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.986960395838661, log_density = 14.654886973196566, hamiltonian_energy = -12.710289803933332, hamiltonian_energy_error = -0.08656615991706929, max_hamiltonian_energy_error = -0.08656615991706929, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8340816311317109, log_density = 14.75222823155144, hamiltonian_energy = -11.001866277684732, hamiltonian_energy_error = 0.015011383352151242, max_hamiltonian_energy_error = 0.36599113313898, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.978252700434003, log_density = 14.192459218603371, hamiltonian_energy = -12.276265901565315, hamiltonian_energy_error = -0.050694005886605, max_hamiltonian_energy_error = 0.10710646059645157, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9643930359828108, log_density = 13.668824612143682, hamiltonian_energy = -9.625674586388758, hamiltonian_energy_error = -0.06574343601273469, max_hamiltonian_energy_error = 0.09079142648264593, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8681405392854544, log_density = 13.521777931332817, hamiltonian_energy = -10.38255717896765, hamiltonian_energy_error = -0.06439587497977861, max_hamiltonian_energy_error = 0.2978021447518717, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8040491272089427, log_density = 14.402823636301392, hamiltonian_energy = -9.536591511296436, hamiltonian_energy_error = 0.11932041712374009, max_hamiltonian_energy_error = 0.30483613513251306, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9139105336342214, log_density = 14.48463423897433, hamiltonian_energy = -12.726612435383743, hamiltonian_energy_error = 0.0030510520292157395, max_hamiltonian_energy_error = 0.21148991784264481, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.93574278983972, log_density = 13.345563042527086, hamiltonian_energy = -10.864498550999347, hamiltonian_energy_error = 0.08903148886967216, max_hamiltonian_energy_error = 0.18244192636651668, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9990097589732891, log_density = 14.359389586914237, hamiltonian_energy = -11.923810070488486, hamiltonian_energy_error = -0.06734634744445067, max_hamiltonian_energy_error = -0.21586075061026655, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9871566946871891, log_density = 14.366500664526088, hamiltonian_energy = -12.525011236253755, hamiltonian_energy_error = 0.01670216580467354, max_hamiltonian_energy_error = -0.1397158725372627, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 14.744837032176186, hamiltonian_energy = -13.603142758406516, hamiltonian_energy_error = -0.03839416292434272, max_hamiltonian_energy_error = -0.13310793987582237, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9905356191297022, log_density = 13.839613746535978, hamiltonian_energy = -13.051865657910113, hamiltonian_energy_error = 0.04916427601322937, max_hamiltonian_energy_error = -0.1461501341897531, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9953541061986707, log_density = 12.774639045523816, hamiltonian_energy = -11.15194452583235, hamiltonian_energy_error = -0.013301950093714154, max_hamiltonian_energy_error = -0.09509468951003441, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 15.409782338227638, hamiltonian_energy = -11.376915598100261, hamiltonian_energy_error = -0.08726579268821588, max_hamiltonian_energy_error = -0.1241835399575617, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9973627933322392, log_density = 14.683307727169694, hamiltonian_energy = -14.261926498764328, hamiltonian_energy_error = 0.012832208546594615, max_hamiltonian_energy_error = -0.02324046868504226, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9983410423712761, log_density = 15.80101423916583, hamiltonian_energy = -13.912135406711478, hamiltonian_energy_error = -0.032413490730052175, max_hamiltonian_energy_error = -0.04811172863241531, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9185625681237453, log_density = 15.028078454172139, hamiltonian_energy = -13.600105922121246, hamiltonian_energy_error = 0.019422578833841797, max_hamiltonian_energy_error = 0.19585238928484827, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9578557017036163, log_density = 15.51833628937344, hamiltonian_energy = -13.19005690074873, hamiltonian_energy_error = -0.06412957028398125, max_hamiltonian_energy_error = 0.14555052825471648, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8061155896442249, log_density = 15.287639011848068, hamiltonian_energy = -12.244522157458887, hamiltonian_energy_error = 0.02447081462369738, max_hamiltonian_energy_error = 0.3950150475438381, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9727715061940672, log_density = 14.591477030684567, hamiltonian_energy = -13.642433993596219, hamiltonian_energy_error = 0.060043977749069555, max_hamiltonian_energy_error = 0.06290956449323559, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6956081934490004, log_density = 12.588657388035724, hamiltonian_energy = -12.261448624749066, hamiltonian_energy_error = 0.5105418779113773, max_hamiltonian_energy_error = 0.8721452207569236, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9968734052744724, log_density = 14.785859882833211, hamiltonian_energy = -11.224364355501294, hamiltonian_energy_error = -0.10725765343188165, max_hamiltonian_energy_error = -0.23436843067091573, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9104838169869878, log_density = 14.725123629190538, hamiltonian_energy = -12.212026049460533, hamiltonian_energy_error = -0.049162376293832466, max_hamiltonian_energy_error = 0.21210917093226556, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9616812095689458, log_density = 13.071414719200975, hamiltonian_energy = -9.499845419152958, hamiltonian_energy_error = 0.0024879312394823216, max_hamiltonian_energy_error = 0.07566343833632772, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9952348496233095, log_density = 14.274504150304152, hamiltonian_energy = -11.395979340136146, hamiltonian_energy_error = -0.02531710790629127, max_hamiltonian_energy_error = -0.10486971505035214, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9215175423923732, log_density = 15.344949671253621, hamiltonian_energy = -11.338534917553682, hamiltonian_energy_error = -0.07982309707506197, max_hamiltonian_energy_error = 0.21414181354333195, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9286636408819601, log_density = 14.310523547370149, hamiltonian_energy = -12.260622329349893, hamiltonian_energy_error = 0.03447848858774272, max_hamiltonian_energy_error = 0.14460002957218876, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9729188847564241, log_density = 15.002650661436416, hamiltonian_energy = -13.266207176746144, hamiltonian_energy_error = -0.04953483768567857, max_hamiltonian_energy_error = -0.11448754570006159, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9671719825654039, log_density = 14.961625137739144, hamiltonian_energy = -12.684358378726895, hamiltonian_energy_error = 0.04891553977117802, max_hamiltonian_energy_error = 0.06352268556675789, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9536374430970199, log_density = 12.84832945852137, hamiltonian_energy = -11.929309472937335, hamiltonian_energy_error = 0.13779470897399726, max_hamiltonian_energy_error = 0.13779470897399726, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8719837712691318, log_density = 14.2324104222423, hamiltonian_energy = -9.608605881871103, hamiltonian_energy_error = -0.03064248806735037, max_hamiltonian_energy_error = 0.42710393527395674, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9269892763732899, log_density = 14.60957786137656, hamiltonian_energy = -12.076617092191347, hamiltonian_energy_error = 0.046662693377971465, max_hamiltonian_energy_error = 0.1635921437537622, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8934439173035965, log_density = 14.451116153044994, hamiltonian_energy = -11.918314267757506, hamiltonian_energy_error = 0.017717780791056015, max_hamiltonian_energy_error = 0.3059890910685965, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9889024183836223, log_density = 12.675839212680714, hamiltonian_energy = -12.212277622466482, hamiltonian_energy_error = 0.05176739560397969, max_hamiltonian_energy_error = -0.06527347011240892, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8537496222673757, log_density = 12.438615363413936, hamiltonian_energy = -10.134431227182114, hamiltonian_energy_error = -0.6540157697747873, max_hamiltonian_energy_error = -0.6540157697747873, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6218003602946309, log_density = 11.102484509835739, hamiltonian_energy = -9.824652232264507, hamiltonian_energy_error = 0.5781950628688381, max_hamiltonian_energy_error = 0.6979218138185903, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8361327929587635, log_density = 12.47571532932367, hamiltonian_energy = -9.86793379349086, hamiltonian_energy_error = 0.29346804833148, max_hamiltonian_energy_error = 0.3581765338986713, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9722579286446964, log_density = 12.694565444680723, hamiltonian_energy = -12.07885878381132, hamiltonian_energy_error = 0.09634226970695003, max_hamiltonian_energy_error = -0.3356325571551899, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9947608823435634, log_density = 15.83506136419769, hamiltonian_energy = -11.836689595970899, hamiltonian_energy_error = -0.1203359784558824, max_hamiltonian_energy_error = -0.2647222762499464, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8918918417379508, log_density = 14.368619996476513, hamiltonian_energy = -12.177959362957823, hamiltonian_energy_error = 0.10088942976105741, max_hamiltonian_energy_error = 0.23373013567244172, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9917717960882422, log_density = 15.119762496919703, hamiltonian_energy = -13.410258305994587, hamiltonian_energy_error = -0.12683963681931942, max_hamiltonian_energy_error = -0.13130480890454344, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8896709305777533, log_density = 14.108970652771939, hamiltonian_energy = -13.283515452008594, hamiltonian_energy_error = 0.09297595529373837, max_hamiltonian_energy_error = 0.16423169691715778, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9784170428945134, log_density = 14.076646524659491, hamiltonian_energy = -12.176548090956398, hamiltonian_energy_error = -0.013475274671431947, max_hamiltonian_energy_error = -0.07220001424777145, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 31, is_accept = true, acceptance_rate = 0.8706351155078809, log_density = 13.883156992558515, hamiltonian_energy = -9.025374315424205, hamiltonian_energy_error = -0.0014635973894012722, max_hamiltonian_energy_error = 0.37758166777138236, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.6706035590495946, log_density = 12.202982631745527, hamiltonian_energy = -10.24303278149121, hamiltonian_energy_error = 0.2382758588913294, max_hamiltonian_energy_error = 0.6030592667914387, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 13.232833107327197, hamiltonian_energy = -11.599193466971593, hamiltonian_energy_error = -0.11369654627300996, max_hamiltonian_energy_error = -0.3962531780984122, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9870214700361885, log_density = 12.1847240843791, hamiltonian_energy = -10.361700880672357, hamiltonian_energy_error = -0.10499266521050465, max_hamiltonian_energy_error = -0.25494555897605586, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9984694883279824, log_density = 12.731287494317968, hamiltonian_energy = -10.887776133256093, hamiltonian_energy_error = -0.11681370976704208, max_hamiltonian_energy_error = -0.20611516204042069, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8686169902972491, log_density = 12.633261673499938, hamiltonian_energy = -8.975642899086917, hamiltonian_energy_error = 0.31335795151166757, max_hamiltonian_energy_error = 0.31335795151166757, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 15.42524542830404, hamiltonian_energy = -12.372354750007794, hamiltonian_energy_error = -0.33746894874351696, max_hamiltonian_energy_error = -0.3375483830173387, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9763050331726123, log_density = 14.693681259675284, hamiltonian_energy = -13.621862867610254, hamiltonian_energy_error = -0.013468449233515756, max_hamiltonian_energy_error = 0.06993782910742041, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.915453422187493, log_density = 12.933304872059656, hamiltonian_energy = -10.76964350735304, hamiltonian_energy_error = 0.04174833980551362, max_hamiltonian_energy_error = 0.2461925970538843, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9660854781668883, log_density = 12.878863736646856, hamiltonian_energy = -10.990206819805056, hamiltonian_energy_error = 0.05006467359218014, max_hamiltonian_energy_error = -0.08060897934677769, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9782422293990093, log_density = 14.695890492944672, hamiltonian_energy = -11.883205059641641, hamiltonian_energy_error = -0.0285944440176511, max_hamiltonian_energy_error = -0.18810039601065753, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 15.730223615057994, hamiltonian_energy = -14.490139638084266, hamiltonian_energy_error = -0.07864062141355177, max_hamiltonian_energy_error = -0.07864062141355177, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9104266762635491, log_density = 14.597774737188622, hamiltonian_energy = -13.48634603942586, hamiltonian_energy_error = 0.10278770995685527, max_hamiltonian_energy_error = 0.1519688032577875, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 15.639145124500391, hamiltonian_energy = -13.555308059582751, hamiltonian_energy_error = -0.10332049429485579, max_hamiltonian_energy_error = -0.11216097657182722, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.91050450921893, log_density = 12.826499586312195, hamiltonian_energy = -11.56801009350444, hamiltonian_energy_error = 0.12314482902003299, max_hamiltonian_energy_error = 0.18380043779431254, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8213946092872727, log_density = 10.208552709160074, hamiltonian_energy = -8.382652623404173, hamiltonian_energy_error = 0.32821218042589173, max_hamiltonian_energy_error = 0.32821218042589173, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 12.315206101565265, hamiltonian_energy = -9.682579486447217, hamiltonian_energy_error = -0.04812828006827807, max_hamiltonian_energy_error = -0.3126359833992556, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7596090930348119, log_density = 13.93510979324538, hamiltonian_energy = -9.648493540105157, hamiltonian_energy_error = -0.21853851637230903, max_hamiltonian_energy_error = 0.5223977954047623, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9026480892026455, log_density = 14.798292570107543, hamiltonian_energy = -11.614751553090562, hamiltonian_energy_error = 0.06997395371582016, max_hamiltonian_energy_error = 0.2886588542981485, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8722116675027111, log_density = 15.194590350680475, hamiltonian_energy = -10.458717231777683, hamiltonian_energy_error = 0.15032704112648432, max_hamiltonian_energy_error = 0.2621365923239214, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9087698036756912, log_density = 14.862883683479682, hamiltonian_energy = -11.09770241253497, hamiltonian_energy_error = 0.06271435673863301, max_hamiltonian_energy_error = 0.1920578911724693, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9995121323225855, log_density = 14.074312361222816, hamiltonian_energy = -13.611412862592546, hamiltonian_energy_error = -0.0320094749668165, max_hamiltonian_energy_error = -0.09332636137878048, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9696549010103007, log_density = 14.476836628290958, hamiltonian_energy = -11.733904367530112, hamiltonian_energy_error = 0.05301327040480608, max_hamiltonian_energy_error = 0.0688710714486227, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9842827746529769, log_density = 15.716128246756403, hamiltonian_energy = -12.302673438147918, hamiltonian_energy_error = -0.05212938210315521, max_hamiltonian_energy_error = -0.05212938210315521, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9407225768895529, log_density = 14.45334056482837, hamiltonian_energy = -13.44302386955847, hamiltonian_energy_error = 0.06429128887493007, max_hamiltonian_energy_error = 0.11707392882287948, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9880186010469043, log_density = 15.143316720432267, hamiltonian_energy = -13.593345413214458, hamiltonian_energy_error = -0.03502085718906933, max_hamiltonian_energy_error = -0.03502085718906933, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9680719605736334, log_density = 14.906448372575655, hamiltonian_energy = -13.79307847170548, hamiltonian_energy_error = 0.06418761230449554, max_hamiltonian_energy_error = 0.09989673083447848, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9649836416214563, log_density = 14.480247412089522, hamiltonian_energy = -12.290649333404087, hamiltonian_energy_error = -0.0059727776508466945, max_hamiltonian_energy_error = 0.15415325259030865, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8728773406560705, log_density = 12.833868671340815, hamiltonian_energy = -11.34832931844639, hamiltonian_energy_error = 0.15803004153079492, max_hamiltonian_energy_error = 0.28091280322488643, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9777541716411909, log_density = 11.230054930691084, hamiltonian_energy = -9.566666396996087, hamiltonian_energy_error = -0.33855004825865365, max_hamiltonian_energy_error = -0.33855004825865365, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.028246816212367652, log_density = 11.230054930691084, hamiltonian_energy = -0.36851631457641965, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 6.787797978984674, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9896753915622045, log_density = 11.826339903564376, hamiltonian_energy = -8.307624863232334, hamiltonian_energy_error = -0.3395644234666566, max_hamiltonian_energy_error = -0.5178815219137629, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9897672454111628, log_density = 13.316526079044015, hamiltonian_energy = -10.142756547992013, hamiltonian_energy_error = -0.0356272379673257, max_hamiltonian_energy_error = -0.12558288305541865, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9771235450022168, log_density = 13.690803653381721, hamiltonian_energy = -11.686673589013644, hamiltonian_energy_error = 0.08428987064752569, max_hamiltonian_energy_error = -0.1346815159885253, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 31, is_accept = true, acceptance_rate = 0.9316404242907101, log_density = 13.379103917784578, hamiltonian_energy = -10.164670324315072, hamiltonian_energy_error = -0.0363184788825226, max_hamiltonian_energy_error = -0.2419852653860115, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9474283533082861, log_density = 12.407969614266642, hamiltonian_energy = -10.379943066581614, hamiltonian_energy_error = 0.04739946955960406, max_hamiltonian_energy_error = 0.09233838552700036, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8468763500574206, log_density = 12.407969614266642, hamiltonian_energy = -9.772844235658521, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 0.35269500449101976, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 13.378514323209172, hamiltonian_energy = -11.516547139071534, hamiltonian_energy_error = -0.04467312248864985, max_hamiltonian_energy_error = -0.22366944221665008, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9129069895422952, log_density = 13.878009705940148, hamiltonian_energy = -9.557198740813062, hamiltonian_energy_error = 0.028617874975294555, max_hamiltonian_energy_error = 0.3240158094497616, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9789412631226712, log_density = 12.80883391631381, hamiltonian_energy = -10.09915243585642, hamiltonian_energy_error = -0.15258181010238125, max_hamiltonian_energy_error = -0.2753245471441197, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.979627163259399, log_density = 14.582802910851225, hamiltonian_energy = -12.005973644911524, hamiltonian_energy_error = -0.07036185517096527, max_hamiltonian_energy_error = -0.07036185517096527, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9964469913576635, log_density = 14.814911547833791, hamiltonian_energy = -14.21962663507419, hamiltonian_energy_error = -0.024232196743064094, max_hamiltonian_energy_error = -0.06053743947831158, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8894996088690832, log_density = 13.47493772765231, hamiltonian_energy = -11.709942821460508, hamiltonian_energy_error = 0.08950785990422716, max_hamiltonian_energy_error = 0.2449782182870397, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9997353527060999, log_density = 15.752237055621295, hamiltonian_energy = -12.927296299010486, hamiltonian_energy_error = -0.1459811824400088, max_hamiltonian_energy_error = -0.17385745263609387, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9167543259686944, log_density = 14.418794889106959, hamiltonian_energy = -12.600214885712349, hamiltonian_energy_error = 0.003488158370833716, max_hamiltonian_energy_error = 0.17553985941598604, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9292744018249995, log_density = 13.700162769784585, hamiltonian_energy = -11.696462047503104, hamiltonian_energy_error = 0.10586398213357384, max_hamiltonian_energy_error = 0.15203703732953144, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9947058671902288, log_density = 14.268782230057374, hamiltonian_energy = -11.890359103452512, hamiltonian_energy_error = -0.1000716201772125, max_hamiltonian_energy_error = -0.11063626465999477, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9940516898722078, log_density = 14.889540333678058, hamiltonian_energy = -13.202083780902335, hamiltonian_energy_error = 0.0033691771685866456, max_hamiltonian_energy_error = -0.05698402172120254, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9848408114508149, log_density = 14.638221653228507, hamiltonian_energy = -11.282693550894004, hamiltonian_energy_error = -0.006359852572145996, max_hamiltonian_energy_error = 0.07873596989350595, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9905911948927513, log_density = 15.598254620657094, hamiltonian_energy = -13.442116613951658, hamiltonian_energy_error = -0.05151417306366923, max_hamiltonian_energy_error = -0.08955418515988711, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9859092253681302, log_density = 15.243794840007075, hamiltonian_energy = -14.821507751274675, hamiltonian_energy_error = 0.03449091131867199, max_hamiltonian_energy_error = 0.057994323939576375, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9979097298973402, log_density = 14.512317527393, hamiltonian_energy = -13.811968234834426, hamiltonian_energy_error = -0.012561466682463163, max_hamiltonian_energy_error = -0.07797218616644308, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8906261061917793, log_density = 14.453735959886364, hamiltonian_energy = -12.209216390730614, hamiltonian_energy_error = 0.08804410280923314, max_hamiltonian_energy_error = 0.24460302924806498, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.994760677448195, log_density = 15.160964334245342, hamiltonian_energy = -10.866078591109748, hamiltonian_energy_error = -0.05956095731716182, max_hamiltonian_energy_error = -0.18638036791889867, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9208776787572681, log_density = 13.930583604240905, hamiltonian_energy = -11.28710116511677, hamiltonian_energy_error = 0.06746051532093134, max_hamiltonian_energy_error = 0.16052740052085923, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9886307567201957, log_density = 15.148912585520296, hamiltonian_energy = -11.497484086300682, hamiltonian_energy_error = -0.0985513638206914, max_hamiltonian_energy_error = -0.17051269836652594, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9935057286648205, log_density = 15.624488473383494, hamiltonian_energy = -14.527935972706658, hamiltonian_energy_error = -0.03127011555620207, max_hamiltonian_energy_error = -0.03127011555620207, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9503408059030362, log_density = 13.704239942268398, hamiltonian_energy = -12.276305212454245, hamiltonian_energy_error = 0.0613184933978701, max_hamiltonian_energy_error = 0.0839955097455487, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9882013146247319, log_density = 14.34497772753366, hamiltonian_energy = -12.262909202420461, hamiltonian_energy_error = 0.01722830873480774, max_hamiltonian_energy_error = -0.07781178347639717, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9974606069209689, log_density = 14.326420656204553, hamiltonian_energy = -12.437583122564837, hamiltonian_energy_error = 0.0008061883041019513, max_hamiltonian_energy_error = -0.06208221663344915, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8569578818486733, log_density = 12.779785542033473, hamiltonian_energy = -11.75001072180258, hamiltonian_energy_error = 0.32186426046202854, max_hamiltonian_energy_error = 0.34869333638338595, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9809578517804647, log_density = 13.072822871936339, hamiltonian_energy = -9.930199563781791, hamiltonian_energy_error = -0.1987542135554392, max_hamiltonian_energy_error = -0.332658112640166, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9911940743408271, log_density = 11.862412850100267, hamiltonian_energy = -8.032603952615897, hamiltonian_energy_error = -0.1849327234012872, max_hamiltonian_energy_error = -0.26117700121007204, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9762827947938578, log_density = 13.65965849119758, hamiltonian_energy = -11.327688990253163, hamiltonian_energy_error = 0.033556938181705576, max_hamiltonian_energy_error = 0.05851957052948009, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9969054907905043, log_density = 13.921930201680214, hamiltonian_energy = -12.138648116390538, hamiltonian_energy_error = 0.006244740844776331, max_hamiltonian_energy_error = -0.0699750865365818, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9285921443964352, log_density = 12.86949993151805, hamiltonian_energy = -11.864891779964955, hamiltonian_energy_error = 0.09662958682238632, max_hamiltonian_energy_error = 0.1370092836541712, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 31, is_accept = true, acceptance_rate = 0.9735490822933467, log_density = 12.270452879936663, hamiltonian_energy = -9.230439670414327, hamiltonian_energy_error = 0.006340430644275585, max_hamiltonian_energy_error = 0.5242213188354672, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.9944523872851794, log_density = 12.862602327728524, hamiltonian_energy = -9.86247428658767, hamiltonian_energy_error = -0.01563704510994235, max_hamiltonian_energy_error = -0.06716111021505888, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.4334577173415767, log_density = 8.691739600492294, hamiltonian_energy = -6.944544003016011, hamiltonian_energy_error = 1.16736751819945, max_hamiltonian_energy_error = 2.3109222972212713, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9828537742277557, log_density = 9.939021684542823, hamiltonian_energy = -5.616839729174801, hamiltonian_energy_error = -0.10072443776799567, max_hamiltonian_energy_error = -0.23972366928713562, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8693567605193618, log_density = 7.835865913751967, hamiltonian_energy = -6.4650101902700765, hamiltonian_energy_error = 0.1710829709309598, max_hamiltonian_energy_error = 0.2674630156965243, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.49939603738252114, log_density = 8.364116555088614, hamiltonian_energy = -1.86143421452842, hamiltonian_energy_error = 0.38510832056241195, max_hamiltonian_energy_error = 2.7291153335086804, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.4754334491914829, log_density = 7.282149820750879, hamiltonian_energy = -4.320038849319165, hamiltonian_energy_error = 1.4556365832791727, max_hamiltonian_energy_error = 1.4556365832791727, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9141649974896924, log_density = 10.286335220551084, hamiltonian_energy = -4.533217570769194, hamiltonian_energy_error = -0.2030944993140098, max_hamiltonian_energy_error = -1.1549278005083687, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9529335564499912, log_density = 10.615590506394222, hamiltonian_energy = -7.235761428305773, hamiltonian_energy_error = 0.258488605738842, max_hamiltonian_energy_error = -0.7488699445309734, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 12.262679048230115, hamiltonian_energy = -10.296417628915432, hamiltonian_energy_error = -0.15344008467714865, max_hamiltonian_energy_error = -0.15344008467714865, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9804689886002411, log_density = 12.715170574348777, hamiltonian_energy = -11.306193872529429, hamiltonian_energy_error = 0.01999619210408987, max_hamiltonian_energy_error = -0.23044087694132465, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9521765755834178, log_density = 14.277045318093927, hamiltonian_energy = -9.563224583239624, hamiltonian_energy_error = 0.06051420392708273, max_hamiltonian_energy_error = -0.2898577083171734, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9767909136696067, log_density = 14.300808886710534, hamiltonian_energy = -12.230339622957427, hamiltonian_energy_error = 0.034123748026850365, max_hamiltonian_energy_error = -0.18973004515652647, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.943989835589856, log_density = 14.312312970272146, hamiltonian_energy = -10.398564090429291, hamiltonian_energy_error = -0.13730395616362934, max_hamiltonian_energy_error = -0.22536561729262772, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.97602635464393, log_density = 13.528403132886526, hamiltonian_energy = -11.618471237677936, hamiltonian_energy_error = 0.07295498610862694, max_hamiltonian_energy_error = -0.0751382992777323, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9812646205335875, log_density = 15.516408475287655, hamiltonian_energy = -11.78298685284448, hamiltonian_energy_error = -0.18507959848620636, max_hamiltonian_energy_error = -0.2736936030329371, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8756950546967884, log_density = 14.180805363415, hamiltonian_energy = -11.974448411761566, hamiltonian_energy_error = 0.12744239198267415, max_hamiltonian_energy_error = 0.2309717049104485, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.907218694531748, log_density = 13.20928996385253, hamiltonian_energy = -11.195734165666382, hamiltonian_energy_error = -0.2193052411782883, max_hamiltonian_energy_error = 0.29629116893562824, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.24240863355379152, log_density = 7.323216521737596, hamiltonian_energy = -6.004395278013929, hamiltonian_energy_error = 1.844093558022018, max_hamiltonian_energy_error = 2.1730096241885573, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9980134812829888, log_density = 12.301378704663188, hamiltonian_energy = -2.2532698829210798, hamiltonian_energy_error = -0.9784450627206533, max_hamiltonian_energy_error = -0.9784450627206533, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9973939794596132, log_density = 14.04663195576076, hamiltonian_energy = -10.463445672478551, hamiltonian_energy_error = -0.3478936399426278, max_hamiltonian_energy_error = -0.3799120813020913, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9980219032984662, log_density = 15.4760633555296, hamiltonian_energy = -13.369464888416987, hamiltonian_energy_error = -0.14805282569100697, max_hamiltonian_energy_error = -0.14805282569100697, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9736914373005763, log_density = 15.90313973729691, hamiltonian_energy = -14.667776413724614, hamiltonian_energy_error = 0.015101552627358572, max_hamiltonian_energy_error = 0.05517917538697148, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9829960988255576, log_density = 14.778927553545806, hamiltonian_energy = -13.247645862095835, hamiltonian_energy_error = 0.016252368343000256, max_hamiltonian_energy_error = 0.03764911956278638, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9868586292035266, log_density = 14.942845302726845, hamiltonian_energy = -13.309455871765113, hamiltonian_energy_error = 0.02250973717192295, max_hamiltonian_energy_error = 0.03428846812667885, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6598293835507552, log_density = 13.933455852342675, hamiltonian_energy = -9.308204935965135, hamiltonian_energy_error = 0.22025135834428333, max_hamiltonian_energy_error = 0.7312025068663246, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.97299056555323, log_density = 13.104739158654096, hamiltonian_energy = -11.269377056794474, hamiltonian_energy_error = 0.06442147956497557, max_hamiltonian_energy_error = -0.14386411503692287, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 15.43509481854008, hamiltonian_energy = -13.168158703399925, hamiltonian_energy_error = -0.2503510694569613, max_hamiltonian_energy_error = -0.2503510694569613, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8160105387507782, log_density = 12.353260712467472, hamiltonian_energy = -8.65172320384357, hamiltonian_energy_error = 0.23319589878351543, max_hamiltonian_energy_error = 0.3352106014082725, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9664297911055901, log_density = 15.407587141466493, hamiltonian_energy = -6.611311567092871, hamiltonian_energy_error = -0.2094018591889446, max_hamiltonian_energy_error = -0.22780295103655046, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9185129924318379, log_density = 13.427188686196018, hamiltonian_energy = -11.578787484481174, hamiltonian_energy_error = -0.015460119866219202, max_hamiltonian_energy_error = 0.21002159242333995, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9709227672008038, log_density = 14.852733255793044, hamiltonian_energy = -12.102706650208443, hamiltonian_energy_error = -0.11567244980138369, max_hamiltonian_energy_error = 0.13188993498500956, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9992580084779064, log_density = 14.200303877544805, hamiltonian_energy = -12.912377352459835, hamiltonian_energy_error = -0.04888296870946718, max_hamiltonian_energy_error = -0.08406481035179425, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8834380573132535, log_density = 13.792192384961528, hamiltonian_energy = -10.555055087737736, hamiltonian_energy_error = 0.1669519679200011, max_hamiltonian_energy_error = 0.21545898261129892, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9680272661852036, log_density = 13.821440909237623, hamiltonian_energy = -11.76318286705358, hamiltonian_energy_error = -0.043688129451755486, max_hamiltonian_energy_error = -0.19620316395862325, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 15.508922351908232, hamiltonian_energy = -12.435053973115222, hamiltonian_energy_error = -0.1817911051374672, max_hamiltonian_energy_error = -0.18250842266371414, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.987316081823643, log_density = 15.987087097518874, hamiltonian_energy = -14.780547242625687, hamiltonian_energy_error = -0.021812659475234142, max_hamiltonian_energy_error = 0.03248487877280226, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9736079160863379, log_density = 15.604762413373214, hamiltonian_energy = -15.463179377941504, hamiltonian_energy_error = 0.020935301604225742, max_hamiltonian_energy_error = 0.040962836544256476, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.92615989829359, log_density = 13.797215022161383, hamiltonian_energy = -12.27419046215216, hamiltonian_energy_error = 0.03472630459505943, max_hamiltonian_energy_error = 0.16246920101342788, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9979133969218691, log_density = 15.763481330858582, hamiltonian_energy = -13.373596660279947, hamiltonian_energy_error = -0.053152987562194554, max_hamiltonian_energy_error = -0.053152987562194554, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9420605659115479, log_density = 14.991111786385893, hamiltonian_energy = -13.078091042803848, hamiltonian_energy_error = 0.042032614855056494, max_hamiltonian_energy_error = 0.1210591050980856, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6885146204312894, log_density = 12.095691181444256, hamiltonian_energy = -8.471444497054165, hamiltonian_energy_error = 0.5028456877433101, max_hamiltonian_energy_error = 0.8970728431646204, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 14.032554650903862, hamiltonian_energy = -12.04014150166486, hamiltonian_energy_error = -0.2427151239298606, max_hamiltonian_energy_error = -0.40356595111640914, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.990158985374666, log_density = 14.031030049905048, hamiltonian_energy = -12.357305931647206, hamiltonian_energy_error = 0.034819307601042127, max_hamiltonian_energy_error = -0.15766947618866212, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9591356058678153, log_density = 15.208237151543791, hamiltonian_energy = -12.988447105002319, hamiltonian_energy_error = -0.19581742273619795, max_hamiltonian_energy_error = -0.19581742273619795, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8699695598505239, log_density = 15.384097307166511, hamiltonian_energy = -13.006420087460716, hamiltonian_energy_error = 0.010267335307558412, max_hamiltonian_energy_error = 0.2868335907839654, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9781150244438189, log_density = 14.61615131711969, hamiltonian_energy = -13.283593238735426, hamiltonian_energy_error = 0.03044809355459499, max_hamiltonian_energy_error = 0.046887899046369697, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.973449893431687, log_density = 13.673477835338879, hamiltonian_energy = -11.92755929802641, hamiltonian_energy_error = 0.013371921813089216, max_hamiltonian_energy_error = 0.06352988060490183, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9984462346172123, log_density = 15.404145263662901, hamiltonian_energy = -13.479030668672154, hamiltonian_energy_error = -0.060656120727340834, max_hamiltonian_energy_error = -0.08336876262881354, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8533541072849793, log_density = 10.87192285941697, hamiltonian_energy = -9.35217374549369, hamiltonian_energy_error = 0.2816013472457044, max_hamiltonian_energy_error = -0.33997997530168256, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 11.178039401925815, hamiltonian_energy = -8.925673922407862, hamiltonian_energy_error = -0.12881518338324582, max_hamiltonian_energy_error = -0.42594757709736264, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8687189667828618, log_density = 11.574615738791753, hamiltonian_energy = -8.076945376221678, hamiltonian_energy_error = 0.20542093409155626, max_hamiltonian_energy_error = -0.5025433947577227, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9987695833904688, log_density = 13.239627365264502, hamiltonian_energy = -10.253268987346667, hamiltonian_energy_error = -0.1971438308889244, max_hamiltonian_energy_error = -0.385168740035132, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9965936163002185, log_density = 12.671864915290564, hamiltonian_energy = -11.263432255417118, hamiltonian_energy_error = -0.07621885458549826, max_hamiltonian_energy_error = -0.1881003017516356, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8252085147028597, log_density = 12.337152055502408, hamiltonian_energy = -6.575187883288159, hamiltonian_energy_error = 0.0852521023203634, max_hamiltonian_energy_error = 0.41106842911472885, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9503590530222579, log_density = 11.948351862484426, hamiltonian_energy = -9.669831467922576, hamiltonian_energy_error = 0.10900575394148149, max_hamiltonian_energy_error = -0.22741315643532722, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.910197696579343, log_density = 12.701805548926343, hamiltonian_energy = -7.098781328237045, hamiltonian_energy_error = -0.06940903910399498, max_hamiltonian_energy_error = -1.7115167384086192, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9176136523126576, log_density = 11.031385300169438, hamiltonian_energy = -10.057061163135787, hamiltonian_energy_error = 0.28413923616016135, max_hamiltonian_energy_error = 0.3000991607745238, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9592606374449386, log_density = 13.497323269222909, hamiltonian_energy = -8.496373767764437, hamiltonian_energy_error = -0.324852381778296, max_hamiltonian_energy_error = -0.558056059791582, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9886875322738228, log_density = 14.624891017015287, hamiltonian_energy = -12.946269116563261, hamiltonian_energy_error = -0.11064460378155516, max_hamiltonian_energy_error = -0.23825772370545906, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8903511352349623, log_density = 15.754101235780421, hamiltonian_energy = -12.274970409070882, hamiltonian_energy_error = -0.09328927667439046, max_hamiltonian_energy_error = 0.3121132750273343, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9275233316879941, log_density = 14.257361196822057, hamiltonian_energy = -12.890827767108759, hamiltonian_energy_error = 0.018304278862460777, max_hamiltonian_energy_error = 0.16361942802154772, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.980752586269089, log_density = 14.772766873315891, hamiltonian_energy = -13.113989539179594, hamiltonian_energy_error = 0.029547450640672324, max_hamiltonian_energy_error = 0.060604532634252806, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9814151311276711, log_density = 13.435086067762718, hamiltonian_energy = -11.49992854209222, hamiltonian_energy_error = 0.03472181797887508, max_hamiltonian_energy_error = 0.14057616510772952, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9420091037617934, log_density = 14.502638141528767, hamiltonian_energy = -11.203385831922102, hamiltonian_energy_error = 0.06204267897419413, max_hamiltonian_energy_error = 0.27998667810492783, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9942749746748927, log_density = 14.82820103755381, hamiltonian_energy = -13.881035646941266, hamiltonian_energy_error = -0.026276068212755632, max_hamiltonian_energy_error = -0.1162945446032797, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.925894213029743, log_density = 14.323002837846039, hamiltonian_energy = -11.776209703662975, hamiltonian_energy_error = 0.04948425191594019, max_hamiltonian_energy_error = 0.16699447385484945, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9295537841443502, log_density = 12.36812355116615, hamiltonian_energy = -10.439974852811696, hamiltonian_energy_error = 0.06863965400818728, max_hamiltonian_energy_error = 0.22760676642579014, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9908292792351854, log_density = 14.245331474345067, hamiltonian_energy = -10.256422053920735, hamiltonian_energy_error = -0.006363051120439778, max_hamiltonian_energy_error = 0.09704068753341666, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9930192310794266, log_density = 13.169664907939854, hamiltonian_energy = -11.94345893126634, hamiltonian_energy_error = 0.026127878265388205, max_hamiltonian_energy_error = -0.1312149662104236, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7599590858933326, log_density = 10.87236745919719, hamiltonian_energy = -5.4038121963226144, hamiltonian_energy_error = 0.5760970837537274, max_hamiltonian_energy_error = 0.5760970837537274, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 14.589181246953633, hamiltonian_energy = -10.786409265119186, hamiltonian_energy_error = -0.646424036182708, max_hamiltonian_energy_error = -0.646424036182708, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9167268066676235, log_density = 13.15963777071692, hamiltonian_energy = -8.525038636501225, hamiltonian_energy_error = -0.010890148586579329, max_hamiltonian_energy_error = 0.1978246076930663, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9848315646321026, log_density = 12.817813668676632, hamiltonian_energy = -11.72769539656617, hamiltonian_energy_error = 0.03925188118975598, max_hamiltonian_energy_error = -0.051352510987610955, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6503782886737076, log_density = 10.35596016112417, hamiltonian_energy = -7.3942575216723165, hamiltonian_energy_error = 0.6573060978071394, max_hamiltonian_energy_error = 0.7856530417322976, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9895043470601026, log_density = 9.659237717463782, hamiltonian_energy = -6.496296905487469, hamiltonian_energy_error = -0.0990570775231463, max_hamiltonian_energy_error = -0.9813697665498671, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 1, is_accept = true, acceptance_rate = 0.956393230909967, log_density = 9.08363908763432, hamiltonian_energy = -8.770162506306043, hamiltonian_energy_error = 0.04458612109975313, max_hamiltonian_energy_error = 0.04458612109975313, tree_depth = 1, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9852913727201639, log_density = 13.346437756325015, hamiltonian_energy = -7.315596518209766, hamiltonian_energy_error = -0.43764076818225206, max_hamiltonian_energy_error = -0.43764076818225206, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9849812349915753, log_density = 14.1136776643369, hamiltonian_energy = -11.435927694656868, hamiltonian_energy_error = -0.01798080546526215, max_hamiltonian_energy_error = -0.13893308940130744, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 15.115117390933388, hamiltonian_energy = -14.114845186656371, hamiltonian_energy_error = -0.08201959085952026, max_hamiltonian_energy_error = -0.14733069152363854, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9906377591886051, log_density = 13.486945522539, hamiltonian_energy = -13.2317240688825, hamiltonian_energy_error = 0.05039290186374146, max_hamiltonian_energy_error = 0.05039290186374146, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.837195638849721, log_density = 10.828226210653842, hamiltonian_energy = -9.668986532639362, hamiltonian_energy_error = 0.30044389917920356, max_hamiltonian_energy_error = 0.36077183180254124, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9651594506110166, log_density = 10.325558374164327, hamiltonian_energy = -5.753709134634174, hamiltonian_energy_error = -0.8962752697263037, max_hamiltonian_energy_error = -0.8962752697263037, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9981626143304517, log_density = 14.890625447481613, hamiltonian_energy = -10.429901140811609, hamiltonian_energy_error = -0.3748800208553238, max_hamiltonian_energy_error = -0.4034998095893503, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9830666461175313, log_density = 13.943357844580724, hamiltonian_energy = -13.088470158224268, hamiltonian_energy_error = -0.0618613514452484, max_hamiltonian_energy_error = 0.07141756782779929, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.835289949367881, log_density = 13.41793103520607, hamiltonian_energy = -11.664922854379748, hamiltonian_energy_error = 0.18682191190068487, max_hamiltonian_energy_error = 0.3415808691152673, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9859102558584726, log_density = 14.066391898926875, hamiltonian_energy = -11.240612977979971, hamiltonian_energy_error = -0.13408388522968195, max_hamiltonian_energy_error = -0.13408388522968195, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.999691499216996, log_density = 15.5599022843478, hamiltonian_energy = -13.104377876658551, hamiltonian_energy_error = -0.04314204050815107, max_hamiltonian_energy_error = -0.07270803078780119, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9716157614386749, log_density = 15.709797685036902, hamiltonian_energy = -14.939618442588467, hamiltonian_energy_error = 0.0072288466279832875, max_hamiltonian_energy_error = 0.06078674426779607, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8337410774947228, log_density = 14.300789356579756, hamiltonian_energy = -11.818548219681464, hamiltonian_energy_error = 0.06330467144474206, max_hamiltonian_energy_error = 0.39173978446877555, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9967822926996319, log_density = 14.636670024848536, hamiltonian_energy = -12.664052712434795, hamiltonian_energy_error = -0.01463926126115922, max_hamiltonian_energy_error = -0.1124442491664901, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9931544184691543, log_density = 15.021599674196388, hamiltonian_energy = -14.008320594991112, hamiltonian_energy_error = 0.0024385949044845034, max_hamiltonian_energy_error = -0.10383125498008461, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9078189880802119, log_density = 14.762362328081684, hamiltonian_energy = -12.175315625167341, hamiltonian_energy_error = -0.09240924763969183, max_hamiltonian_energy_error = 0.29333375931492967, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.94718252384193, log_density = 15.853437998636181, hamiltonian_energy = -13.07738282722355, hamiltonian_energy_error = -0.05532788824568158, max_hamiltonian_energy_error = 0.11178870861490608, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9007514772618384, log_density = 15.960956172458111, hamiltonian_energy = -13.271722943405061, hamiltonian_energy_error = -0.052959302668368125, max_hamiltonian_energy_error = 0.19997257087279152, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9527681927973501, log_density = 14.805342378590005, hamiltonian_energy = -13.722722762256401, hamiltonian_energy_error = 0.06361570723976406, max_hamiltonian_energy_error = 0.07067145420022669, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.895510606097114, log_density = 14.454911705737418, hamiltonian_energy = -12.518286472938343, hamiltonian_energy_error = 0.08378039092920453, max_hamiltonian_energy_error = 0.22438067298261366, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9384832703477715, log_density = 13.827549862078131, hamiltonian_energy = -11.70285923994326, hamiltonian_energy_error = 0.008584730518132133, max_hamiltonian_energy_error = 0.21261715080738952, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9281783892640816, log_density = 14.910452105667382, hamiltonian_energy = -11.669354203577926, hamiltonian_energy_error = -0.03175659600524838, max_hamiltonian_energy_error = 0.22066995351510954, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9675294875554112, log_density = 13.883126794669783, hamiltonian_energy = -13.360161144867108, hamiltonian_energy_error = 0.05844251907758746, max_hamiltonian_energy_error = -0.13630056837426885, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9078531448393617, log_density = 11.697991319493035, hamiltonian_energy = -10.935505611991188, hamiltonian_energy_error = 0.1644222406821303, max_hamiltonian_energy_error = 0.3097280204266948, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 14.341775912506197, hamiltonian_energy = -10.742911373366855, hamiltonian_energy_error = -0.2203482077125365, max_hamiltonian_energy_error = -0.257369850556449, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7819850806911359, log_density = 13.291572955018097, hamiltonian_energy = -9.725623446127376, hamiltonian_energy_error = 0.14129782940083224, max_hamiltonian_energy_error = 0.5759686515739126, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9947075887293991, log_density = 14.122939661899732, hamiltonian_energy = -12.08994253151788, hamiltonian_energy_error = -0.04366340186028772, max_hamiltonian_energy_error = -0.12069027630145435, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.996050768712229, log_density = 14.179501831981918, hamiltonian_energy = -13.028874208211128, hamiltonian_energy_error = 0.028033923045835962, max_hamiltonian_energy_error = -0.09920579823781672, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9539399960361463, log_density = 10.230148738345243, hamiltonian_energy = -7.471099095866562, hamiltonian_energy_error = 0.054103714120751434, max_hamiltonian_energy_error = 0.1848837669545942, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.959888048781103, log_density = 9.536794222098347, hamiltonian_energy = -6.504286088276789, hamiltonian_energy_error = 0.17271995309488375, max_hamiltonian_energy_error = -0.22480434683184658, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9968313044785447, log_density = 11.855950395373092, hamiltonian_energy = -8.390059505117561, hamiltonian_energy_error = -0.07527726991889949, max_hamiltonian_energy_error = -0.3985251644210539, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8279706676845867, log_density = 10.55524363930915, hamiltonian_energy = -6.547244984329183, hamiltonian_energy_error = 0.042722026806561786, max_hamiltonian_energy_error = 0.6293033171978504, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.983631687250132, log_density = 11.806686196096285, hamiltonian_energy = -8.357150021183896, hamiltonian_energy_error = 0.019574260483011585, max_hamiltonian_energy_error = -0.38927674102601806, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9572295099789756, log_density = 11.248097197466063, hamiltonian_energy = -7.643713931880976, hamiltonian_energy_error = -0.08106846531024381, max_hamiltonian_energy_error = -0.5626898682334094, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9840684064904072, log_density = 13.602678002339001, hamiltonian_energy = -8.97653695194669, hamiltonian_energy_error = -0.10912095723503157, max_hamiltonian_energy_error = -0.2970352621174328, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9259684492805392, log_density = 12.32633112291721, hamiltonian_energy = -11.776304603144322, hamiltonian_energy_error = 0.26378906214574904, max_hamiltonian_energy_error = 0.352454188610988, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9558277183765279, log_density = 14.192308038764438, hamiltonian_energy = -10.331234327375295, hamiltonian_energy_error = -0.24894044452849862, max_hamiltonian_energy_error = -0.6046578408013819, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9786372064995739, log_density = 13.57605873660099, hamiltonian_energy = -9.66225969739535, hamiltonian_energy_error = -0.007130616348181462, max_hamiltonian_energy_error = -0.20180697730327246, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9617019395393704, log_density = 11.979146367452623, hamiltonian_energy = -9.76813641581327, hamiltonian_energy_error = -0.005811429165662574, max_hamiltonian_energy_error = 0.11253872241575635, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9828407938140413, log_density = 12.959413613387195, hamiltonian_energy = -10.149857387486408, hamiltonian_energy_error = -0.16658104763980752, max_hamiltonian_energy_error = -0.16658104763980752, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9154527557715065, log_density = 13.76882024048235, hamiltonian_energy = -10.97134793388502, hamiltonian_energy_error = 0.06350032469740796, max_hamiltonian_energy_error = 0.18236447331032757, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9454830839015813, log_density = 14.506559545033344, hamiltonian_energy = -11.060180103540734, hamiltonian_energy_error = 0.08708623545571648, max_hamiltonian_energy_error = 0.1362373412675808, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9978003137837768, log_density = 15.16689458170929, hamiltonian_energy = -13.878770403592654, hamiltonian_energy_error = -0.11175852560754507, max_hamiltonian_energy_error = -0.1568374928570737, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9193668828745357, log_density = 13.479889841454185, hamiltonian_energy = -10.965670548423624, hamiltonian_energy_error = 0.07542757229041186, max_hamiltonian_energy_error = 0.22039546219773065, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8925250298496398, log_density = 12.494518541147862, hamiltonian_energy = -9.036938752672793, hamiltonian_energy_error = 0.1956564224515276, max_hamiltonian_energy_error = 0.3582362238061645, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 15.719555374123733, hamiltonian_energy = -12.108314686472426, hamiltonian_energy_error = -0.3115656439040215, max_hamiltonian_energy_error = -0.3115656439040215, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9981955956623055, log_density = 15.699840964171043, hamiltonian_energy = -15.013427012851183, hamiltonian_energy_error = -0.0011621332235431936, max_hamiltonian_energy_error = -0.015153916785695998, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8322733351120828, log_density = 14.698658667583025, hamiltonian_energy = -12.336374393006944, hamiltonian_energy_error = 0.15911520004917, max_hamiltonian_energy_error = 0.2560437485142977, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9986455806368607, log_density = 15.586880565183431, hamiltonian_energy = -14.22900441000164, hamiltonian_energy_error = -0.0880004636208973, max_hamiltonian_energy_error = -0.14021004543963755, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9803472778332977, log_density = 15.668924726065045, hamiltonian_energy = -14.605142387448645, hamiltonian_energy_error = -0.0351174995300525, max_hamiltonian_energy_error = 0.06108350082288716, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9057810872554661, log_density = 14.992173826990172, hamiltonian_energy = -14.215760528564003, hamiltonian_energy_error = 0.1427890623777639, max_hamiltonian_energy_error = 0.1848805490111829, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9915345428110408, log_density = 13.967356857855282, hamiltonian_energy = -13.299294915465529, hamiltonian_energy_error = 0.04020575481250255, max_hamiltonian_energy_error = -0.1430524859946125, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9902157416423317, log_density = 15.478060667107652, hamiltonian_energy = -11.957986263792332, hamiltonian_energy_error = -0.18462366524913243, max_hamiltonian_energy_error = -0.18462366524913243, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9210746582428148, log_density = 12.062121589922306, hamiltonian_energy = -11.553522567538158, hamiltonian_energy_error = 0.11068947352077174, max_hamiltonian_energy_error = 0.17156654824004214, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9745137019023045, log_density = 12.57710672436452, hamiltonian_energy = -10.301279298563232, hamiltonian_energy_error = 0.04322794984736156, max_hamiltonian_energy_error = -0.18861069183171608, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9843173815934307, log_density = 13.45606502045631, hamiltonian_energy = -9.838502490320455, hamiltonian_energy_error = -0.027259913662380342, max_hamiltonian_energy_error = -0.18924096909650956, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8138525849211327, log_density = 8.95113745174392, hamiltonian_energy = -7.0183551399412, hamiltonian_energy_error = 0.32238526353994246, max_hamiltonian_energy_error = 0.7889465048926194, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 11.845032231075804, hamiltonian_energy = -7.855106559934077, hamiltonian_energy_error = -0.04713133130832858, max_hamiltonian_energy_error = -0.38977581806179984, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9666000863655511, log_density = 15.03371931734879, hamiltonian_energy = -7.953186354215246, hamiltonian_energy_error = -0.22582286986533795, max_hamiltonian_energy_error = -0.27105469495393564, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.808933739273343, log_density = 15.197753523566577, hamiltonian_energy = -10.092128517297263, hamiltonian_energy_error = 0.12893031504978403, max_hamiltonian_energy_error = 0.3708679302991005, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.99878823399278, log_density = 15.164097887342402, hamiltonian_energy = -14.699636248512475, hamiltonian_energy_error = -0.013412555525089687, max_hamiltonian_energy_error = -0.027017723705649033, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9481331544774138, log_density = 14.690854809145401, hamiltonian_energy = -13.243977688158418, hamiltonian_energy_error = 0.06235036507035474, max_hamiltonian_energy_error = 0.1327916417964694, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9849536439771364, log_density = 14.982046438568645, hamiltonian_energy = -12.54712639866995, hamiltonian_energy_error = -0.10105052018183791, max_hamiltonian_energy_error = -0.10154801852116968, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9360381160441213, log_density = 12.835139430213527, hamiltonian_energy = -10.118636780161221, hamiltonian_energy_error = 0.0713827104160547, max_hamiltonian_energy_error = 0.13714490081351194, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8467176753540059, log_density = 13.722633080785446, hamiltonian_energy = -9.35201243079269, hamiltonian_energy_error = -0.10111261331056909, max_hamiltonian_energy_error = 0.38318008873573284, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9915174700874154, log_density = 14.93107854196609, hamiltonian_energy = -12.862982283199084, hamiltonian_energy_error = -0.03396218642743598, max_hamiltonian_energy_error = -0.03396218642743598, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8827158325980894, log_density = 13.653415515392584, hamiltonian_energy = -11.465616264872095, hamiltonian_energy_error = 0.2343364637077947, max_hamiltonian_energy_error = 0.25891410719082764, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9605509364191251, log_density = 10.854589688568513, hamiltonian_energy = -8.60403066839799, hamiltonian_energy_error = -0.016946097874878774, max_hamiltonian_energy_error = -0.2593204436490293, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 12.807472846432999, hamiltonian_energy = -9.781045867482106, hamiltonian_energy_error = -0.07780493508339248, max_hamiltonian_energy_error = -0.27095541738590967, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 14.13665571489848, hamiltonian_energy = -12.080047567061968, hamiltonian_energy_error = -0.1639456769931389, max_hamiltonian_energy_error = -0.2514795092869413, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9997931389463162, log_density = 14.875032890220755, hamiltonian_energy = -13.513203893338613, hamiltonian_energy_error = -0.04608859707042612, max_hamiltonian_energy_error = -0.11768606499979839, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8918100054204873, log_density = 13.240504021115523, hamiltonian_energy = -10.962141761810368, hamiltonian_energy_error = 0.02088050914766626, max_hamiltonian_energy_error = 0.2708006081870309, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8868725281585552, log_density = 12.523195764020107, hamiltonian_energy = -8.886878947845952, hamiltonian_energy_error = 0.13199726735753892, max_hamiltonian_energy_error = -0.6222659244236439, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9964209390495211, log_density = 15.235723697025719, hamiltonian_energy = -11.32472262740609, hamiltonian_energy_error = -0.25354217762018827, max_hamiltonian_energy_error = -0.25354217762018827, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9626908315706206, log_density = 14.710375758649292, hamiltonian_energy = -12.80010630282145, hamiltonian_energy_error = 0.01305954993476277, max_hamiltonian_energy_error = 0.07337287110838453, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.915501728961815, log_density = 14.262772282736448, hamiltonian_energy = -11.42272891346926, hamiltonian_energy_error = 0.005245652004150614, max_hamiltonian_energy_error = 0.22257686508135244, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8988957656407082, log_density = 13.51985005515877, hamiltonian_energy = -12.08401654107421, hamiltonian_energy_error = 0.15674386183786915, max_hamiltonian_energy_error = 0.21311342147200918, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9841391856011692, log_density = 14.707752891283352, hamiltonian_energy = -11.83906188876049, hamiltonian_energy_error = -0.1302912139856076, max_hamiltonian_energy_error = -0.15057820205203853, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9594216354704221, log_density = 15.56005084178649, hamiltonian_energy = -11.72204714133154, hamiltonian_energy_error = -0.09847639367088235, max_hamiltonian_energy_error = -0.09847639367088235, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9796878863587271, log_density = 15.237739700449971, hamiltonian_energy = -13.80467429103469, hamiltonian_energy_error = -0.018476168820299677, max_hamiltonian_energy_error = -0.08608024498573741, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9517138673956207, log_density = 14.164373141498176, hamiltonian_energy = -13.469255138679658, hamiltonian_energy_error = 0.12650542704461465, max_hamiltonian_energy_error = 0.12650542704461465, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9997035669281965, log_density = 13.643722350118763, hamiltonian_energy = -12.517996954144827, hamiltonian_energy_error = -0.0031799992847112435, max_hamiltonian_energy_error = -0.15170366930624724, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9707984705126569, log_density = 13.503123392271103, hamiltonian_energy = -11.782677257827821, hamiltonian_energy_error = 0.024309686336914993, max_hamiltonian_energy_error = 0.15474309568328515, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9969092202648586, log_density = 12.575723274926407, hamiltonian_energy = -11.896381985123622, hamiltonian_energy_error = 0.003504861569876283, max_hamiltonian_energy_error = -0.20357634708916095, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9414297318793693, log_density = 12.055567868526511, hamiltonian_energy = -9.061469479894964, hamiltonian_energy_error = 0.22711782663607316, max_hamiltonian_energy_error = -0.32055608024161053, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 12.381253245129363, hamiltonian_energy = -10.654987464026195, hamiltonian_energy_error = -0.17167883539470097, max_hamiltonian_energy_error = -0.44165533140204793, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9987531694874282, log_density = 14.315629697151738, hamiltonian_energy = -11.060006109197918, hamiltonian_energy_error = -0.2496978462230075, max_hamiltonian_energy_error = -0.424184063848978, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8969152073059925, log_density = 15.815320562389083, hamiltonian_energy = -10.511792152157124, hamiltonian_energy_error = 0.05975217730277471, max_hamiltonian_energy_error = 0.20716745290394734, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8992084817851277, log_density = 13.62064187356648, hamiltonian_energy = -13.162273561338932, hamiltonian_energy_error = 0.18155763739549258, max_hamiltonian_energy_error = 0.18155763739549258, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.676518832404611, log_density = 14.972763063940626, hamiltonian_energy = -9.54361439526954, hamiltonian_energy_error = 0.00505945536302832, max_hamiltonian_energy_error = 0.7118652004729054, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8719316447657476, log_density = 12.431022330441818, hamiltonian_energy = -11.414885323824896, hamiltonian_energy_error = 0.132323306719341, max_hamiltonian_energy_error = 0.2249443778161755, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9695428693862032, log_density = 11.04878749954077, hamiltonian_energy = -8.87493251673659, hamiltonian_energy_error = 0.025125381351363885, max_hamiltonian_energy_error = -0.18293353010899338, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9312866963439151, log_density = 12.161422788089412, hamiltonian_energy = -8.035654585872273, hamiltonian_energy_error = -0.029083044468112718, max_hamiltonian_energy_error = -0.3961696797606926, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9470516691815355, log_density = 8.932818611456845, hamiltonian_energy = -7.567644717615105, hamiltonian_energy_error = 0.025839989334423663, max_hamiltonian_energy_error = -0.8490088231516566, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9910386820236422, log_density = 13.065722788955545, hamiltonian_energy = -4.071062235145925, hamiltonian_energy_error = -0.06143194777382277, max_hamiltonian_energy_error = -0.25538617018282217, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9687762150387252, log_density = 11.75607820052768, hamiltonian_energy = -10.090726207345346, hamiltonian_energy_error = 0.07139996253776282, max_hamiltonian_energy_error = -0.2743643542155496, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9561264317582464, log_density = 11.870532149760127, hamiltonian_energy = -8.195067434289719, hamiltonian_energy_error = -0.2028884647596758, max_hamiltonian_energy_error = 0.33014842398776256, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 12.494552562102992, hamiltonian_energy = -11.31553092497192, hamiltonian_energy_error = -0.0778759362284589, max_hamiltonian_energy_error = -0.16449567460448478, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9845429310727383, log_density = 14.022185588437068, hamiltonian_energy = -8.447795434586997, hamiltonian_energy_error = 0.013905385117109148, max_hamiltonian_energy_error = -0.15551926922813664, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 1.0, log_density = 14.74970472905242, hamiltonian_energy = -11.735990279365287, hamiltonian_energy_error = -0.1630909636490241, max_hamiltonian_energy_error = -0.1975633036760076, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8199802774484455, log_density = 13.556499130627023, hamiltonian_energy = -12.618993966390056, hamiltonian_energy_error = 0.046724126997023774, max_hamiltonian_energy_error = 0.40590314712719255, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7616243134122265, log_density = 11.494495108588854, hamiltonian_energy = -7.861209254901186, hamiltonian_energy_error = 0.21209677433219465, max_hamiltonian_energy_error = 0.5169786973002823, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8879316557910412, log_density = 14.16274174302286, hamiltonian_energy = -8.147161463222432, hamiltonian_energy_error = -0.08884426242932442, max_hamiltonian_energy_error = 0.2733754468689016, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9987258524052164, log_density = 15.281256963127412, hamiltonian_energy = -13.369311388422673, hamiltonian_energy_error = -0.06659803001593367, max_hamiltonian_energy_error = -0.10892134270843634, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9269533008533128, log_density = 13.872462674726734, hamiltonian_energy = -13.31131661978731, hamiltonian_energy_error = 0.10810172274020147, max_hamiltonian_energy_error = 0.15530448068249214, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9019962045187657, log_density = 13.473448212778651, hamiltonian_energy = -10.032140548548725, hamiltonian_energy_error = 0.17592142974348945, max_hamiltonian_energy_error = 0.25312373307982305, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 13.775476437100963, hamiltonian_energy = -11.606575285737115, hamiltonian_energy_error = -0.06591755008704858, max_hamiltonian_energy_error = -0.32126747260033106, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9968249568534512, log_density = 12.253662652527247, hamiltonian_energy = -11.106902930035144, hamiltonian_energy_error = 0.008349234786258819, max_hamiltonian_energy_error = -0.30753255168640337, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9473592202873972, log_density = 13.312215186066071, hamiltonian_energy = -8.664454723585635, hamiltonian_energy_error = 0.07074315508655005, max_hamiltonian_energy_error = -0.2770002382795447, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9981442022606054, log_density = 15.000742459580096, hamiltonian_energy = -12.409523202996198, hamiltonian_energy_error = -0.27707341122389373, max_hamiltonian_energy_error = -0.27707341122389373, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8677679608745907, log_density = 13.896383578674278, hamiltonian_energy = -12.313225979929856, hamiltonian_energy_error = 0.12083035655743224, max_hamiltonian_energy_error = 0.310800992581699, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9385818769895088, log_density = 13.289275530061275, hamiltonian_energy = -10.654162957045186, hamiltonian_energy_error = -0.014827722609444649, max_hamiltonian_energy_error = 0.13324270023182017, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 19, is_accept = true, acceptance_rate = 0.43344905274927786, log_density = 13.576015412400944, hamiltonian_energy = -7.517763584636461, hamiltonian_energy_error = -0.46721584070436695, max_hamiltonian_energy_error = 2.01650174738978, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.993873290558245, log_density = 14.330776857237547, hamiltonian_energy = -13.005353736279526, hamiltonian_energy_error = -0.08410818499359074, max_hamiltonian_energy_error = -0.09712348967031303, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.7751509641511767, log_density = 12.151807041094596, hamiltonian_energy = -11.703778725361968, hamiltonian_energy_error = 0.29466868442210803, max_hamiltonian_energy_error = 0.33149690126926146, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9787510880486274, log_density = 13.462376495969355, hamiltonian_energy = -10.632558038609004, hamiltonian_energy_error = -0.03949007214694156, max_hamiltonian_energy_error = -0.2442835731329378, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 12.846494758771403, hamiltonian_energy = -8.699718686317357, hamiltonian_energy_error = -0.08712017859928878, max_hamiltonian_energy_error = -0.2164747072133455, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 14.572452877858883, hamiltonian_energy = -11.893429804131891, hamiltonian_energy_error = -0.062150528896847135, max_hamiltonian_energy_error = -0.062150528896847135, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9937663306779145, log_density = 15.538466454004555, hamiltonian_energy = -14.272495809591868, hamiltonian_energy_error = -0.010131917880269015, max_hamiltonian_energy_error = 0.012323790638896881, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8877405852237283, log_density = 14.974718529170609, hamiltonian_energy = -11.828631275350617, hamiltonian_energy_error = 0.030879794623555057, max_hamiltonian_energy_error = 0.32230628536749606, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9898063113372549, log_density = 15.51265402424184, hamiltonian_energy = -13.576873466748644, hamiltonian_energy_error = -0.06386650892826218, max_hamiltonian_energy_error = -0.06386650892826218, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9800039139232013, log_density = 15.009468719464866, hamiltonian_energy = -13.84833364962566, hamiltonian_energy_error = 0.02153685662222493, max_hamiltonian_energy_error = 0.0432865350302265, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.986807292111386, log_density = 14.962855532802816, hamiltonian_energy = -12.088856352401704, hamiltonian_energy_error = -0.02400623734990326, max_hamiltonian_energy_error = 0.03289657429329296, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9796411043918359, log_density = 14.59816820547761, hamiltonian_energy = -12.412280583231434, hamiltonian_energy_error = 0.023401033613673405, max_hamiltonian_energy_error = 0.0776028530450823, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9171906245421931, log_density = 14.658525005466498, hamiltonian_energy = -12.670448851136593, hamiltonian_energy_error = 0.014712147571454892, max_hamiltonian_energy_error = 0.21301936034473634, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6670206596490432, log_density = 12.330120645439038, hamiltonian_energy = -9.842294978181087, hamiltonian_energy_error = 0.322241697060921, max_hamiltonian_energy_error = 0.5236137824696439, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9749060135088204, log_density = 12.05618906585468, hamiltonian_energy = -11.17872569252757, hamiltonian_energy_error = 0.11319717108797711, max_hamiltonian_energy_error = -0.13946347426786687, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.8746582317257975, log_density = 13.282114533018408, hamiltonian_energy = -8.722941478148545, hamiltonian_energy_error = -0.11456717678555961, max_hamiltonian_energy_error = 0.8292984501557372, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 14.318015390493347, hamiltonian_energy = -12.878084515556898, hamiltonian_energy_error = -0.12874126683471054, max_hamiltonian_energy_error = -0.21810154457291553, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8651392990387445, log_density = 14.819679153627934, hamiltonian_energy = -11.197410266366159, hamiltonian_energy_error = 0.002115967717358558, max_hamiltonian_energy_error = 0.34156455159603105, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9290586044155685, log_density = 15.63063887780162, hamiltonian_energy = -12.129317135190908, hamiltonian_energy_error = -0.0808409235323495, max_hamiltonian_energy_error = 0.20132032555567925, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9103054483083672, log_density = 13.912442187168391, hamiltonian_energy = -12.746947846145673, hamiltonian_energy_error = 0.0895833217336861, max_hamiltonian_energy_error = 0.14468644963195665, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.910002273859111, log_density = 13.967494433774757, hamiltonian_energy = -10.948652863292864, hamiltonian_energy_error = 0.03061486376518019, max_hamiltonian_energy_error = 0.19569811214835298, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.990847547381075, log_density = 14.9517328338817, hamiltonian_energy = -13.347246502454698, hamiltonian_energy_error = -0.08994144756870881, max_hamiltonian_energy_error = -0.11527069545848789, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9243218197626132, log_density = 15.899270381238395, hamiltonian_energy = -14.03950266629204, hamiltonian_energy_error = -0.01708499073243175, max_hamiltonian_energy_error = 0.15700494830596057, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9347484794687503, log_density = 14.488671676508869, hamiltonian_energy = -13.069064452841905, hamiltonian_energy_error = 0.0773230969527745, max_hamiltonian_energy_error = 0.12255630446519739, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8385335816566654, log_density = 11.864559442226307, hamiltonian_energy = -11.023794498979502, hamiltonian_energy_error = 0.24129690890001498, max_hamiltonian_energy_error = 0.24295921540005416, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9858218002190166, log_density = 12.967913168366046, hamiltonian_energy = -10.767547163375474, hamiltonian_energy_error = -0.0660478675493863, max_hamiltonian_energy_error = -0.4010532447699777, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.969261308379231, log_density = 12.603902484339555, hamiltonian_energy = -8.622115388724302, hamiltonian_energy_error = -0.21745552339680607, max_hamiltonian_energy_error = -0.2604251999580587, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9288662263003927, log_density = 10.56372840995051, hamiltonian_energy = -8.999750638056572, hamiltonian_energy_error = 0.1672122256721167, max_hamiltonian_energy_error = 0.1672122256721167, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9547846908953825, log_density = 13.573639767088267, hamiltonian_energy = -9.199346268586842, hamiltonian_energy_error = -0.02923168604832682, max_hamiltonian_energy_error = -0.45927638237433754, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9729245909845423, log_density = 13.205938523666692, hamiltonian_energy = -10.990190747595634, hamiltonian_energy_error = -0.09905432107116496, max_hamiltonian_energy_error = -0.1984655965529818, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9568697419499074, log_density = 13.988296530383362, hamiltonian_energy = -11.340398636840746, hamiltonian_energy_error = -0.08381964288225063, max_hamiltonian_energy_error = -0.17741879426363028, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.982072342515838, log_density = 14.383210778798455, hamiltonian_energy = -12.10167959290921, hamiltonian_energy_error = 0.0062539157383074695, max_hamiltonian_energy_error = -0.14823492128713234, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.893866017911509, log_density = 10.41147757972946, hamiltonian_energy = -9.656533626380098, hamiltonian_energy_error = 0.19320122552163888, max_hamiltonian_energy_error = 0.19320122552163888, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 14.276499457138641, hamiltonian_energy = -9.872843946198667, hamiltonian_energy_error = -0.12686084888504467, max_hamiltonian_energy_error = -0.2687527870182631, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9800688350073163, log_density = 14.306383533583176, hamiltonian_energy = -11.999845951236107, hamiltonian_energy_error = -0.03327119597400241, max_hamiltonian_energy_error = -0.10370201039228988, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9907152485972134, log_density = 14.375504383706353, hamiltonian_energy = -12.823164483633995, hamiltonian_energy_error = -0.041939924044616106, max_hamiltonian_energy_error = -0.12518899978213938, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9909267375669221, log_density = 13.714115072540059, hamiltonian_energy = -12.041005311269238, hamiltonian_energy_error = -0.0009903121428962436, max_hamiltonian_energy_error = -0.10319192205228056, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9872824876070692, log_density = 14.260226762143954, hamiltonian_energy = -12.577675000764419, hamiltonian_energy_error = -0.012463032743863067, max_hamiltonian_energy_error = -0.061047492082501265, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.7768898523613412, log_density = 12.738732166740421, hamiltonian_energy = -11.909442614796262, hamiltonian_energy_error = 0.3195896546003354, max_hamiltonian_energy_error = 0.3195896546003354, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 12.882821443091395, hamiltonian_energy = -10.309175529282557, hamiltonian_energy_error = -0.20322765666568365, max_hamiltonian_energy_error = -0.3029116189001204, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 15.112370777648952, hamiltonian_energy = -11.912835309894987, hamiltonian_energy_error = -0.03813797495938864, max_hamiltonian_energy_error = -0.08743656973877911, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.971262480788656, log_density = 15.139352279196604, hamiltonian_energy = -13.843213796335675, hamiltonian_energy_error = 0.04950265922196273, max_hamiltonian_energy_error = 0.06270105164776041, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8057885244718082, log_density = 11.8458895092908, hamiltonian_energy = -8.92717327152018, hamiltonian_energy_error = 0.2241640551811983, max_hamiltonian_energy_error = 0.4786904920308448, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9599774916130818, log_density = 11.720823611505345, hamiltonian_energy = -8.38812095619053, hamiltonian_energy_error = -0.10027730904849896, max_hamiltonian_energy_error = -0.32558294031820445, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 31, is_accept = true, acceptance_rate = 0.9098250635742738, log_density = 10.205613039510464, hamiltonian_energy = -8.584846483146883, hamiltonian_energy_error = 0.20127399572587024, max_hamiltonian_energy_error = 0.31944069892149685, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 11.756828285017633, hamiltonian_energy = -9.161322633705616, hamiltonian_energy_error = -0.044964774801592, max_hamiltonian_energy_error = -0.1927877947915544, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9578095259380464, log_density = 11.41317201239734, hamiltonian_energy = -7.1567401161519335, hamiltonian_energy_error = 0.0729650865503304, max_hamiltonian_energy_error = 0.13868843257641306, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 12.163292127878147, hamiltonian_energy = -10.871122271425678, hamiltonian_energy_error = -0.07164728021818334, max_hamiltonian_energy_error = -0.11728980047643311, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7520355461457742, log_density = 10.891874104457608, hamiltonian_energy = -6.204237003112148, hamiltonian_energy_error = 0.05755198863974087, max_hamiltonian_energy_error = 0.7374212217234994, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8919493923523002, log_density = 11.93817356830381, hamiltonian_energy = -8.198563005021281, hamiltonian_energy_error = 0.1660809682821487, max_hamiltonian_energy_error = 0.519633491095127, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7983777296035621, log_density = 8.952239198692975, hamiltonian_energy = -5.932811662760991, hamiltonian_energy_error = 0.40323403621633425, max_hamiltonian_energy_error = -0.6142850872318819, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 14.892459888470025, hamiltonian_energy = -8.369045296223913, hamiltonian_energy_error = -0.8409982800222586, max_hamiltonian_energy_error = -0.8409982800222586, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9858859569712897, log_density = 14.83970353330227, hamiltonian_energy = -12.259872606385585, hamiltonian_energy_error = -0.01075060097502245, max_hamiltonian_energy_error = -0.09133296779545219, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9997404344577732, log_density = 15.616893106926463, hamiltonian_energy = -14.47502912979773, hamiltonian_energy_error = -0.04324276882445055, max_hamiltonian_energy_error = -0.05057214918651276, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9635449011706066, log_density = 15.655996554479016, hamiltonian_energy = -14.769144032701789, hamiltonian_energy_error = 0.05371851908604697, max_hamiltonian_energy_error = 0.09034596968362862, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8838300549136366, log_density = 15.851763506290425, hamiltonian_energy = -12.615473570648529, hamiltonian_energy_error = -0.04409173022661683, max_hamiltonian_energy_error = 0.24117683226165276, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9725794800425139, log_density = 14.808844947957787, hamiltonian_energy = -14.315686690089647, hamiltonian_energy_error = 0.03456138001148368, max_hamiltonian_energy_error = 0.05674283547242709, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7529428231884974, log_density = 14.53349371679439, hamiltonian_energy = -10.21313529946496, hamiltonian_energy_error = 0.14373245946227264, max_hamiltonian_energy_error = 0.5041248585012568, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9975025992655915, log_density = 14.44568011149661, hamiltonian_energy = -13.329131134296432, hamiltonian_energy_error = -0.08338066919911391, max_hamiltonian_energy_error = -0.14339762282760304, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9676208741604145, log_density = 13.943629555667286, hamiltonian_energy = -12.002584588282842, hamiltonian_energy_error = -0.030781047901479397, max_hamiltonian_energy_error = 0.08471595169658208, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6966158307492201, log_density = 12.947395669528127, hamiltonian_energy = -10.039473092160051, hamiltonian_energy_error = 0.15519720110938096, max_hamiltonian_energy_error = 0.5617761793092484, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9502902790314597, log_density = 13.510667503620812, hamiltonian_energy = -10.31649556240065, hamiltonian_energy_error = -0.06575516515876778, max_hamiltonian_energy_error = 0.19038954732164548, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.99868372498422, log_density = 14.77473856462994, hamiltonian_energy = -12.902296144990334, hamiltonian_energy_error = -0.038939973816431106, max_hamiltonian_energy_error = -0.11165619914045521, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9975067474177811, log_density = 14.9154780022156, hamiltonian_energy = -12.954618288584577, hamiltonian_energy_error = -0.03920654403067303, max_hamiltonian_energy_error = -0.09147323129728946, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9775631690441796, log_density = 15.754832489160194, hamiltonian_energy = -13.449810867739854, hamiltonian_energy_error = 0.0005785811560290455, max_hamiltonian_energy_error = 0.06322586576734501, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9981463389352759, log_density = 15.865777838957975, hamiltonian_energy = -15.300442982794152, hamiltonian_energy_error = -0.022833225437137727, max_hamiltonian_energy_error = -0.02343943197584686, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9207489588892382, log_density = 15.210699647889207, hamiltonian_energy = -14.650547313017265, hamiltonian_energy_error = 0.05512752133368615, max_hamiltonian_energy_error = 0.11683193738336506, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9292605728422195, log_density = 13.462533650298248, hamiltonian_energy = -12.93144642818596, hamiltonian_energy_error = 0.13072851547575226, max_hamiltonian_energy_error = 0.14586485107215452, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9111049099315528, log_density = 15.10432230678634, hamiltonian_energy = -11.281369914699676, hamiltonian_energy_error = 0.04190638670664093, max_hamiltonian_energy_error = 0.21531603780379172, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9805629059954792, log_density = 14.825418382981294, hamiltonian_energy = -14.323907367674785, hamiltonian_energy_error = 0.023493516008745274, max_hamiltonian_energy_error = -0.13890385217142764, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9967201237301946, log_density = 14.37337342894105, hamiltonian_energy = -13.73523236036811, hamiltonian_energy_error = 0.013478455487994978, max_hamiltonian_energy_error = -0.15105694669463077, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9959054051348338, log_density = 14.894026812360318, hamiltonian_energy = -13.782666201915566, hamiltonian_energy_error = -0.10778196290985065, max_hamiltonian_energy_error = -0.13641387446957332, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9837833446089097, log_density = 14.178553338942768, hamiltonian_energy = -12.20630226961368, hamiltonian_energy_error = -0.0029878720697453787, max_hamiltonian_energy_error = 0.06219339678025371, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9909365051170382, log_density = 13.94729684097696, hamiltonian_energy = -11.357947968066544, hamiltonian_energy_error = -0.03939210852593433, max_hamiltonian_energy_error = -0.14045028053182307, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 31, is_accept = true, acceptance_rate = 0.9716625482075996, log_density = 13.602628942991117, hamiltonian_energy = -12.02317778304454, hamiltonian_energy_error = -0.009113051470608369, max_hamiltonian_energy_error = -0.261080048388564, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9447738620538997, log_density = 11.229427715480725, hamiltonian_energy = -8.60361604745016, hamiltonian_energy_error = 0.09354957772311323, max_hamiltonian_energy_error = 0.23174001290446533, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9601358348713099, log_density = 9.923310870376845, hamiltonian_energy = -7.6058420683611345, hamiltonian_energy_error = 0.017157122272200453, max_hamiltonian_energy_error = -0.22203458321154645, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9976365499517771, log_density = 11.513336417112072, hamiltonian_energy = -8.606577042032294, hamiltonian_energy_error = -0.04934353565312044, max_hamiltonian_energy_error = -0.2825223852940688, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9845372878864864, log_density = 11.763675379740945, hamiltonian_energy = -8.358571505687387, hamiltonian_energy_error = 0.02802380719908726, max_hamiltonian_energy_error = 0.11174550970248909, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9797958462173225, log_density = 10.012123623767927, hamiltonian_energy = -9.216660843912132, hamiltonian_energy_error = 0.03987855326800194, max_hamiltonian_energy_error = -0.1492906290001823, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 31, is_accept = true, acceptance_rate = 0.9988973780107329, log_density = 15.229654261410156, hamiltonian_energy = -7.787619139211007, hamiltonian_energy_error = -0.15222946140231386, max_hamiltonian_energy_error = -0.23973730296918294, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8139179853899996, log_density = 14.890154057220318, hamiltonian_energy = -12.520388460214127, hamiltonian_energy_error = 0.08492308746110488, max_hamiltonian_energy_error = 0.34342372778930574, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9193013923732406, log_density = 14.116930456120754, hamiltonian_energy = -12.359738469754818, hamiltonian_energy_error = 0.09982781149683184, max_hamiltonian_energy_error = 0.1395072504649395, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9936550528039975, log_density = 12.111301394792783, hamiltonian_energy = -10.568929638633072, hamiltonian_energy_error = 0.04257123675748531, max_hamiltonian_energy_error = -0.11822022430455448, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9328006170768705, log_density = 14.362128009064724, hamiltonian_energy = -10.425687175822823, hamiltonian_energy_error = -0.18219386760904754, max_hamiltonian_energy_error = -0.18219386760904754, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9843805455478882, log_density = 15.765178456451808, hamiltonian_energy = -13.542080999434859, hamiltonian_energy_error = -0.04992702784555725, max_hamiltonian_energy_error = 0.05317415284266325, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8889252963053319, log_density = 13.69239693314961, hamiltonian_energy = -12.847526075988426, hamiltonian_energy_error = 0.17468618412145176, max_hamiltonian_energy_error = 0.18938995069592401, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9910051949510319, log_density = 12.654097390745067, hamiltonian_energy = -11.740209850275992, hamiltonian_energy_error = -0.017782443245492274, max_hamiltonian_energy_error = -0.22706527548941757, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9908313302070955, log_density = 14.95339581879045, hamiltonian_energy = -12.217102459550267, hamiltonian_energy_error = -0.11360864142793758, max_hamiltonian_energy_error = -0.35861426130550633, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9814940297462814, log_density = 14.202640296924859, hamiltonian_energy = -13.656840904351236, hamiltonian_energy_error = 0.034177848626740115, max_hamiltonian_energy_error = -0.15515581683784596, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9904105698974605, log_density = 15.457357384684764, hamiltonian_energy = -13.702630749351854, hamiltonian_energy_error = -0.09963687191309312, max_hamiltonian_energy_error = -0.17491016920581437, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9995818308385988, log_density = 15.117075611478604, hamiltonian_energy = -14.379043522742228, hamiltonian_energy_error = -0.029179451409339308, max_hamiltonian_energy_error = -0.06493082538094441, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7873004949827738, log_density = 13.256209903841393, hamiltonian_energy = -11.999675903386331, hamiltonian_energy_error = 0.3504752849793924, max_hamiltonian_energy_error = 0.3737658590831128, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.92739496626957, log_density = 9.99811204627354, hamiltonian_energy = -6.574204302039886, hamiltonian_energy_error = 0.15517829293113383, max_hamiltonian_energy_error = 0.5158041708799299, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 10.47161995464878, hamiltonian_energy = -9.552216704094056, hamiltonian_energy_error = -0.13684276733930822, max_hamiltonian_energy_error = -0.5458248928300886, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 10.495689692236713, hamiltonian_energy = -9.402245889338444, hamiltonian_energy_error = -0.01157670874535377, max_hamiltonian_energy_error = -0.4260000855727011, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9962925721697701, log_density = 13.128788276567661, hamiltonian_energy = -9.056713595076024, hamiltonian_energy_error = -0.15642098223230327, max_hamiltonian_energy_error = -0.3995810775978761, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 13.814196152188082, hamiltonian_energy = -10.861299728742853, hamiltonian_energy_error = -0.10164050684451809, max_hamiltonian_energy_error = -0.2900699071681938, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9744853149536573, log_density = 13.694581717277014, hamiltonian_energy = -11.135255224056387, hamiltonian_energy_error = -0.002696558081677125, max_hamiltonian_energy_error = -0.1974034475550006, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9705655892413861, log_density = 12.20567196790408, hamiltonian_energy = -11.611254185140474, hamiltonian_energy_error = 0.10576949519910173, max_hamiltonian_energy_error = -0.28311630672651944, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9902406319163423, log_density = 13.709169515340514, hamiltonian_energy = -10.287523688892936, hamiltonian_energy_error = -0.1130769753482408, max_hamiltonian_energy_error = -0.3256125438165416, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9880715275166531, log_density = 15.615049129056237, hamiltonian_energy = -11.933352755318804, hamiltonian_energy_error = -0.17313789991049333, max_hamiltonian_energy_error = -0.17313789991049333, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8897074892193747, log_density = 10.859544338123065, hamiltonian_energy = -9.248272184050913, hamiltonian_energy_error = 0.22508880111785778, max_hamiltonian_energy_error = 0.22508880111785778, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 11.652030377791595, hamiltonian_energy = -10.05726665854335, hamiltonian_energy_error = -0.06437265085850008, max_hamiltonian_energy_error = -0.16015127268538976, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6755495763336585, log_density = 11.452446894046448, hamiltonian_energy = -6.884582191900069, hamiltonian_energy_error = 0.3342829311846405, max_hamiltonian_energy_error = 0.8740854367694766, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9743416382326743, log_density = 13.923295600505025, hamiltonian_energy = -10.282716726462123, hamiltonian_energy_error = -0.12625734494385554, max_hamiltonian_energy_error = -0.3440689837007742, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9950913624983959, log_density = 13.73695081125165, hamiltonian_energy = -12.702379172088913, hamiltonian_energy_error = -0.012570557836360408, max_hamiltonian_energy_error = -0.30784087620518363, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9813498596424831, log_density = 10.097490010325668, hamiltonian_energy = -8.730738958082007, hamiltonian_energy_error = -0.0035776147376083145, max_hamiltonian_energy_error = -0.7030091635040847, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6038497251813085, log_density = 13.45029844345467, hamiltonian_energy = -5.58259553607883, hamiltonian_energy_error = 0.1176533740635568, max_hamiltonian_energy_error = 1.2064317923409797, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9568156642967717, log_density = 13.129194478229184, hamiltonian_energy = -10.453511730776688, hamiltonian_energy_error = 0.05850580748202283, max_hamiltonian_energy_error = 0.20061567283512893, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9956418679556361, log_density = 15.298569887545167, hamiltonian_energy = -12.499511496524704, hamiltonian_energy_error = -0.19144594777573687, max_hamiltonian_energy_error = -0.19144594777573687, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9352208109734252, log_density = 12.48531125702349, hamiltonian_energy = -11.653243944943338, hamiltonian_energy_error = 0.08544328706608795, max_hamiltonian_energy_error = 0.10991571788924936, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9669624289568065, log_density = 12.688665681622815, hamiltonian_energy = -9.295316334135386, hamiltonian_energy_error = -0.15872314640562735, max_hamiltonian_energy_error = -0.15872314640562735, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9892157965820007, log_density = 13.777375909747276, hamiltonian_energy = -12.184364152239187, hamiltonian_energy_error = 0.01178249116283503, max_hamiltonian_energy_error = 0.022020674444656052, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9140467927349444, log_density = 15.358164115908155, hamiltonian_energy = -11.138084922691316, hamiltonian_energy_error = 0.04895008862416539, max_hamiltonian_energy_error = 0.1525205008974826, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9168460267767115, log_density = 13.377753860459658, hamiltonian_energy = -10.87586806437995, hamiltonian_energy_error = 0.13597192088781185, max_hamiltonian_energy_error = 0.2609221853901893, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9967603901121371, log_density = 13.677101706011452, hamiltonian_energy = -11.71026899426992, hamiltonian_energy_error = -0.007714420263582156, max_hamiltonian_energy_error = -0.12640730721701843, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9926006240830376, log_density = 14.155995807307379, hamiltonian_energy = -12.491095143643006, hamiltonian_energy_error = 0.019206922637664547, max_hamiltonian_energy_error = -0.10280426067839521, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8947998879230609, log_density = 11.947840886303274, hamiltonian_energy = -10.709236952499314, hamiltonian_energy_error = 0.17661094969608726, max_hamiltonian_energy_error = -0.20625054425214806, tree_depth = 2, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.853516469224985, log_density = 11.523193920673009, hamiltonian_energy = -7.42438955337125, hamiltonian_energy_error = 0.15186796671923464, max_hamiltonian_energy_error = 0.5582480768284874, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9605965327519852, log_density = 13.121932055339732, hamiltonian_energy = -9.632781521754637, hamiltonian_energy_error = -0.4794662789929891, max_hamiltonian_energy_error = -0.4794662789929891, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9560896030182418, log_density = 14.354346610897558, hamiltonian_energy = -10.954557927329827, hamiltonian_energy_error = 0.03414696394509242, max_hamiltonian_energy_error = 0.09650788618528061, tree_depth = 4, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9727533621604373, log_density = 14.434349837963369, hamiltonian_energy = -12.61590179969476, hamiltonian_energy_error = -0.07308001791252572, max_hamiltonian_energy_error = -0.1153248878637747, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9587953809133227, log_density = 13.821841621375716, hamiltonian_energy = -13.081174983725274, hamiltonian_energy_error = 0.08959991761813413, max_hamiltonian_energy_error = 0.1471232126230575, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9935916173987197, log_density = 14.077009144374621, hamiltonian_energy = -12.125136398482356, hamiltonian_energy_error = -0.02590589440447033, max_hamiltonian_energy_error = -0.1779668832861514, tree_depth = 3, numerical_error = false, step_size = 0.12023901756971271, nom_step_size = 0.12023901756971271, is_adapt = false)])

Inspect posterior distribution over hyperparameters.

hypers = map(unpack, samples);
h_l1 = histogram(getindex.(hypers, :l1); label="l1");
h_l2 = histogram(getindex.(hypers, :l2); label="l2");
h_s1 = histogram(getindex.(hypers, :s1); label="s1");
h_s2 = histogram(getindex.(hypers, :s2); label="s2");
plot(h_l1, h_l2, h_s1, h_s2; layout=(2, 2))

As expected, the sampler converges to the posterior distribution quickly. One could combine this code with that from the previous sections to make predictions under the posterior over the hyperparameters.

Conclusion

So you now know how to fit GPs using Stheno.jl, and to investigate their posterior distributions. It's also straightforward to utilise Stheno.jl inside probabilistic programming frameworks like Soss.jl and Turing.jl (see examples folder).

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