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)

15.770039648744202

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     9.709467e+00     2.849876e+01
 * time: 0.03371119499206543
     1    -1.040060e+01     1.297317e+01
 * time: 1.9387240409851074
     2    -1.864734e+01     1.168979e+01
 * time: 2.004240036010742
     3    -1.971475e+01     9.457742e+00
 * time: 2.014320135116577
     4    -2.095108e+01     6.262340e+00
 * time: 2.0245261192321777
     5    -2.133340e+01     4.029365e+00
 * time: 2.0345041751861572
     6    -2.185563e+01     7.217823e-01
 * time: 2.0451409816741943
     7    -2.189079e+01     1.559606e-01
 * time: 2.0549380779266357
     8    -2.189262e+01     8.607501e-02
 * time: 2.065014123916626
     9    -2.189275e+01     2.665654e-03
 * time: 2.0747151374816895
    10    -2.189275e+01     1.242890e-04
 * time: 2.1049680709838867
    11    -2.189275e+01     5.372462e-06
 * time: 2.115149974822998
    12    -2.189275e+01     1.370073e-07
 * time: 2.1247661113739014
    13    -2.189275e+01     7.240302e-10
 * time: 2.134287118911743

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}:
 -0.6935225909367065
 -1.847275439238848
  1.8330234769841731
  0.06939342386539255
 -2.205995144214174

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)

([[-0.6935225909367065, -1.847275439238848, 1.8330234769841731, 0.06939342386539255, -2.205995144214174], [-0.6935225909367065, -1.847275439238848, 1.8330234769841731, 0.06939342386539255, -2.205995144214174], [-1.0158757960518194, -0.993448504055429, 0.9688831561159174, -0.3359397310509096, -3.975835044341129], [-1.5825669708745254, -1.647734695239275, 2.1492785418928757, 0.3801744974483343, -4.094799240519998], [-1.2167615126664715, -1.2389099287562728, 1.8308815043759785, -0.32898634693729895, -4.075846620329423], [-1.311298547987431, -1.5502393010518951, 1.3779309910102469, 0.11943434814502119, -4.06110092867434], [-1.420272401116318, -1.2903093219144364, 1.8595588294776013, 0.21574703183897515, -3.6172264122871933], [-1.5239129456721443, -1.2372888053617774, 0.9891520655644306, -0.3372663516551437, -4.324623073380345], [-1.342035515460668, -1.571261438553059, 0.9871459802742953, -0.30988639475966884, -4.047600814994611], [-1.474143489109068, -1.328261170615093, 1.3015912931411477, -0.3930908173839305, -3.963789176262948], [-1.4719944854669265, -1.480352110700912, 1.700174660538471, -0.18282150295629354, -4.244873474061534], [-1.44374414704285, -1.4113054493624038, 1.2106023569845612, -0.446031433376445, -3.770307087913426], [-1.5105924926400245, -1.2805198973049392, 1.6863202046556771, 0.41902842225677434, -4.278624672472315], [-1.401604184639144, -1.4920527738797797, 2.3411512978228677, 0.22153659670008397, -3.7992005860805813], [-1.4103997559899881, -1.3518073738221401, 2.468115024637904, 0.22441998348310366, -3.6620153969622042], [-1.3478147579965283, -1.5662451925492673, 2.2737346030178656, 0.550523513520539, -4.00604357456145], [-1.2780001768799567, -1.3075286701280666, 2.2434498813475647, 0.5115066248829281, -4.066242293882331], [-1.4009322222315448, -1.4704293529572794, 2.0293585177745355, 0.2570037219429686, -4.06527205312171], [-1.3672273103346062, -1.5180881368891592, 2.0791364338302456, 0.505605872420674, -3.8969295403234816], [-1.553480311320186, -1.564075320771142, 2.1951823027127313, 0.2198122638231905, -3.9032098593063127], [-1.6586685721621373, -1.4555411558534725, 2.177379650198025, 0.22870268891513457, -4.077351532236575], [-1.3136761666586, -1.4901595494064952, 2.539638177676161, 0.4410488087762162, -4.036583694110641], [-1.3004193421507826, -1.433191531428675, 1.6876134381759496, 0.9816874524604666, -4.042449521807221], [-1.3796494774815466, -1.3625718550779082, 2.171470836701285, 0.7747911463995779, -4.08904305412548], [-1.4162878017940401, -1.4288290603324096, 1.7590264349013656, 1.0035960964917219, -4.027291190383203], [-1.4369172514187374, -1.2581640812692787, 2.0411385159105513, 0.7949866354208567, -4.020252796047762], [-1.5213360410452739, -1.3552284496434686, 1.8892283411020803, -0.3660448367639364, -3.9091363747123684], [-1.4489332730309679, -1.235702119236211, 1.3978581539153019, 0.03554351404212905, -4.137818111475697], [-1.1404224017825744, -1.4849179297794697, 1.0206599835854717, -0.012055927416771653, -3.8872952333137962], [-1.3672690697444843, -1.4056985980221637, 0.9459171156068771, -0.2025462744065057, -3.8467539111337405], [-1.327280688254811, -1.4782738211556259, 1.2615642783827026, -0.33781542531828435, -4.053716178966767], [-1.3079978833822639, -1.4561450751057998, 1.7148436129258495, -0.5212708476255364, -4.099144328526245], [-1.3886191984703251, -1.5110203436022007, 1.3239965397498996, 0.13241912274280698, -3.9175483118922587], [-1.480260528919093, -1.4752654614930554, 1.7482974515595027, -0.2863419487517231, -4.198587922399813], [-1.2709387081270147, -1.1554734275692577, 1.4071374595765305, 0.15115580730987366, -3.9759729725661574], [-1.2709387081270147, -1.1554734275692577, 1.4071374595765305, 0.15115580730987366, -3.9759729725661574], [-1.4272762372546022, -1.5384046408088357, 1.5913820561829581, -0.5496222979815613, -4.120845840937352], [-1.4823717213051235, -1.405395813490023, 1.631532864882927, -0.39418862312934133, -4.28504074466639], [-1.245675216782085, -1.3112463357489212, 1.451166048052336, 0.10597644957223248, -4.207023769564687], [-1.379168836790068, -1.4118308269276238, 1.320423454549608, -0.12785933146147185, -4.160824784886233], [-1.327013741562663, -1.5575752918156647, 2.1270307705484752, 0.5296614245372891, -3.9419219951437663], [-1.363664500941715, -1.533438252491385, 1.9307321016014856, 0.24573635173795472, -4.374703668103882], [-1.231484053495, -1.464188198285191, 1.2246260917531793, -0.8958951328451219, -3.779693833257456], [-1.1708531996988936, -1.482564315037219, 1.388317889346732, -0.8400192808480447, -3.8683435326907443], [-1.3852371563562706, -1.3887275746626362, 1.6378875257793426, -1.0302860961909635, -3.7897989343691774], [-1.3230961870128435, -1.3514213785901714, 1.5182352381823634, -1.0294935698238634, -4.065591013434624], [-1.3789207848418155, -1.216996081151263, 1.262536384346416, -0.5955429885261896, -3.947034443851977], [-1.3402931007411332, -1.3424794557276882, 0.6172568687887685, -0.26730431080532263, -4.397931822959701], [-1.2251441395097635, -1.400335723398406, 1.848876473068551, -0.22148870595777614, -3.6716924043639674], [-1.2139413700515713, -1.3382695087916272, 1.9442093211876343, -0.15622834865819346, -3.6721449206548247], [-1.6557543221722728, -1.6386196216501487, 2.1868243436043966, 0.44583911036593027, -4.228479432742524], [-1.2199631933900463, -1.1012895879267106, 1.8805163991861213, 0.6741375881160941, -3.85590766607892], [-1.19587146242678, -1.2537703069207051, 1.3961639823841419, 0.6700721273618189, -4.058207570239686], [-1.192298748292821, -1.114062165379844, 1.4963861733619293, 0.4462703909009599, -3.997584872455099], [-1.6274134458020562, -1.6816263870732084, 1.9638222861603518, -0.11382270168664854, -4.108396926897639], [-1.3022534574134441, -1.870564395011042, 1.9947253254610708, -0.07325290995610464, -4.165128027117223], [-0.9743319295259737, -1.2630629299388674, 1.6033548767230732, -0.41858281830315575, -3.925773480100138], [-1.7232067170354812, 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-0.40467977769078844, -3.878322607179071], [-1.340661879076979, -1.2631402677154335, 1.8379670726374737, -0.3470996038646714, -4.19806380505535], [-1.4449929571098192, -1.6965834343579107, 1.6208008935378468, 0.3143008642517264, -3.576638487582014], [-1.5044679489266588, -1.4444962071882257, 2.0253506923648086, -0.2539134626456967, -4.05719228403569], [-1.167738116198881, -1.4620537433214222, 1.6967571736163278, 0.43342073697522193, -3.7542505599663816], [-1.4733821891906895, -1.5063742500046944, 0.9156048772504106, -0.8325297477106339, -4.221412037008591], [-1.3225562691812462, -1.247962499255645, 0.9660271825876842, 0.4083754566345845, -3.905660331100335], [-1.5110161491620022, -1.522774603315705, 1.0340949063488722, 0.4284700497038583, -4.017679550876103], [-1.2066550227393065, -0.9010370614489771, 0.943225695919342, -0.5610612879464025, -4.121493242038668], [-1.3406702233362489, -1.6492996900702444, 0.5931547864714133, -0.20255749703011494, -3.9484635507443073], [-1.0911734073635362, -1.1057127767771546, 0.28121504436835326, -0.6250684206015752, -4.182447227006859], [-1.1910731574568278, -0.9818492294959615, 0.306134661288012, -0.6769205327775879, -4.139037912155024], [-1.2938520888300233, -1.3309988652954419, 1.7118362105430927, -0.1305435778751536, -3.620524183688628], [-1.3417286533778094, -1.233692867406513, 1.806992372396194, -0.04584253432137553, -4.1207330852584185], [-1.319713955440812, -1.1699520211234966, 0.6381741549718576, -0.7316737094084884, -4.012457599658821], [-1.347563060498028, -1.297930497994606, 0.30151490522642876, -0.4305996784729464, -3.838673139348691], [-1.2818172473396654, -1.122699842172121, 0.08176262787738431, -0.3940106592147651, -3.9461202875355808], [-1.5196392710135407, -1.506561674169807, 1.9731868782759925, -0.3408020921233706, -4.0991536213264], [-1.2417162629163092, -1.2505587345047466, 1.1664761791544629, -0.03576281577452997, -4.143950983655028], [-1.5046807923175405, -1.3256009215385103, 2.484105542575866, 0.40571038484008043, -4.355403423261662], [-1.3920021185549294, -1.5408920490812847, 2.4909520256246407, 0.4419736485339421, -4.057860292407926], [-1.372815422219755, -1.313185170061324, 1.2240885088100042, -0.17496143432556624, -4.234482033802265], [-1.4532470783134857, -1.5171050237226709, 1.3813212780058959, -0.5749913170348848, -3.960893733630716], [-1.4082526681498622, -1.4141978501629178, 1.5408758879263544, 0.15676418532977762, -4.244919069144677], [-1.4431591708057967, -1.3239755581311323, 1.2773877848231117, -0.5530673073593122, -3.9738604151172257], [-1.107020254053504, -1.0179842848337568, 1.5159360668803088, -0.49627984489513877, -4.147045214206338], [-1.3232072521616298, -1.16541075165481, 1.5795339844665992, 0.2203916614807249, -3.964515867500264]], NamedTuple[(n_steps = 1, is_accept = true, acceptance_rate = 0.0, log_density = -21.01569862851668, hamiltonian_energy = 21.5167610959162, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 162511.10795691406, 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 = -21.01569862851668, hamiltonian_energy = 23.978389712484166, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 4481.984881574327, tree_depth = 0, numerical_error = true, step_size = 1.8680518327273068, nom_step_size = 1.8680518327273068, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.400090045887174, log_density = 5.777585448968432, hamiltonian_energy = 23.827675955731138, hamiltonian_energy_error = -3.0396656459395075, max_hamiltonian_energy_error = 436.9814561344992, tree_depth = 3, numerical_error = false, step_size = 0.18418867766839725, nom_step_size = 0.18418867766839725, is_adapt = true), (n_steps = 39, is_accept = true, acceptance_rate = 0.9875993348300504, log_density = 7.430748710601767, hamiltonian_energy = -3.0143111364649124, hamiltonian_energy_error = -0.033777581662710165, max_hamiltonian_energy_error = 0.058619136518911485, tree_depth = 5, numerical_error = false, step_size = 0.03878562410228977, nom_step_size = 0.03878562410228977, is_adapt = true), (n_steps = 31, is_accept = true, acceptance_rate = 0.9999883162240645, log_density = 8.302642181911724, hamiltonian_energy = -6.265274642609502, hamiltonian_energy_error = 0.00036226266319872025, max_hamiltonian_energy_error = -0.014970217763900173, tree_depth = 5, numerical_error = false, step_size = 0.045112820745833344, nom_step_size = 0.045112820745833344, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9448787386624423, log_density = 8.105216331861747, hamiltonian_energy = -6.48243944097478, hamiltonian_energy_error = 0.0588269546271496, max_hamiltonian_energy_error = 0.11628363016567977, tree_depth = 4, numerical_error = false, step_size = 0.06537765013213985, nom_step_size = 0.06537765013213985, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9473534330567539, log_density = 6.205039948644949, hamiltonian_energy = -3.588657657966464, hamiltonian_energy_error = 0.09044062846197765, max_hamiltonian_energy_error = 0.17368431876286472, tree_depth = 4, numerical_error = false, step_size = 0.08948641909259604, nom_step_size = 0.08948641909259604, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9856926958093576, log_density = 6.766231068912219, hamiltonian_energy = -3.699858360125459, hamiltonian_energy_error = 0.11414143137831578, max_hamiltonian_energy_error = -0.5460935355484691, tree_depth = 3, numerical_error = false, step_size = 0.131396585453789, nom_step_size = 0.131396585453789, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 0.3347074703754335, log_density = 8.174329616935815, hamiltonian_energy = -7.082829678389732, hamiltonian_energy_error = -0.7160276340609508, max_hamiltonian_energy_error = 31.724053412131827, tree_depth = 2, numerical_error = false, step_size = 0.22636067270591428, nom_step_size = 0.22636067270591428, is_adapt = true), (n_steps = 23, is_accept = true, acceptance_rate = 0.9999958202258066, log_density = 8.779318321086091, hamiltonian_energy = -7.911779119735971, hamiltonian_energy_error = -0.004143932271062134, max_hamiltonian_energy_error = -0.04497375320772257, tree_depth = 4, numerical_error = false, step_size = 0.051190005049957535, nom_step_size = 0.051190005049957535, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.938042390682451, log_density = 9.172169273768596, hamiltonian_energy = -7.102513982651116, hamiltonian_energy_error = -0.1379210963389994, max_hamiltonian_energy_error = 0.16057483487380342, tree_depth = 3, numerical_error = false, step_size = 0.09567674740243942, nom_step_size = 0.09567674740243942, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.7828871380191504, log_density = 8.123747841543317, hamiltonian_energy = -7.143612771521746, hamiltonian_energy_error = 0.26760588504654503, max_hamiltonian_energy_error = 0.4850684017585589, tree_depth = 3, numerical_error = false, step_size = 0.14871469803983398, nom_step_size = 0.14871469803983398, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9243208858719478, log_density = 7.206731525229122, hamiltonian_energy = -5.620613447527576, hamiltonian_energy_error = 0.20145555966447937, max_hamiltonian_energy_error = 0.20145555966447937, tree_depth = 3, numerical_error = false, step_size = 0.14261271419886892, nom_step_size = 0.14261271419886892, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.518545379833154, log_density = 7.201292183056669, hamiltonian_energy = -6.9879943722587345, hamiltonian_energy_error = -0.7411873482524873, max_hamiltonian_energy_error = 3.94907393128345, tree_depth = 3, numerical_error = false, step_size = 0.21437209919384223, nom_step_size = 0.21437209919384223, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9025734832475791, log_density = 5.320091642832564, hamiltonian_energy = -3.147214998462532, hamiltonian_energy_error = 0.1280425095834694, max_hamiltonian_energy_error = 0.21652183944986225, tree_depth = 3, numerical_error = false, step_size = 0.09092155445170669, nom_step_size = 0.09092155445170669, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 7.36249718889791, hamiltonian_energy = -4.771863241898782, hamiltonian_energy_error = -0.14038792192689975, max_hamiltonian_energy_error = -0.3576321842198844, tree_depth = 4, numerical_error = false, step_size = 0.12851438143189262, nom_step_size = 0.12851438143189262, is_adapt = true), (n_steps = 3, is_accept = true, acceptance_rate = 0.3535137624072553, log_density = 7.8211777398602855, hamiltonian_energy = -7.146734560877945, hamiltonian_energy_error = -0.41557005684523585, max_hamiltonian_energy_error = 3.924751124449079, tree_depth = 2, numerical_error = false, step_size = 0.24470254793861426, nom_step_size = 0.24470254793861426, is_adapt = true), (n_steps = 15, is_accept = true, acceptance_rate = 0.9545184742835829, log_density = 8.932630639316656, hamiltonian_energy = -6.534000760110265, hamiltonian_energy_error = 0.009269178233421549, max_hamiltonian_energy_error = 0.09848840384082802, tree_depth = 4, numerical_error = false, step_size = 0.06421347483308897, nom_step_size = 0.06421347483308897, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.8732030490993715, log_density = 7.988607076237788, hamiltonian_energy = -7.307272304723751, hamiltonian_energy_error = 0.059255462166052375, max_hamiltonian_energy_error = 0.19453209838661234, tree_depth = 3, numerical_error = false, step_size = 0.10647475215901481, nom_step_size = 0.10647475215901481, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.9247515438408584, log_density = 7.639708998664652, hamiltonian_energy = -6.133287485035327, hamiltonian_energy_error = 0.07624959920796659, max_hamiltonian_energy_error = 0.1794766531103198, tree_depth = 3, numerical_error = false, step_size = 0.13736340823761264, nom_step_size = 0.13736340823761264, is_adapt = true), (n_steps = 7, is_accept = true, acceptance_rate = 0.8833977175214294, log_density = 7.135776637229165, hamiltonian_energy = -5.882212151642232, hamiltonian_energy_error = 0.16371967064994486, max_hamiltonian_energy_error = 0.3311369231120347, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9497312950271013, log_density = 6.809218638428543, hamiltonian_energy = -5.348966374414931, hamiltonian_energy_error = -0.1768990243812807, max_hamiltonian_energy_error = -0.316111933155252, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9863432465606988, log_density = 6.259283614448105, hamiltonian_energy = -5.260094631708194, hamiltonian_energy_error = -0.02411774650734788, max_hamiltonian_energy_error = -0.13328208760540416, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9587488047963433, log_density = 7.689947594405453, hamiltonian_energy = -5.573579923364681, hamiltonian_energy_error = -0.1562127440085881, max_hamiltonian_energy_error = -0.1855003366629564, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9672018759217031, log_density = 6.63045539603641, hamiltonian_energy = -5.7207479096152, hamiltonian_energy_error = 0.033170545433710785, max_hamiltonian_energy_error = 0.07651017878125099, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7715996003666105, log_density = 6.955953056896302, hamiltonian_energy = -5.179682573638437, hamiltonian_energy_error = 0.1913884834706039, max_hamiltonian_energy_error = 0.4358935149640173, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9394012889044434, log_density = 7.701197840591494, hamiltonian_energy = -5.133980613124999, hamiltonian_energy_error = 0.1024793467195515, max_hamiltonian_energy_error = 0.31632427382517214, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9995716886974447, log_density = 8.350011011617546, hamiltonian_energy = -6.906628828228174, hamiltonian_energy_error = -0.08472900582524989, max_hamiltonian_energy_error = -0.3579859356483084, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7665715560962787, log_density = 6.157047271348471, hamiltonian_energy = -5.070668276479768, hamiltonian_energy_error = 0.46476478891462847, max_hamiltonian_energy_error = 0.6211916801690691, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9584576625674985, log_density = 8.310152813265468, hamiltonian_energy = -5.236990407331322, hamiltonian_energy_error = -0.5813736762172352, max_hamiltonian_energy_error = -0.6990771332738053, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8950865131537462, log_density = 9.148744920689143, hamiltonian_energy = -4.0050977102634695, hamiltonian_energy_error = 0.0518774684691623, max_hamiltonian_energy_error = 0.3408554301273612, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9764445738960331, log_density = 8.53566403423395, hamiltonian_energy = -7.60656906230873, hamiltonian_energy_error = 0.0595047550994261, max_hamiltonian_energy_error = -0.07950691651662911, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9889234340953439, log_density = 8.49048630309014, hamiltonian_energy = -7.831016156885406, hamiltonian_energy_error = -0.07655946433055494, max_hamiltonian_energy_error = -0.1515180193556107, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9557366730787479, log_density = 9.180945260828988, hamiltonian_energy = -7.380554020528836, hamiltonian_energy_error = -0.07338349075062833, max_hamiltonian_energy_error = 0.10566320619713654, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9242300314924977, log_density = 8.242369955646419, hamiltonian_energy = -7.479259305156844, hamiltonian_energy_error = 0.08423079703408032, max_hamiltonian_energy_error = 0.13882301926659935, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.4374091433039751, log_density = 8.242369955646419, hamiltonian_energy = -4.157363250284888, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 2.2356628048222054, tree_depth = 1, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9832107581179114, log_density = 8.854892915213156, hamiltonian_energy = -7.5041656544706, hamiltonian_energy_error = -0.05578102209247504, max_hamiltonian_energy_error = -0.0749487157932558, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9338658123012537, log_density = 8.785736699847252, hamiltonian_energy = -6.947938018811039, hamiltonian_energy_error = -0.003978618489740349, max_hamiltonian_energy_error = 0.15135765819940605, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8614705603373183, log_density = 8.284007726928433, hamiltonian_energy = -6.389435400186005, hamiltonian_energy_error = 0.20170600039186493, max_hamiltonian_energy_error = 0.2660831490430846, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9658872984664434, log_density = 9.331062298163529, hamiltonian_energy = -7.544868762779713, hamiltonian_energy_error = -0.23908167910024236, max_hamiltonian_energy_error = -0.23908167910024236, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8627927702654336, log_density = 7.5729407589998985, hamiltonian_energy = -5.986392676578859, hamiltonian_energy_error = 0.22189296774763534, max_hamiltonian_energy_error = 0.2906445305479277, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9136576681839124, log_density = 7.003824922187228, hamiltonian_energy = -5.479199569434973, hamiltonian_energy_error = 0.18194052442871467, max_hamiltonian_energy_error = -0.3581990521789624, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9882120051982916, log_density = 6.140654845416979, hamiltonian_energy = -3.943535772324909, hamiltonian_energy_error = -0.26092985849801487, max_hamiltonian_energy_error = -0.591424510088419, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9371503161113832, log_density = 5.995532722133877, hamiltonian_energy = -4.431644544270028, hamiltonian_energy_error = 0.2517862381150069, max_hamiltonian_energy_error = -0.3082322692780419, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8666722102622585, log_density = 4.501316240911619, hamiltonian_energy = -1.5896471729072488, hamiltonian_energy_error = -0.11489948439993558, max_hamiltonian_energy_error = 0.5107979061721677, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9663709013285428, log_density = 5.9925014484030985, hamiltonian_energy = -3.065370497954019, hamiltonian_energy_error = -0.19454055103848544, max_hamiltonian_energy_error = -0.23014920538436234, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9262904987828161, log_density = 8.289895770266131, hamiltonian_energy = -5.0308106121655385, hamiltonian_energy_error = 0.020708009592175003, max_hamiltonian_energy_error = 0.22393565558749629, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9795193889422765, log_density = 6.254369166496918, hamiltonian_energy = -4.7732816801358, hamiltonian_energy_error = -0.07866760099970005, max_hamiltonian_energy_error = -0.08561806176956033, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.999006923870133, log_density = 7.290102843911281, hamiltonian_energy = -4.770198142234632, hamiltonian_energy_error = -0.0401645862926463, max_hamiltonian_energy_error = -0.20656074215743647, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 1.0, log_density = 7.05008585196944, hamiltonian_energy = -6.469556771451769, hamiltonian_energy_error = -0.0014413360107452533, max_hamiltonian_energy_error = -0.19887550602374304, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9847890115465593, log_density = 6.617947743486422, hamiltonian_energy = -4.032648862195883, hamiltonian_energy_error = -0.028626258554982797, max_hamiltonian_energy_error = -0.21905977768112628, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 6.368360756572972, hamiltonian_energy = -5.935234820717863, hamiltonian_energy_error = -0.026019949126878217, max_hamiltonian_energy_error = -0.1918152811725644, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7891338084138582, log_density = 6.339343931487408, hamiltonian_energy = -3.126276485429255, hamiltonian_energy_error = 0.010077566830368756, max_hamiltonian_energy_error = 0.5271340483897089, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9585111660127309, log_density = 7.151380918494137, hamiltonian_energy = -5.181591678913206, hamiltonian_energy_error = -0.13110087026049566, max_hamiltonian_energy_error = -0.23152692075522108, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9663857961493669, log_density = 7.539023109440592, hamiltonian_energy = -5.004889666007552, hamiltonian_energy_error = -0.028888657771910076, max_hamiltonian_energy_error = -0.17927418497248748, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.4390502214321484, log_density = 2.5034802731881456, hamiltonian_energy = -1.3864292608867397, hamiltonian_energy_error = 1.4181381203726973, max_hamiltonian_energy_error = 1.4181381203726973, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 4.658387930438854, hamiltonian_energy = 1.7931962312022325, hamiltonian_energy_error = -1.163673587713399, max_hamiltonian_energy_error = -2.0577441570607418, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 6.59547882357538, hamiltonian_energy = -3.0620887849944705, hamiltonian_energy_error = -0.3598605966883084, max_hamiltonian_energy_error = -1.3268436487318191, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9606146658866103, log_density = 7.744342899154903, hamiltonian_energy = -4.7392185773924105, hamiltonian_energy_error = -0.1435642731775797, max_hamiltonian_energy_error = -0.5114585039096156, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 23, is_accept = true, acceptance_rate = 0.9876643001666505, log_density = 6.919563407620956, hamiltonian_energy = -6.3974294683664965, hamiltonian_energy_error = 0.11229630053721529, max_hamiltonian_energy_error = -0.4850012990668491, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9993548999034523, log_density = 6.017560871494096, hamiltonian_energy = -4.535015555844283, hamiltonian_energy_error = -0.18559450510304298, max_hamiltonian_energy_error = -0.612220689358244, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.994968466876896, log_density = 4.564283144553631, hamiltonian_energy = -2.6278228996785327, hamiltonian_energy_error = -0.11117384452553258, max_hamiltonian_energy_error = -0.4065267547614333, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.5773363966764942, log_density = 4.438144966288441, hamiltonian_energy = 1.1552243508802658, hamiltonian_energy_error = 0.9308150994249189, max_hamiltonian_energy_error = 1.0862291687261536, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9030971393444523, log_density = 8.553109793127938, hamiltonian_energy = -3.5850129289226453, hamiltonian_energy_error = -1.313740997962432, max_hamiltonian_energy_error = -1.313740997962432, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7093661865941565, log_density = 7.696313531885464, hamiltonian_energy = -5.671283675203225, hamiltonian_energy_error = 0.24738758724644772, max_hamiltonian_energy_error = 0.6093807022396192, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9961758292543373, log_density = 7.561901726799931, hamiltonian_energy = -6.24331769728952, hamiltonian_energy_error = -0.15633883779088542, max_hamiltonian_energy_error = -0.27996678223112603, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9620018926367173, log_density = 6.578817321774508, hamiltonian_energy = -5.427792115527302, hamiltonian_energy_error = 0.11363328436341646, max_hamiltonian_energy_error = 0.13090524200379772, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9332512553237832, log_density = 7.060291939917054, hamiltonian_energy = -5.292977350090648, hamiltonian_energy_error = -0.1943066723818605, max_hamiltonian_energy_error = -0.1943066723818605, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8688781846451464, log_density = 8.366142809055933, hamiltonian_energy = -4.202402622052769, hamiltonian_energy_error = -0.003774033044727787, max_hamiltonian_energy_error = 0.29834383870722103, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.910877144636428, log_density = 6.681150136765755, hamiltonian_energy = -6.3731763298845046, hamiltonian_energy_error = 0.19747066218552156, max_hamiltonian_energy_error = 0.19747066218552156, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9636605563683306, log_density = 7.443064780691666, hamiltonian_energy = -5.329586760433063, hamiltonian_energy_error = -0.07267545624631033, max_hamiltonian_energy_error = -0.34387279705571494, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.3539330833265237, log_density = 3.065199635326131, hamiltonian_energy = 0.890217309688127, hamiltonian_energy_error = 1.8143730163201064, max_hamiltonian_energy_error = 1.9198851537826798, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9577550614881819, log_density = -2.6625211348611906, hamiltonian_energy = 5.27312561632517, hamiltonian_energy_error = 0.13551600699570532, max_hamiltonian_energy_error = -1.703058246572967, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 7.657311766077571, hamiltonian_energy = 4.305652282703711, hamiltonian_energy_error = -1.7915269208578817, max_hamiltonian_energy_error = -1.7915269208578817, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 19, is_accept = true, acceptance_rate = 0.7643642695248781, log_density = 7.176657610223547, hamiltonian_energy = -4.737319906273566, hamiltonian_energy_error = 0.2887655183778577, max_hamiltonian_energy_error = 0.4952770085647664, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 8.341334500401725, hamiltonian_energy = -6.8645203519831455, hamiltonian_energy_error = -0.03775623916275883, max_hamiltonian_energy_error = -0.25901001671010704, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9646011341777679, log_density = 7.123688558963581, hamiltonian_energy = -4.326470542709779, hamiltonian_energy_error = 0.0829482903629426, max_hamiltonian_energy_error = -0.22118121712471694, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9888688790690882, log_density = 9.102317132996719, hamiltonian_energy = -5.916727991639404, hamiltonian_energy_error = -0.2310753819328637, max_hamiltonian_energy_error = -0.2310753819328637, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8806626751601007, log_density = 5.839537793189404, hamiltonian_energy = -5.067623374747867, hamiltonian_energy_error = 0.08466330335079864, max_hamiltonian_energy_error = 0.2069932910457446, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8341188128571524, log_density = 4.664372490529022, hamiltonian_energy = -3.47041997286086, hamiltonian_energy_error = 0.13793554692476473, max_hamiltonian_energy_error = 0.3359129018979803, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 6.059821811918075, hamiltonian_energy = -4.31688560654331, hamiltonian_energy_error = -0.09205654775223149, max_hamiltonian_energy_error = -0.18242995245536786, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.645897257740569, log_density = 2.945080792682125, hamiltonian_energy = -1.3981104784768745, hamiltonian_energy_error = 0.4844838492008754, max_hamiltonian_energy_error = 0.4844838492008754, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8891562434801037, log_density = 8.208659957342476, hamiltonian_energy = 0.2164270633701637, hamiltonian_energy_error = 0.016855244321213547, max_hamiltonian_energy_error = 0.6960622698618106, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9320170285805425, log_density = 7.999004346847958, hamiltonian_energy = -4.90521671177164, hamiltonian_energy_error = -0.10056389582976166, max_hamiltonian_energy_error = 0.30197139207428947, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9757395296713606, log_density = 8.346580174623307, hamiltonian_energy = -6.355370644815695, hamiltonian_energy_error = -0.06337546434801844, max_hamiltonian_energy_error = -0.15938102961851008, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6509757538036145, log_density = 7.008495413533932, hamiltonian_energy = -3.804421477259151, hamiltonian_energy_error = 0.3556463290725862, max_hamiltonian_energy_error = 0.96207387089511, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.935424172665949, log_density = 8.0039759466371, hamiltonian_energy = -3.976115447849261, hamiltonian_energy_error = -0.030276968059493647, max_hamiltonian_energy_error = 0.1548444121574435, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9655383437933663, log_density = 7.57044307354502, hamiltonian_energy = -5.617569019960694, hamiltonian_energy_error = 0.00016889993997626362, max_hamiltonian_energy_error = 0.13425150812537456, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8675114302148109, log_density = 7.047187725924058, hamiltonian_energy = -4.796300464148448, hamiltonian_energy_error = -0.00444556165000165, max_hamiltonian_energy_error = 0.7540906603864128, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9861403313317398, log_density = 6.619036225362315, hamiltonian_energy = -5.858169507569535, hamiltonian_energy_error = 0.019161307289004448, max_hamiltonian_energy_error = -0.34688186401999843, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9738781096847816, log_density = 7.1288043546465865, hamiltonian_energy = -1.8382131615468564, hamiltonian_energy_error = -0.11272605819108783, max_hamiltonian_energy_error = -0.4226309284450016, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9812455664079965, log_density = 7.493503671025632, hamiltonian_energy = -4.597713406596386, hamiltonian_energy_error = -0.08227909841726166, max_hamiltonian_energy_error = -0.24152625963035135, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.833520705010075, log_density = 5.076820650088116, hamiltonian_energy = -4.020918813090162, hamiltonian_energy_error = 0.38581455328932, max_hamiltonian_energy_error = 0.38581455328932, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9685885001898156, log_density = 5.49726382843814, hamiltonian_energy = -3.622471856014074, hamiltonian_energy_error = -0.2740423129314462, max_hamiltonian_energy_error = -0.41725185210993576, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8123312414502689, log_density = 6.519337403640058, hamiltonian_energy = -1.2838770182227446, hamiltonian_energy_error = -0.020825507839261626, max_hamiltonian_energy_error = 0.6198162426732297, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9163038773562274, log_density = 9.479041093104756, hamiltonian_energy = -5.091151107007613, hamiltonian_energy_error = -0.1944260855347535, max_hamiltonian_energy_error = 0.27284196954161377, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9768786686303518, log_density = 8.836586015498565, hamiltonian_energy = -8.727235078994699, hamiltonian_energy_error = 0.05675270251363074, max_hamiltonian_energy_error = 0.06657584717517295, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9139856897495509, log_density = 8.21580881829553, hamiltonian_energy = -6.871560265632738, hamiltonian_energy_error = 0.07230828696090974, max_hamiltonian_energy_error = 0.15965426698371576, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9450826049412756, log_density = 8.70589314739271, hamiltonian_energy = -7.431617319379545, hamiltonian_energy_error = -0.21810293347671017, max_hamiltonian_energy_error = -0.24568777334576541, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9553802975746533, log_density = 8.238862606276264, hamiltonian_energy = -6.799162333432822, hamiltonian_energy_error = 0.08311292859175978, max_hamiltonian_energy_error = 0.12267148715164033, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9915894626572559, log_density = 8.693265458413759, hamiltonian_energy = -7.852498751864434, hamiltonian_energy_error = -0.0449143482609724, max_hamiltonian_energy_error = -0.05226985751215896, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7641381195073826, log_density = 7.383811531122246, hamiltonian_energy = -5.0260920863648995, hamiltonian_energy_error = 0.39337199395623035, max_hamiltonian_energy_error = 0.4585895048470787, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9950025773013181, log_density = 8.84137154832531, hamiltonian_energy = -6.899235981876194, hamiltonian_energy_error = -0.37606344180186824, max_hamiltonian_energy_error = -0.3807859890302687, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7675540304620458, log_density = 4.783858996751638, hamiltonian_energy = -1.3981916926286582, hamiltonian_energy_error = 0.14351785999283528, max_hamiltonian_energy_error = 0.6188178280135435, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9564082096002243, log_density = 5.214462749093922, hamiltonian_energy = -3.627016481783374, hamiltonian_energy_error = -0.07120327746727684, max_hamiltonian_energy_error = 0.1401536959798091, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9890937540960492, log_density = 7.70611775514301, hamiltonian_energy = -4.724918123520893, hamiltonian_energy_error = -0.09222240552930394, max_hamiltonian_energy_error = -0.09222240552930394, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.5877862851424076, log_density = 1.6938210466008314, hamiltonian_energy = -0.06467052855645172, hamiltonian_energy_error = 0.9728362427389265, max_hamiltonian_energy_error = 1.053971940585714, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9910248922011268, log_density = 2.2907494523202505, hamiltonian_energy = -0.9183164755043747, hamiltonian_energy_error = -0.20311283825243165, max_hamiltonian_energy_error = -0.9765945503657045, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8979246436269068, log_density = 1.5280848100659732, hamiltonian_energy = 1.557138764437625, hamiltonian_energy_error = -0.17247610893279175, max_hamiltonian_energy_error = -0.6280127967620261, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8855690187343284, log_density = 4.588379814823538, hamiltonian_energy = 1.312929412392859, hamiltonian_energy_error = 0.012233422425356189, max_hamiltonian_energy_error = -0.5320536802016491, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9987542063049395, log_density = 7.743540076513531, hamiltonian_energy = -3.9809459147205772, hamiltonian_energy_error = -0.26206061998548114, max_hamiltonian_energy_error = -0.46732852945678616, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7042191343829189, log_density = 8.264773568123164, hamiltonian_energy = -4.3508684007459255, hamiltonian_energy_error = 0.021127633122157263, max_hamiltonian_energy_error = 0.7228427708313463, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9584334287449526, log_density = 6.873345545815612, hamiltonian_energy = -5.624743564916947, hamiltonian_energy_error = -0.02868055180930451, max_hamiltonian_energy_error = 0.1942672457151362, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 7.64183763149985, hamiltonian_energy = -5.911673524444824, hamiltonian_energy_error = -0.10582562393687489, max_hamiltonian_energy_error = -0.18657948624010867, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9230714011397895, log_density = 5.359466140703653, hamiltonian_energy = -4.99703712957662, hamiltonian_energy_error = 0.14441577054899124, max_hamiltonian_energy_error = 0.14441577054899124, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9942208214203164, log_density = 5.015286014220296, hamiltonian_energy = -2.4817878791467836, hamiltonian_energy_error = -0.05167587695166853, max_hamiltonian_energy_error = -0.27832731345054595, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.993026004059011, log_density = 6.898189869636457, hamiltonian_energy = -4.849134955836182, hamiltonian_energy_error = -0.2033438712457052, max_hamiltonian_energy_error = -0.2033438712457052, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7934649803946753, log_density = 5.467775977946603, hamiltonian_energy = -4.659980146388591, hamiltonian_energy_error = 0.2804070619017942, max_hamiltonian_energy_error = 0.36980255830725817, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 6.091512203579622, hamiltonian_energy = -5.225780686360149, hamiltonian_energy_error = -0.07751668035453907, max_hamiltonian_energy_error = -0.23458845902016368, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8018673849441674, log_density = 3.4323444587277994, hamiltonian_energy = -1.9128260059485476, hamiltonian_energy_error = 0.24535418384272423, max_hamiltonian_energy_error = 0.49139981343849826, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9293163413273905, log_density = 5.180265918008146, hamiltonian_energy = -1.6153252237762317, hamiltonian_energy_error = -0.33380409357578555, max_hamiltonian_energy_error = -0.5698063625386012, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9250078250404117, log_density = 6.677127959918064, hamiltonian_energy = -2.677948937817725, hamiltonian_energy_error = -0.11065814127513196, max_hamiltonian_energy_error = 0.20484231070771308, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9178884224664913, log_density = 7.167323345454783, hamiltonian_energy = -5.526620387625666, hamiltonian_energy_error = -0.07293325208281765, max_hamiltonian_energy_error = 0.14425338790955244, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9159361431296832, log_density = 7.030674110451757, hamiltonian_energy = -5.779304512985573, hamiltonian_energy_error = 0.0286371242838106, max_hamiltonian_energy_error = 0.11786749605175206, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.5664163350631782, log_density = 7.211521221090129, hamiltonian_energy = -2.7724535790896203, hamiltonian_energy_error = -0.06966414749160332, max_hamiltonian_energy_error = 1.259417293471123, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 7.668338939311997, hamiltonian_energy = -6.36379746575364, hamiltonian_energy_error = -0.14572890375912095, max_hamiltonian_energy_error = -0.2608388899966041, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8058672701255097, log_density = 6.85658855015879, hamiltonian_energy = -6.599120934069813, hamiltonian_energy_error = 0.27108135718095117, max_hamiltonian_energy_error = 0.3135756380670651, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9030727069051256, log_density = 6.391190417856226, hamiltonian_energy = -5.767374047551509, hamiltonian_energy_error = 0.23790233091994129, max_hamiltonian_energy_error = -0.4335787392604562, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.665215409758024, log_density = 7.62383626292749, hamiltonian_energy = -4.375491625454629, hamiltonian_energy_error = -0.0025517363009299743, max_hamiltonian_energy_error = 0.800136343794787, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9540082545997942, log_density = 8.897384776923685, hamiltonian_energy = -6.306458784104115, hamiltonian_energy_error = -0.2136913035735981, max_hamiltonian_energy_error = -0.4274402264438457, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9648476014897547, log_density = 8.415208570843678, hamiltonian_energy = -7.294483426759906, hamiltonian_energy_error = -0.0643807947683408, max_hamiltonian_energy_error = 0.09539014281962377, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7287246751121185, log_density = 8.826869094118324, hamiltonian_energy = -6.441343659148377, hamiltonian_energy_error = 0.1321311660775324, max_hamiltonian_energy_error = 0.553975228660172, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9752171845170649, log_density = 8.765539290295441, hamiltonian_energy = -8.183075441832809, hamiltonian_energy_error = -0.057593579608338885, max_hamiltonian_energy_error = 0.07725740721292595, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9701273871126754, log_density = 8.566581834443564, hamiltonian_energy = -8.093792289055573, hamiltonian_energy_error = 0.04724038900311456, max_hamiltonian_energy_error = 0.04724038900311456, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9092203298988171, log_density = 6.861947990513093, hamiltonian_energy = -5.9837287177707355, hamiltonian_energy_error = 0.17350311468999813, max_hamiltonian_energy_error = 0.19943945065416369, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9573736190783977, log_density = 6.65495421872828, hamiltonian_energy = -5.867537261397822, hamiltonian_energy_error = 0.04152631794203554, max_hamiltonian_energy_error = -0.33349624718854187, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9233082470803389, log_density = 8.566637537054337, hamiltonian_energy = -6.060737540161058, hamiltonian_energy_error = -0.2461839986105243, max_hamiltonian_energy_error = -0.5927331768781929, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9311490637822438, log_density = 7.8776203548991575, hamiltonian_energy = -5.040779456649295, hamiltonian_energy_error = 0.07151800648730422, max_hamiltonian_energy_error = 0.13926656242014435, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9451738826831323, log_density = 8.827722331508125, hamiltonian_energy = -5.590858055059508, hamiltonian_energy_error = -0.05430772002289874, max_hamiltonian_energy_error = 0.2528130811197906, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8782044250726062, log_density = 5.382510578042453, hamiltonian_energy = -3.794436502939414, hamiltonian_energy_error = 0.2821954438896901, max_hamiltonian_energy_error = 0.3912027591132068, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9006240858633351, log_density = 8.049652050011291, hamiltonian_energy = -3.119227180683386, hamiltonian_energy_error = -0.4879700220551326, max_hamiltonian_energy_error = -0.5582741623327871, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.893015728991921, log_density = 8.238733894701719, hamiltonian_energy = -6.648137143975675, hamiltonian_energy_error = 0.015112353580822635, max_hamiltonian_energy_error = 0.3931354655801753, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9067176052434389, log_density = 4.944828105533212, hamiltonian_energy = -2.3049512151835883, hamiltonian_energy_error = 0.11934394804176929, max_hamiltonian_energy_error = 0.4990166584419875, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9865618786840338, log_density = 7.856766636567951, hamiltonian_energy = -2.9850184183125767, hamiltonian_energy_error = -0.18262206128150593, max_hamiltonian_energy_error = -0.30745193603081544, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8694969129871821, log_density = 5.552939033275706, hamiltonian_energy = -3.832296603809194, hamiltonian_energy_error = -0.12724190093376908, max_hamiltonian_energy_error = 0.4382786502418332, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9681402276338843, log_density = 7.146941055466041, hamiltonian_energy = -2.446919489828158, hamiltonian_energy_error = -0.23963296885933394, max_hamiltonian_energy_error = -0.311937814929395, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8727015997210975, log_density = 7.576602113227349, hamiltonian_energy = -3.6585596417465807, hamiltonian_energy_error = 0.08117875314568224, max_hamiltonian_energy_error = 0.20159656813835358, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9736556328732829, log_density = 6.042214952532312, hamiltonian_energy = -5.646870472213311, hamiltonian_energy_error = 0.1342522542880813, max_hamiltonian_energy_error = -0.19716852602182833, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.979300338527375, log_density = 8.537857670841065, hamiltonian_energy = -5.290758478830271, hamiltonian_energy_error = -0.26756328066032875, max_hamiltonian_energy_error = -0.26756328066032875, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9767335519720154, log_density = 8.410631507928937, hamiltonian_energy = -6.8641595983500245, hamiltonian_energy_error = 0.006686111937418637, max_hamiltonian_energy_error = 0.08527929235778497, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9248273229794133, log_density = 8.632711283053208, hamiltonian_energy = -4.90560655073179, hamiltonian_energy_error = 0.02329520605294455, max_hamiltonian_energy_error = 0.19056313835966332, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7707275468103354, log_density = 9.096814238010879, hamiltonian_energy = -6.109810885471484, hamiltonian_energy_error = 0.007836065355999011, max_hamiltonian_energy_error = 0.48737292271594423, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.94229434207413, log_density = 7.6244309873331435, hamiltonian_energy = -6.55602133200243, hamiltonian_energy_error = -0.006973916962159876, max_hamiltonian_energy_error = 0.16120255759515967, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.5662227809533228, log_density = 6.104719500859661, hamiltonian_energy = -4.265058731870455, hamiltonian_energy_error = 0.9457033878282015, max_hamiltonian_energy_error = 0.9457033878282015, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 8.841429443392201, hamiltonian_energy = -5.6770465945422135, hamiltonian_energy_error = -0.3531466362087272, max_hamiltonian_energy_error = -0.6518164888875866, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9921909404556793, log_density = 9.336874401511446, hamiltonian_energy = -8.492914821024332, hamiltonian_energy_error = -0.14860754319653502, max_hamiltonian_energy_error = -0.17175495632917936, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7251992042362264, log_density = 8.06432572626446, hamiltonian_energy = -6.883947245615925, hamiltonian_energy_error = 0.46238300548852873, max_hamiltonian_energy_error = 0.6472210049167044, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9566447489748064, log_density = 9.285486272759535, hamiltonian_energy = -7.46498015224165, hamiltonian_energy_error = -0.4019946270055481, max_hamiltonian_energy_error = -0.4808559158462531, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8923779950878326, log_density = 7.800929873409373, hamiltonian_energy = -6.101108094907875, hamiltonian_energy_error = 0.12547796438060121, max_hamiltonian_energy_error = 0.1743918183744979, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.5398201561160756, log_density = 4.408858669274135, hamiltonian_energy = 1.796924967054597, hamiltonian_energy_error = -1.1251563080987008, max_hamiltonian_energy_error = 2.430364433271757, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.6720566836208574, log_density = 8.952872344709107, hamiltonian_energy = -3.5130569425313345, hamiltonian_energy_error = -0.2214210030027779, max_hamiltonian_energy_error = 0.843126853757417, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9871311672771589, log_density = 9.291878756602312, hamiltonian_energy = -8.390721886632653, hamiltonian_energy_error = -0.015476805347979905, max_hamiltonian_energy_error = -0.0596850564803848, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9604239773160982, log_density = 8.176419990781547, hamiltonian_energy = -7.743545591523536, hamiltonian_energy_error = 0.10139411056582226, max_hamiltonian_energy_error = 0.10139411056582226, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9806895305645001, log_density = 7.750955931604082, hamiltonian_energy = -6.7328371961505, hamiltonian_energy_error = -0.013936799129785626, max_hamiltonian_energy_error = 0.07784697819049846, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9794947676922109, log_density = 9.026948143161604, hamiltonian_energy = -6.295544192524449, hamiltonian_energy_error = -0.0686008843675765, max_hamiltonian_energy_error = 0.09308981617872902, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9937359777236843, log_density = 9.389140997314417, hamiltonian_energy = -7.428673529950859, hamiltonian_energy_error = -0.03265670446870139, max_hamiltonian_energy_error = 0.047561539059884694, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.644416311800287, log_density = 8.696495237525895, hamiltonian_energy = -7.140191304822017, hamiltonian_energy_error = 0.37932489320568674, max_hamiltonian_energy_error = 0.916549829760168, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9948528921054418, log_density = 8.707596547629887, hamiltonian_energy = -7.786351895097773, hamiltonian_energy_error = -0.030482832606273824, max_hamiltonian_energy_error = -0.2601774450374723, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6475067098038058, log_density = 7.821617042160867, hamiltonian_energy = -5.449723724186853, hamiltonian_energy_error = -0.02577931706066927, max_hamiltonian_energy_error = 0.7964454217310859, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7316421064365645, log_density = 8.167946106914844, hamiltonian_energy = -6.057274062233412, hamiltonian_energy_error = 0.1438215481630598, max_hamiltonian_energy_error = 0.6236065812815319, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9203727007346115, log_density = 8.189710983552192, hamiltonian_energy = -7.555830553505578, hamiltonian_energy_error = 0.12668634820545854, max_hamiltonian_energy_error = 0.1277104897612258, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9804481296708231, log_density = 9.125637733884272, hamiltonian_energy = -7.110511730459586, hamiltonian_energy_error = -0.4036391438231197, max_hamiltonian_energy_error = -0.4036391438231197, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9160633036429341, log_density = 8.151758744775101, hamiltonian_energy = -6.503493280565892, hamiltonian_energy_error = 0.05147973837519526, max_hamiltonian_energy_error = 0.18352501534780163, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9697044513678038, log_density = 8.285936895573075, hamiltonian_energy = -6.759765870011912, hamiltonian_energy_error = -0.023984225398096193, max_hamiltonian_energy_error = 0.0937164504910184, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7448737255127149, log_density = 6.276574675994372, hamiltonian_energy = -5.500634317600821, hamiltonian_energy_error = 0.5591296406097408, max_hamiltonian_energy_error = 0.6997068514648976, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8911239477596975, log_density = 6.71821919347472, hamiltonian_energy = -2.9528300873415594, hamiltonian_energy_error = 0.11807883906603056, max_hamiltonian_energy_error = 1.0347612597250437, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.949720478567525, log_density = 7.448404012568755, hamiltonian_energy = -5.379826591883348, hamiltonian_energy_error = -0.340233272437211, max_hamiltonian_energy_error = -0.6102737628366697, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8329243172913559, log_density = 6.313245211127915, hamiltonian_energy = -3.051245332017522, hamiltonian_energy_error = -0.25860199250554894, max_hamiltonian_energy_error = 0.47501972283451366, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6038940057518468, log_density = 5.020109706275459, hamiltonian_energy = -2.816049093083953, hamiltonian_energy_error = 0.5005160523742709, max_hamiltonian_energy_error = 1.0527080554086368, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.997374080271898, log_density = 6.836166883811925, hamiltonian_energy = -3.011657978436607, hamiltonian_energy_error = -0.1463443287849815, max_hamiltonian_energy_error = -0.5601864051753207, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.7631220083155913, log_density = 4.595336145914601, hamiltonian_energy = -4.0531767449292815, hamiltonian_energy_error = 0.6983644253508388, max_hamiltonian_energy_error = 0.6983644253508388, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 4.4343907272485605, hamiltonian_energy = 0.451460531668781, hamiltonian_energy_error = -0.691638972159935, max_hamiltonian_energy_error = -1.2286824205123947, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9836975777482977, log_density = 7.034066168980932, hamiltonian_energy = -3.571979959930221, hamiltonian_energy_error = -0.08159409620115454, max_hamiltonian_energy_error = -0.38975085032477397, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8681058566084499, log_density = 8.854978186602128, hamiltonian_energy = -2.609150111828905, hamiltonian_energy_error = -0.3910179966740017, max_hamiltonian_energy_error = 0.49054465162747496, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9311853652385902, log_density = 8.813388747630096, hamiltonian_energy = -8.25632404447742, hamiltonian_energy_error = 0.02583732085792434, max_hamiltonian_energy_error = 0.147250178766674, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.6895837097391332, log_density = 7.84318854697646, hamiltonian_energy = -6.303595675674602, hamiltonian_energy_error = 0.37782713355113096, max_hamiltonian_energy_error = 0.8057561478006123, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9154213482792716, log_density = 6.996710200138718, hamiltonian_energy = -5.60773099363839, hamiltonian_energy_error = -0.28106703990419746, max_hamiltonian_energy_error = 0.43379044719977866, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9989001739800525, log_density = 8.45393772010874, hamiltonian_energy = -6.268970656269925, hamiltonian_energy_error = -0.03741036611181947, max_hamiltonian_energy_error = -0.05377120493637655, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9994812117122331, log_density = 8.9873649424596, hamiltonian_energy = -8.110731394999458, hamiltonian_energy_error = 0.003638127983579764, max_hamiltonian_energy_error = -0.054640282792268735, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.5397443176501404, log_density = 4.562320793551688, hamiltonian_energy = -3.5593573901112476, hamiltonian_energy_error = 1.1158622304542067, max_hamiltonian_energy_error = 1.9154180577837039, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 6.08781297530631, hamiltonian_energy = -4.062757388187234, hamiltonian_energy_error = -0.47893264946682823, max_hamiltonian_energy_error = -0.7956197801382636, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 7.335301436959524, hamiltonian_energy = -5.741621466318457, hamiltonian_energy_error = -0.1709174718272921, max_hamiltonian_energy_error = -0.2875776049494654, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9530735177086412, log_density = 7.69200133635119, hamiltonian_energy = -5.491036201675575, hamiltonian_energy_error = -0.06209634505801631, max_hamiltonian_energy_error = 0.16170656035487063, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8721053748733129, log_density = 3.341431764007309, hamiltonian_energy = -2.5347084909596287, hamiltonian_energy_error = 0.15987494390083512, max_hamiltonian_energy_error = 0.1840408587375686, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.5906244914190221, log_density = 2.823717189070212, hamiltonian_energy = 0.7969962260752848, hamiltonian_energy_error = 0.3242090677236944, max_hamiltonian_energy_error = 0.824559233921407, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.5907243710038635, log_density = 8.495638603609276, hamiltonian_energy = 1.006763686642099, hamiltonian_energy_error = -0.24258147388515816, max_hamiltonian_energy_error = 1.1878431043897804, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 5, is_accept = true, acceptance_rate = 0.5405238746200951, log_density = 8.661842918434814, hamiltonian_energy = -5.206436651094652, hamiltonian_energy_error = -0.012361229840053056, max_hamiltonian_energy_error = 1.1681600385014548, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8726681783781469, log_density = 7.472424432271554, hamiltonian_energy = -5.855894326000568, hamiltonian_energy_error = 0.09908024147230421, max_hamiltonian_energy_error = 0.19198569778953622, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.5494160009370845, log_density = 6.944640079025547, hamiltonian_energy = -2.849631277281282, hamiltonian_energy_error = 0.5851530696724767, max_hamiltonian_energy_error = 0.7243385098204884, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.999826692046409, log_density = 8.985301269844918, hamiltonian_energy = -6.9329410137429255, hamiltonian_energy_error = -0.7516055174741458, max_hamiltonian_energy_error = -0.7516055174741458, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.743004864202963, log_density = 8.388882724178238, hamiltonian_energy = -6.776325301261849, hamiltonian_energy_error = -0.043348722478292245, max_hamiltonian_energy_error = 0.6530446374730667, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8730153061584827, log_density = 6.7328503571764085, hamiltonian_energy = -5.833495539881693, hamiltonian_energy_error = 0.1327011009836392, max_hamiltonian_energy_error = 0.16125025540326288, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9875892340419767, log_density = 7.448248743399702, hamiltonian_energy = -5.010621760090414, hamiltonian_energy_error = 0.009012196338000322, max_hamiltonian_energy_error = -0.06259818508007964, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 7.631231503328786, hamiltonian_energy = -6.452756420742391, hamiltonian_energy_error = -0.03560798350123662, max_hamiltonian_energy_error = -0.05916930087231442, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7945263628843603, log_density = 8.187332225367431, hamiltonian_energy = -4.446810830869866, hamiltonian_energy_error = 0.07815836230870055, max_hamiltonian_energy_error = 0.5446290928883304, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.6676730115459178, log_density = 8.425285274864958, hamiltonian_energy = -4.350857728251226, hamiltonian_energy_error = 0.14007993764662174, max_hamiltonian_energy_error = 1.145949901074668, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7693292517330851, log_density = 6.91418385059721, hamiltonian_energy = -4.022443477613193, hamiltonian_energy_error = 0.4791917258277234, max_hamiltonian_energy_error = 0.7471848004643, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8738721329540263, log_density = 6.3883395480415786, hamiltonian_energy = -2.8920720170269885, hamiltonian_energy_error = 0.23537371670848062, max_hamiltonian_energy_error = -0.642110976206193, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9671671865875301, log_density = 7.904123842373503, hamiltonian_energy = -2.1252664107571038, hamiltonian_energy_error = -0.5884151703627012, max_hamiltonian_energy_error = -0.8771344391538318, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8999816575788019, log_density = 8.305782635506459, hamiltonian_energy = -6.393851271042474, hamiltonian_energy_error = -0.1721557842856427, max_hamiltonian_energy_error = 0.35675355740525383, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8491637546544494, log_density = 8.399830619395184, hamiltonian_energy = -6.941668146070459, hamiltonian_energy_error = -0.056659757873740446, max_hamiltonian_energy_error = 0.3727118409128227, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8454100413879558, log_density = 7.402427734028329, hamiltonian_energy = -6.6595315284535115, hamiltonian_energy_error = 0.266968929256465, max_hamiltonian_energy_error = 0.266968929256465, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9430484416130207, log_density = 4.139482784608504, hamiltonian_energy = -3.574795969694606, hamiltonian_energy_error = 0.18690528838424036, max_hamiltonian_energy_error = -0.24841864587422302, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 6.208669539776006, hamiltonian_energy = -3.3150471620429673, hamiltonian_energy_error = -0.1912171359743473, max_hamiltonian_energy_error = -0.4443137928916747, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7926860063896587, log_density = 2.5701265055410225, hamiltonian_energy = -0.6778071083231478, hamiltonian_energy_error = 0.28539220307836866, max_hamiltonian_energy_error = 0.47534859388942907, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9966010381766137, log_density = 6.744418449547492, hamiltonian_energy = -0.6135966289803694, hamiltonian_energy_error = -0.23049969392802172, max_hamiltonian_energy_error = -0.4824383832523398, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7704456744684554, log_density = 5.703311085639925, hamiltonian_energy = -2.8823684629975874, hamiltonian_energy_error = 0.404495964406681, max_hamiltonian_energy_error = 0.9887851203059239, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9668904521149436, log_density = 8.459456103768858, hamiltonian_energy = -4.379079826240517, hamiltonian_energy_error = -0.5008319686479936, max_hamiltonian_energy_error = -0.8962873994405243, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8745163094299107, log_density = 6.842863631034817, hamiltonian_energy = -5.295365345794931, hamiltonian_energy_error = -0.0010954810302941098, max_hamiltonian_energy_error = 0.4430547743619746, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9914855366487195, log_density = 6.812849955495253, hamiltonian_energy = -5.713425799181275, hamiltonian_energy_error = 0.0020617491582850533, max_hamiltonian_energy_error = -0.3008299218572015, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8888215270039433, log_density = 3.932252805210279, hamiltonian_energy = -2.173563134781251, hamiltonian_energy_error = 0.13877311477715404, max_hamiltonian_energy_error = 0.25377200262745525, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8233379332064305, log_density = 5.381994943159542, hamiltonian_energy = -2.2248500670097098, hamiltonian_energy_error = 0.24134806525558528, max_hamiltonian_energy_error = 0.39705267319252524, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9216547546489906, log_density = 6.092181974457347, hamiltonian_energy = -1.6433789168785893, hamiltonian_energy_error = -0.00646288083690294, max_hamiltonian_energy_error = -0.5012929475007883, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8946488683904964, log_density = 8.51198738941741, hamiltonian_energy = -2.157737125135541, hamiltonian_energy_error = -0.5342311505730732, max_hamiltonian_energy_error = -0.5342311505730732, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9953320296850287, log_density = 8.391106543574079, hamiltonian_energy = -7.916909552337149, hamiltonian_energy_error = -0.15422155337405918, max_hamiltonian_energy_error = -0.2836130326568984, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9779589450515507, log_density = 8.774292212932414, hamiltonian_energy = -8.011698184472468, hamiltonian_energy_error = -0.08849670506872442, max_hamiltonian_energy_error = -0.11734370446980513, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9868055992429224, log_density = 8.304600221038172, hamiltonian_energy = -7.019935521850102, hamiltonian_energy_error = 0.021136255295587603, max_hamiltonian_energy_error = -0.04819696829713482, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8215959817022613, log_density = 6.228136807587429, hamiltonian_energy = -3.3725324539997654, hamiltonian_energy_error = 0.166794761293648, max_hamiltonian_energy_error = 0.3284187603778417, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9841220150883727, log_density = 9.535805732546477, hamiltonian_energy = -5.430718744263746, hamiltonian_energy_error = -0.11912300743807158, max_hamiltonian_energy_error = -0.11912300743807158, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.427110393328191, log_density = 9.535805732546477, hamiltonian_energy = -5.128162015089528, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 2.4538866744886043, tree_depth = 1, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8315432465054791, log_density = 9.097250049656449, hamiltonian_energy = -6.206122030403817, hamiltonian_energy_error = 0.0418268022184769, max_hamiltonian_energy_error = 0.31279229827689026, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.992114337442859, log_density = 7.127489922248294, hamiltonian_energy = -6.751125910834787, hamiltonian_energy_error = 0.04348080896797679, max_hamiltonian_energy_error = 0.04348080896797679, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8145790046075242, log_density = 8.89012618108542, hamiltonian_energy = -5.077815286069379, hamiltonian_energy_error = 0.012048163328771011, max_hamiltonian_energy_error = 0.46549676620619707, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.974185820446282, log_density = 8.577961661150612, hamiltonian_energy = -7.634656491634004, hamiltonian_energy_error = -0.004501724575450616, max_hamiltonian_energy_error = 0.07645225685114543, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9297301965858412, log_density = 8.662720774366862, hamiltonian_energy = -7.567389836223758, hamiltonian_energy_error = 0.05819255525142797, max_hamiltonian_energy_error = 0.14722271686474908, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.7442963949791177, log_density = 8.45631482154278, hamiltonian_energy = -6.622736898433276, hamiltonian_energy_error = 0.2716298527018228, max_hamiltonian_energy_error = 0.705450148222905, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9857731992189684, log_density = 6.129720765525624, hamiltonian_energy = -5.019470813566868, hamiltonian_energy_error = -0.0072122301472941075, max_hamiltonian_energy_error = -0.07179978561075107, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9975892228804245, log_density = 9.028128756718612, hamiltonian_energy = -4.04768586189371, hamiltonian_energy_error = -0.2544802485086488, max_hamiltonian_energy_error = -0.3179768594014267, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9151289325525138, log_density = 8.354244918779708, hamiltonian_energy = -6.021077487869558, hamiltonian_energy_error = 0.1036108490615888, max_hamiltonian_energy_error = 0.16066773890132602, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8655417722612315, log_density = 7.501497766711903, hamiltonian_energy = -5.253000308980502, hamiltonian_energy_error = 0.07224349725052903, max_hamiltonian_energy_error = 0.3134007662125855, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9588351615403279, log_density = 8.154686813398731, hamiltonian_energy = -6.3109212324222, hamiltonian_energy_error = 0.03815398047229035, max_hamiltonian_energy_error = -0.24723161787289438, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9206018794555996, log_density = 7.385064377753432, hamiltonian_energy = -6.098605600870561, hamiltonian_energy_error = 0.2260478424767367, max_hamiltonian_energy_error = 0.3221076587642173, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9922454687475147, log_density = 9.604065468070523, hamiltonian_energy = -4.545240922641464, hamiltonian_energy_error = -0.6161561212253281, max_hamiltonian_energy_error = -0.6161561212253281, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9323833375369107, log_density = 9.159506424161208, hamiltonian_energy = -8.33408962669214, hamiltonian_energy_error = 0.048912651713413524, max_hamiltonian_energy_error = 0.12635757659358937, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9629702314596021, log_density = 9.014782380717033, hamiltonian_energy = -8.101608716481486, hamiltonian_energy_error = -0.01231502024524822, max_hamiltonian_energy_error = 0.11050756255205574, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.5370544340890869, log_density = 7.636315367913099, hamiltonian_energy = -5.107485523865492, hamiltonian_energy_error = 0.566333430990472, max_hamiltonian_energy_error = 1.3862227477782723, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9929846446494429, log_density = 7.603299627249241, hamiltonian_energy = -6.828037650179495, hamiltonian_energy_error = -0.1523957005979213, max_hamiltonian_energy_error = -0.34648016026418116, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8020877968107802, log_density = 7.556325548874472, hamiltonian_energy = -4.776820787386625, hamiltonian_energy_error = 0.1395063441423856, max_hamiltonian_energy_error = 0.629421883294226, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9931847723627276, log_density = 8.980088548747144, hamiltonian_energy = -6.662485542861622, hamiltonian_energy_error = -0.193454034499573, max_hamiltonian_energy_error = -0.193454034499573, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.852664223712537, log_density = 7.572297651953981, hamiltonian_energy = -5.312079084014053, hamiltonian_energy_error = 0.1251637074612093, max_hamiltonian_energy_error = 0.26612319976602006, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.844304107508222, log_density = 3.646501471504351, hamiltonian_energy = -0.41532731996579253, hamiltonian_energy_error = 0.2355724536832402, max_hamiltonian_energy_error = 0.40506799066840626, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.977332438708338, log_density = 8.089741085530632, hamiltonian_energy = -1.6739474995354282, hamiltonian_energy_error = -0.33838131615517497, max_hamiltonian_energy_error = -0.33838131615517497, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7686930973012644, log_density = 5.033070759474192, hamiltonian_energy = -0.6009063084971142, hamiltonian_energy_error = 0.2193258710541457, max_hamiltonian_energy_error = 0.40826571536084355, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 1, is_accept = true, acceptance_rate = 0.6386101412110208, log_density = 5.033070759474192, hamiltonian_energy = -2.9515961625208984, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 0.4484611184469949, tree_depth = 1, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9257120027284517, log_density = 7.004742058248592, hamiltonian_energy = -2.1329845748912994, hamiltonian_energy_error = 0.10615370749934172, max_hamiltonian_energy_error = -0.390225918779584, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9925876776837005, log_density = 8.52553772955864, hamiltonian_energy = -5.080248286439144, hamiltonian_energy_error = -0.32173762199708733, max_hamiltonian_energy_error = -0.4376123362683453, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9460629998708081, log_density = 5.488937204870975, hamiltonian_energy = -5.115646991604997, hamiltonian_energy_error = 0.15700864248008894, max_hamiltonian_energy_error = 0.16239616882526597, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9012437398627048, log_density = 6.548213276364109, hamiltonian_energy = -2.9199630185133305, hamiltonian_energy_error = -0.15325504395114686, max_hamiltonian_energy_error = 0.32914638874382707, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9277745393206356, log_density = 7.69146703881237, hamiltonian_energy = -5.350479554461598, hamiltonian_energy_error = -0.1352192325880095, max_hamiltonian_energy_error = 0.1463947733917097, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9818365241441162, log_density = 7.478784287695698, hamiltonian_energy = -6.066816314166167, hamiltonian_energy_error = 0.08939254719466216, max_hamiltonian_energy_error = 0.08939254719466216, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8729209395315736, log_density = 6.174892773365775, hamiltonian_energy = -3.83914147798413, hamiltonian_energy_error = 0.28596046913372497, max_hamiltonian_energy_error = 0.587903122731257, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9609055974305093, log_density = 6.761912476754219, hamiltonian_energy = -3.3748310821375784, hamiltonian_energy_error = 0.049181841914291535, max_hamiltonian_energy_error = -0.397411539483433, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9077428005648428, log_density = 4.8848795125092295, hamiltonian_energy = -4.368691045982208, hamiltonian_energy_error = 0.3240301984207026, max_hamiltonian_energy_error = -0.5206556426739537, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9909411716380989, log_density = 5.6901268858552, hamiltonian_energy = -2.7572335735239495, hamiltonian_energy_error = -0.3296640253711782, max_hamiltonian_energy_error = -0.8315611982731843, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9394772560147027, log_density = 5.887707817939937, hamiltonian_energy = -2.028783481133049, hamiltonian_energy_error = -0.05089942305433359, max_hamiltonian_energy_error = -0.5156827355291993, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.46530799016727076, log_density = 6.4166886361292, hamiltonian_energy = -2.520971828218983, hamiltonian_energy_error = 0.6188506930692119, max_hamiltonian_energy_error = 1.453314807085933, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8498972155770396, log_density = 7.693614047553076, hamiltonian_energy = -4.502947826898609, hamiltonian_energy_error = -1.0674806018115555, max_hamiltonian_energy_error = -1.1052687202059768, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.999404118968887, log_density = 7.3323101480705635, hamiltonian_energy = -7.037125884657477, hamiltonian_energy_error = -0.04659950245265776, max_hamiltonian_energy_error = -0.19442740978593331, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8406980241657998, log_density = 5.345171901125481, hamiltonian_energy = -3.701474094602342, hamiltonian_energy_error = 0.04758188107683692, max_hamiltonian_energy_error = 0.533798609953239, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8154195920058429, log_density = 2.0277040811804117, hamiltonian_energy = -0.9412999956184884, hamiltonian_energy_error = -0.1444592884314706, max_hamiltonian_energy_error = 0.40545181274429165, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9522694931135185, log_density = 0.27349822182433314, hamiltonian_energy = 4.689115250164687, hamiltonian_energy_error = -0.30438523115965666, max_hamiltonian_energy_error = -0.6614313361732513, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6649180869795231, log_density = 2.5047667146949166, hamiltonian_energy = 5.333837199686896, hamiltonian_energy_error = 1.1551565563576371, max_hamiltonian_energy_error = 1.1551565563576371, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 3.570588518443788, hamiltonian_energy = -0.7201734408543032, hamiltonian_energy_error = -0.5710970684791135, max_hamiltonian_energy_error = -1.822836167222619, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 7.8431589118031795, hamiltonian_energy = -4.002163365464079, hamiltonian_energy_error = -1.1425147722892843, max_hamiltonian_energy_error = -1.1425147722892843, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9448558840626193, log_density = 5.971210462011047, hamiltonian_energy = -4.9333018423537425, hamiltonian_energy_error = 0.11465597070637035, max_hamiltonian_energy_error = 0.1704300552515292, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7509572538484568, log_density = 0.40126900053266823, hamiltonian_energy = 1.9930669061156787, hamiltonian_energy_error = 0.35976637462779104, max_hamiltonian_energy_error = 0.5178896805292412, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 8.723530767462083, hamiltonian_energy = 1.364386499656952, hamiltonian_energy_error = -1.294327385737935, max_hamiltonian_energy_error = -1.294327385737935, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8662084766283488, log_density = 8.576981846557961, hamiltonian_energy = -4.999105617198042, hamiltonian_energy_error = -0.025974186167789348, max_hamiltonian_energy_error = 0.3267619233707899, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8680562874593736, log_density = 8.99592150494107, hamiltonian_energy = -4.678878141810188, hamiltonian_energy_error = 0.016433162666924517, max_hamiltonian_energy_error = 0.29430480504188417, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9062865189952051, log_density = 7.892502404417627, hamiltonian_energy = -7.108408287732143, hamiltonian_energy_error = 0.09557264765330409, max_hamiltonian_energy_error = 0.24557055563079366, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9920687316596402, log_density = 8.049361846390008, hamiltonian_energy = -6.852635370770026, hamiltonian_energy_error = -0.0912411597502798, max_hamiltonian_energy_error = -0.16786256495310692, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8520772928928174, log_density = 7.413134172485089, hamiltonian_energy = -4.941574363277642, hamiltonian_energy_error = 0.29075454073378815, max_hamiltonian_energy_error = 0.29075454073378815, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8016316779082799, log_density = 7.714735857752762, hamiltonian_energy = -3.7492060322785954, hamiltonian_energy_error = -0.015469490102920869, max_hamiltonian_energy_error = 0.6381772899604541, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9852525715070662, log_density = 8.517851861354655, hamiltonian_energy = -7.296364769298491, hamiltonian_energy_error = -0.23029342032786992, max_hamiltonian_energy_error = -0.2556170935155935, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8086934470159983, log_density = 5.567781909173098, hamiltonian_energy = -5.240391637595572, hamiltonian_energy_error = 0.2913630210677418, max_hamiltonian_energy_error = 0.2913630210677418, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9986201932733555, log_density = 8.658389887094582, hamiltonian_energy = -5.368218495323186, hamiltonian_energy_error = -0.27057462867396964, max_hamiltonian_energy_error = -0.27057462867396964, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.7331582386418801, log_density = 7.646020091004681, hamiltonian_energy = -4.851690607714978, hamiltonian_energy_error = 0.08525846758215927, max_hamiltonian_energy_error = 0.48125583914429804, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.793033700504063, log_density = 4.259704974671099, hamiltonian_energy = -1.989144314289014, hamiltonian_energy_error = 0.9679259910667151, max_hamiltonian_energy_error = 0.9679259910667151, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 8.382326659249744, hamiltonian_energy = -3.6272822667146043, hamiltonian_energy_error = -1.5360002756996605, max_hamiltonian_energy_error = -1.5360002756996605, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8472077514757133, log_density = 8.667889260072903, hamiltonian_energy = -7.03125122341595, hamiltonian_energy_error = 0.08229249913045766, max_hamiltonian_energy_error = 0.33455110685644307, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.7098180699254405, log_density = 5.328650094127493, hamiltonian_energy = -4.0153120349712985, hamiltonian_energy_error = 0.2390169573036074, max_hamiltonian_energy_error = 0.5269986312425763, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8890589269995804, log_density = 6.259969537617888, hamiltonian_energy = -1.4704301325999696, hamiltonian_energy_error = -0.3910577354748108, max_hamiltonian_energy_error = 0.473058608087902, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8418869147670556, log_density = 7.7882247948338374, hamiltonian_energy = -4.340664679605475, hamiltonian_energy_error = 0.1601529381164113, max_hamiltonian_energy_error = 0.42231009593088586, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9926029181606217, log_density = 8.375396529417124, hamiltonian_energy = -7.09530100702493, hamiltonian_energy_error = -0.0351727741146215, max_hamiltonian_energy_error = -0.1776122472622994, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.5408862274289907, log_density = 8.100679431868844, hamiltonian_energy = -5.144641538819526, hamiltonian_energy_error = 0.2293529717180931, max_hamiltonian_energy_error = 1.2689802990595433, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9265225329123631, log_density = 5.377215006795474, hamiltonian_energy = -3.1146745548902794, hamiltonian_energy_error = 0.16938699604683194, max_hamiltonian_energy_error = -0.1698072527297585, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.47111112591672405, log_density = 6.694480623355792, hamiltonian_energy = 0.9355633716118836, hamiltonian_energy_error = -0.3429794626639131, max_hamiltonian_energy_error = 1.3275494655726572, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.2875851015852064, log_density = 7.903067646665287, hamiltonian_energy = -2.482486184946021, hamiltonian_energy_error = 0.5960578783279118, max_hamiltonian_energy_error = 2.95711095815361, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9355318807625468, log_density = 7.715010455466164, hamiltonian_energy = -5.624750850045951, hamiltonian_energy_error = -0.05613777450465385, max_hamiltonian_energy_error = 0.16561953268645713, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.36673954348798044, log_density = 6.111037265403086, hamiltonian_energy = 1.785331739927118, hamiltonian_energy_error = 0.7715738898539275, max_hamiltonian_energy_error = 1.7811857370724802, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9250840638022614, log_density = 8.433745937947513, hamiltonian_energy = -5.367745281255246, hamiltonian_energy_error = -0.0022971326215994736, max_hamiltonian_energy_error = 0.3079760578456119, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6955981743237487, log_density = 7.835280777295573, hamiltonian_energy = -5.497197493197035, hamiltonian_energy_error = 0.12775534991079773, max_hamiltonian_energy_error = 0.9411437404178997, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9838960340006812, log_density = 8.832937665588538, hamiltonian_energy = -3.920644018065664, hamiltonian_energy_error = -0.06467198420601417, max_hamiltonian_energy_error = -0.26814246177105616, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9646156276999652, log_density = 8.524156308683278, hamiltonian_energy = -7.840948587589866, hamiltonian_energy_error = 0.09742592182591192, max_hamiltonian_energy_error = -0.18794719382249614, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8558934467719274, log_density = 9.014190638315098, hamiltonian_energy = -7.128484545136215, hamiltonian_energy_error = -0.062304107988150115, max_hamiltonian_energy_error = 0.43352063187269696, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6684339595123111, log_density = 6.971196871285212, hamiltonian_energy = -5.239176176154623, hamiltonian_energy_error = 0.8285898825566429, max_hamiltonian_energy_error = 0.8285898825566429, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 9.356994361941862, hamiltonian_energy = -7.261997852515732, hamiltonian_energy_error = -0.7392776709740909, max_hamiltonian_energy_error = -0.9866415602112353, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9878555550383424, log_density = 9.384185497455839, hamiltonian_energy = -8.902804575119251, hamiltonian_energy_error = -0.003667862739472838, max_hamiltonian_energy_error = 0.033204004673299536, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8147626471141979, log_density = 6.940246892360101, hamiltonian_energy = -6.652357396170768, hamiltonian_energy_error = 0.41428797934166095, max_hamiltonian_energy_error = 0.41428797934166095, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 9.157447800477458, hamiltonian_energy = -6.77580215597555, hamiltonian_energy_error = -0.3723682062911653, max_hamiltonian_energy_error = -0.3723682062911653, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8850794632967169, log_density = 6.775635207524726, hamiltonian_energy = -5.400647848891339, hamiltonian_energy_error = 0.09667729790532853, max_hamiltonian_energy_error = 0.3052335049444288, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9920236473654133, log_density = 7.971722932442601, hamiltonian_energy = -5.5165129582220445, hamiltonian_energy_error = -0.1064294706412543, max_hamiltonian_energy_error = -0.26632297949198236, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9819224300722759, log_density = 8.227833950837796, hamiltonian_energy = -6.758591024417104, hamiltonian_energy_error = -0.10000712415057578, max_hamiltonian_energy_error = -0.10455723907423575, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9688776008700722, log_density = 8.984688607802592, hamiltonian_energy = -6.828959917658329, hamiltonian_energy_error = -0.03524718202093968, max_hamiltonian_energy_error = 0.13209573962141885, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8934585651303851, log_density = 8.317636452164823, hamiltonian_energy = -5.4546953786213965, hamiltonian_energy_error = 0.008433224739836653, max_hamiltonian_energy_error = 0.22473721244544986, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8454812169068056, log_density = 7.8676515444159705, hamiltonian_energy = -5.3750327950510535, hamiltonian_energy_error = 0.1001179839980697, max_hamiltonian_energy_error = 0.4618341388841589, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.990718459407604, log_density = 8.5841306320711, hamiltonian_energy = -6.619838457230293, hamiltonian_energy_error = -0.048938268966785436, max_hamiltonian_energy_error = -0.09181448453853136, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.977016518507079, log_density = 8.848554107318412, hamiltonian_energy = -7.711446922571733, hamiltonian_energy_error = 0.01970966367361715, max_hamiltonian_energy_error = 0.06009541186409262, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9309253558798797, log_density = 6.557803037278859, hamiltonian_energy = -5.186353637450191, hamiltonian_energy_error = 0.0371910125275976, max_hamiltonian_energy_error = 0.26167302044955054, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9947453046248196, log_density = 8.027935485552653, hamiltonian_energy = -5.90355103275204, hamiltonian_energy_error = -0.07848575875648045, max_hamiltonian_energy_error = -0.1774378071211773, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.941103996925127, log_density = 8.77424588893777, hamiltonian_energy = -6.694004708906072, hamiltonian_energy_error = -0.04593736438938745, max_hamiltonian_energy_error = 0.17164149429624143, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.776454395518746, log_density = 8.743695944743688, hamiltonian_energy = -6.793666075387928, hamiltonian_energy_error = 0.10842266000407097, max_hamiltonian_energy_error = 0.3931743708980111, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9506438690407809, log_density = 7.638944306178434, hamiltonian_energy = -5.278678406044428, hamiltonian_energy_error = 0.002666020721212803, max_hamiltonian_energy_error = 0.14079057544229912, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.6201768920532945, log_density = 8.940071868064177, hamiltonian_energy = -5.394355809789213, hamiltonian_energy_error = -0.04813370243778081, max_hamiltonian_energy_error = 0.8810846292589609, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9152872780538258, log_density = 7.242936733669575, hamiltonian_energy = -6.850305227274964, hamiltonian_energy_error = 0.09223605308167127, max_hamiltonian_energy_error = 0.15946237262956675, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.990147101201956, log_density = 8.573372574359956, hamiltonian_energy = -6.035344619513042, hamiltonian_energy_error = -0.018189916649049565, max_hamiltonian_energy_error = -0.11956430015776398, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7867229411705741, log_density = 8.196541532807569, hamiltonian_energy = -6.781058994379167, hamiltonian_energy_error = 0.1676168022118496, max_hamiltonian_energy_error = 0.4675085292717176, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9650957675175426, log_density = 8.727989279651773, hamiltonian_energy = -7.701822274006026, hamiltonian_energy_error = -0.25946894183028313, max_hamiltonian_energy_error = -0.3595701209558504, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9977964732984898, log_density = 8.114822385342944, hamiltonian_energy = -6.959342178073168, hamiltonian_energy_error = -0.051671625139632305, max_hamiltonian_energy_error = -0.09374129195775982, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9617881105160365, log_density = 8.340096006946911, hamiltonian_energy = -7.011611305970358, hamiltonian_energy_error = -0.019894640572602817, max_hamiltonian_energy_error = 0.09818173882867853, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8362564395401574, log_density = 9.164159278869054, hamiltonian_energy = -7.165293201910077, hamiltonian_energy_error = -0.028554161624096963, max_hamiltonian_energy_error = 0.4236257104255312, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9109943575525664, log_density = 7.677548424569894, hamiltonian_energy = -6.220956344075617, hamiltonian_energy_error = 0.10824361616778067, max_hamiltonian_energy_error = 0.18449126819489958, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8902998562152781, log_density = 7.126749894605062, hamiltonian_energy = -1.871327209675255, hamiltonian_energy_error = 0.16828516930352055, max_hamiltonian_energy_error = 0.25514441295170665, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 1.0, log_density = 6.862652398305984, hamiltonian_energy = -5.8551193297681134, hamiltonian_energy_error = -0.10424141353610494, max_hamiltonian_energy_error = -0.4344335958594172, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9224980236177481, log_density = 8.601661292335613, hamiltonian_energy = -4.425981227504342, hamiltonian_energy_error = -0.12698333299154907, max_hamiltonian_energy_error = 0.3493084718415158, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9135435586928488, log_density = 7.4051800701418955, hamiltonian_energy = -6.299326374807663, hamiltonian_energy_error = 0.23456269503154115, max_hamiltonian_energy_error = 0.2772536073682872, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 7.596060153968088, hamiltonian_energy = -6.888936892613705, hamiltonian_energy_error = -0.1421550666309841, max_hamiltonian_energy_error = -0.3679060681090114, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9085439264155944, log_density = 6.459879633657691, hamiltonian_energy = -5.102022120358711, hamiltonian_energy_error = 0.0978691138692751, max_hamiltonian_energy_error = 0.1998370208925362, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8617853332262879, log_density = 7.918048505030566, hamiltonian_energy = -1.2030893648517793, hamiltonian_energy_error = -0.12263881849709435, max_hamiltonian_energy_error = 0.47644630914645436, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8328962673718229, log_density = 7.082945863883845, hamiltonian_energy = -5.328575637908024, hamiltonian_energy_error = 0.24559547765573697, max_hamiltonian_energy_error = 0.39615236540091203, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 7.582379728232649, hamiltonian_energy = -6.399748253854289, hamiltonian_energy_error = -0.21371125310433303, max_hamiltonian_energy_error = -0.5300256727000496, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8314149158232, log_density = 9.015040853558594, hamiltonian_energy = -4.7604939920220675, hamiltonian_energy_error = -0.16064991323579214, max_hamiltonian_energy_error = 0.3865710004092273, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9070908547684685, log_density = 7.5115190888814105, hamiltonian_energy = -6.850653400950019, hamiltonian_energy_error = 0.2762906785191097, max_hamiltonian_energy_error = 0.2762906785191097, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9959046085204256, log_density = 9.53829094981774, hamiltonian_energy = -5.5661731568776, hamiltonian_energy_error = -0.4074413448150418, max_hamiltonian_energy_error = -0.4074413448150418, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8925845433377267, log_density = 8.672481096020999, hamiltonian_energy = -7.505477474717561, hamiltonian_energy_error = 0.14324176668158728, max_hamiltonian_energy_error = 0.209240384165426, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9725095711951869, log_density = 8.544752710372673, hamiltonian_energy = -7.612983760066159, hamiltonian_energy_error = -0.04744903634121389, max_hamiltonian_energy_error = -0.1688790630319339, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8923400001447355, log_density = 7.885581819116904, hamiltonian_energy = -6.002776837175475, hamiltonian_energy_error = 0.15129620606627459, max_hamiltonian_energy_error = 0.2728239381097719, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8992238825904916, log_density = 5.674760758641018, hamiltonian_energy = -2.4020887552762185, hamiltonian_energy_error = 0.1660327119689109, max_hamiltonian_energy_error = 0.42465385364345476, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.988738996401222, log_density = 8.797193960831613, hamiltonian_energy = -3.4111214233963114, hamiltonian_energy_error = -0.33393437599545184, max_hamiltonian_energy_error = -0.44288764783130485, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9229704533667359, log_density = 8.666591058165416, hamiltonian_energy = -7.4235346477954, hamiltonian_energy_error = 0.09486822157890984, max_hamiltonian_energy_error = 0.2070921029354551, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.975540804841207, log_density = 7.281430983763215, hamiltonian_energy = -6.335459581894481, hamiltonian_energy_error = -0.16815999527655556, max_hamiltonian_energy_error = -0.23140310454505286, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8102336707236842, log_density = 9.13621217710277, hamiltonian_energy = -4.0391797728062375, hamiltonian_energy_error = 0.10028575638451454, max_hamiltonian_energy_error = 0.37261196823195775, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9801608074927913, log_density = 8.586500310024352, hamiltonian_energy = -7.902315208133326, hamiltonian_energy_error = -0.009520311301269402, max_hamiltonian_energy_error = -0.07386269442006999, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9987458058986308, log_density = 9.18933611237246, hamiltonian_energy = -7.62179705643752, hamiltonian_energy_error = -0.03140861060887623, max_hamiltonian_energy_error = -0.08155223175022286, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9274691375475695, log_density = 7.970185196117004, hamiltonian_energy = -7.269647844114273, hamiltonian_energy_error = 0.08730593260279029, max_hamiltonian_energy_error = 0.16007401222030282, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8387665106076642, log_density = 7.936618543144997, hamiltonian_energy = -5.829927028260148, hamiltonian_energy_error = -0.11584595444121426, max_hamiltonian_energy_error = 0.36188049745604545, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.4771834577931194, log_density = 7.936618543144997, hamiltonian_energy = -5.85796136689266, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 0.9360813398108299, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.5034690963164578, log_density = 5.47668270905319, hamiltonian_energy = -3.310138154116482, hamiltonian_energy_error = 1.0091436587420284, max_hamiltonian_energy_error = 1.7295170111695937, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.91390172777907, log_density = 6.386866754406814, hamiltonian_energy = -3.9313392160610054, hamiltonian_energy_error = -0.21433803752937797, max_hamiltonian_energy_error = -0.9504584993093239, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8436472213839588, log_density = 7.366530280593812, hamiltonian_energy = -2.5843431678367272, hamiltonian_energy_error = -0.40222524745124755, max_hamiltonian_energy_error = -0.8225649700403461, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9127871211282707, log_density = 5.991497184780039, hamiltonian_energy = -3.524376789339717, hamiltonian_energy_error = 0.2018348221228088, max_hamiltonian_energy_error = 0.20606692252649594, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9506354493334737, log_density = 5.675201422851082, hamiltonian_energy = -4.059104794484362, hamiltonian_energy_error = 0.23907108964757207, max_hamiltonian_energy_error = -0.5257317189908797, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 6.8834832405829065, hamiltonian_energy = -2.055774082656021, hamiltonian_energy_error = -0.44053758360058115, max_hamiltonian_energy_error = -0.9546402740747411, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9255075106330626, log_density = 8.072747574357999, hamiltonian_energy = -5.5839443664564925, hamiltonian_energy_error = -0.5983451630479957, max_hamiltonian_energy_error = -0.5983451630479957, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9656358494591836, log_density = 8.076486738628175, hamiltonian_energy = -7.128677268407981, hamiltonian_energy_error = 0.06969933366724224, max_hamiltonian_energy_error = 0.07559783526787278, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6500903788762348, log_density = 6.887903282896707, hamiltonian_energy = -3.5467886909240147, hamiltonian_energy_error = 0.39610366488148996, max_hamiltonian_energy_error = 0.9397319523226515, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9823895298355765, log_density = 8.311494826447177, hamiltonian_energy = -6.153894359443181, hamiltonian_energy_error = 0.00580869795424821, max_hamiltonian_energy_error = -0.28369040823517633, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9433902604014124, log_density = 9.18050922013024, hamiltonian_energy = -8.040946376560868, hamiltonian_energy_error = -0.3362584039463776, max_hamiltonian_energy_error = -0.3541903584038444, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9335009404134927, log_density = 8.76375638534456, hamiltonian_energy = -8.086044322714587, hamiltonian_energy_error = 0.04373974708873263, max_hamiltonian_energy_error = 0.1609531245994713, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.5973582508544619, log_density = 6.615245466333363, hamiltonian_energy = -5.091410806720251, hamiltonian_energy_error = 0.4047275691168579, max_hamiltonian_energy_error = 1.0689599362746156, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 8.607598844254461, hamiltonian_energy = -5.461309642872332, hamiltonian_energy_error = -0.42450963058754976, max_hamiltonian_energy_error = -0.42450963058754976, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.8711708673347835, log_density = 6.958774142281566, hamiltonian_energy = -4.803384453721232, hamiltonian_energy_error = 0.15544980921689788, max_hamiltonian_energy_error = 0.2535086857965547, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9837382767227475, log_density = 6.897978772717295, hamiltonian_energy = -4.216562797249705, hamiltonian_energy_error = 0.019289712169878293, max_hamiltonian_energy_error = -0.08310183903510637, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9893721847774098, log_density = 5.1436472075499395, hamiltonian_energy = -3.572216270387665, hamiltonian_energy_error = 0.002971081323868141, max_hamiltonian_energy_error = -0.4077126150799364, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9873869864839385, log_density = 8.961675823015252, hamiltonian_energy = -4.0853083448793, hamiltonian_energy_error = -0.2827932938459723, max_hamiltonian_energy_error = -0.3674013572757362, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8902039099937828, log_density = 9.513270955246348, hamiltonian_energy = -7.131864230395458, hamiltonian_energy_error = -0.009093574119010128, max_hamiltonian_energy_error = 0.18517445479069394, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8154554735119977, log_density = 7.557900997792554, hamiltonian_energy = -6.550966478806556, hamiltonian_energy_error = 0.200387319682366, max_hamiltonian_energy_error = 0.3392967891238108, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9686526887825535, log_density = 6.623779368247364, hamiltonian_energy = -4.566733103210852, hamiltonian_energy_error = 0.07769740195449781, max_hamiltonian_energy_error = -0.1808764603120272, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9994875174691105, log_density = 8.943786198649445, hamiltonian_energy = -6.14895290278338, hamiltonian_energy_error = -0.2761668981460783, max_hamiltonian_energy_error = -0.27624615246799955, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9905466199437942, log_density = 8.580458116461052, hamiltonian_energy = -8.34268184555836, hamiltonian_energy_error = 0.03386344977025324, max_hamiltonian_energy_error = -0.07670988651012678, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9996713649318507, log_density = 9.30503747750371, hamiltonian_energy = -8.294463529709914, hamiltonian_energy_error = -0.10542694666061259, max_hamiltonian_energy_error = -0.10876644537777658, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9245897741725032, log_density = 8.716481522909728, hamiltonian_energy = -7.134960783294788, hamiltonian_energy_error = 0.023922757297248687, max_hamiltonian_energy_error = 0.17254265701904803, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9909807368554714, log_density = 9.549169493241832, hamiltonian_energy = -6.966886210750355, hamiltonian_energy_error = -0.03320036338627119, max_hamiltonian_energy_error = -0.03863742882764676, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8684687067049629, log_density = 9.05022655473411, hamiltonian_energy = -6.864934030768144, hamiltonian_energy_error = 0.07380803183575058, max_hamiltonian_energy_error = 0.2303958472496852, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9308351831182712, log_density = 7.089483436033525, hamiltonian_energy = -6.6856281252027285, hamiltonian_energy_error = 0.16277896241821121, max_hamiltonian_energy_error = 0.16277896241821121, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7054595483117432, log_density = 3.0976343137912643, hamiltonian_energy = -2.1342345695752467, hamiltonian_energy_error = 1.0832084839022258, max_hamiltonian_energy_error = 1.1267186173669699, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8915942399985359, log_density = 7.500060220183297, hamiltonian_energy = -2.228099728067046, hamiltonian_energy_error = -2.090261434627587, max_hamiltonian_energy_error = -2.090261434627587, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9687446760529512, log_density = 5.7756934016613055, hamiltonian_energy = -2.921220883846173, hamiltonian_energy_error = 0.01109022549969474, max_hamiltonian_energy_error = -0.08329638157859875, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9911481146893395, log_density = 6.67191491503322, hamiltonian_energy = -3.4759863824966635, hamiltonian_energy_error = -0.02371651101814809, max_hamiltonian_energy_error = -0.07027327589177368, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.886920989118781, log_density = 7.510413538074385, hamiltonian_energy = -4.792164496590308, hamiltonian_energy_error = 0.15189357179295548, max_hamiltonian_energy_error = 0.3093239556474572, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8542919011705539, log_density = 8.413661056033057, hamiltonian_energy = -4.6317632673848195, hamiltonian_energy_error = -0.20125547533660537, max_hamiltonian_energy_error = 0.3669362578103783, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9636138403101902, log_density = 9.146436801293033, hamiltonian_energy = -7.412784315041337, hamiltonian_energy_error = 0.005845586713670414, max_hamiltonian_energy_error = 0.07837573849562052, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7609827808718901, log_density = 8.61305756569008, hamiltonian_energy = -6.486995612931103, hamiltonian_energy_error = 0.15161865374297978, max_hamiltonian_energy_error = 0.4595514805822507, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6957360525099163, log_density = 6.777278253792453, hamiltonian_energy = -5.080067437664615, hamiltonian_energy_error = 0.3734540803409274, max_hamiltonian_energy_error = 0.8758054387269372, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9767771429193327, log_density = 8.851845315389802, hamiltonian_energy = -5.11731328394626, hamiltonian_energy_error = -0.36226392881621106, max_hamiltonian_energy_error = -0.36226392881621106, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8343258087786914, log_density = 8.013056969002307, hamiltonian_energy = -7.020828475234914, hamiltonian_energy_error = 0.13659741016577343, max_hamiltonian_energy_error = 0.2971992772501446, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.886939781953828, log_density = 8.734273566005749, hamiltonian_energy = -6.5172880041165735, hamiltonian_energy_error = -0.06559431224981971, max_hamiltonian_energy_error = 0.35929086222208717, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7393893625033767, log_density = 7.425204043084886, hamiltonian_energy = -5.706670417820001, hamiltonian_energy_error = -0.17656851984089617, max_hamiltonian_energy_error = 0.7496145012326227, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9223460540630332, log_density = 6.505455922553944, hamiltonian_energy = -2.896092054178686, hamiltonian_energy_error = 0.10592251290873733, max_hamiltonian_energy_error = -0.30311904422125124, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8266778100075324, log_density = 9.12132040068985, hamiltonian_energy = -4.4128294213788015, hamiltonian_energy_error = -0.5605757270603422, max_hamiltonian_energy_error = -0.5605757270603422, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9147169134746868, log_density = 8.537852862794294, hamiltonian_energy = -8.40640427614871, hamiltonian_energy_error = 0.1481151955123785, max_hamiltonian_energy_error = 0.1481151955123785, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8879074150833844, log_density = 7.055654027097162, hamiltonian_energy = -4.163642051921965, hamiltonian_energy_error = 0.07583417860752739, max_hamiltonian_energy_error = 0.33250053626363396, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9456974836782496, log_density = 7.797414315483827, hamiltonian_energy = -5.292943306069704, hamiltonian_energy_error = -0.08698265252389259, max_hamiltonian_energy_error = 0.4410783633369899, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.834034075317146, log_density = 7.837454102524358, hamiltonian_energy = -6.457520252343988, hamiltonian_energy_error = 0.1578149165108247, max_hamiltonian_energy_error = 0.4308059277355474, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9770560678743254, log_density = 6.546521178197345, hamiltonian_energy = -6.0670254101048435, hamiltonian_energy_error = 0.14978230816632276, max_hamiltonian_energy_error = 0.14978230816632276, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 1, is_accept = true, acceptance_rate = 0.7130003838225428, log_density = 6.546521178197345, hamiltonian_energy = -5.8835836040454765, hamiltonian_energy_error = 0.0, max_hamiltonian_energy_error = 0.33827332024744905, tree_depth = 1, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7424251171545787, log_density = 5.28499020329056, hamiltonian_energy = -4.012582898698678, hamiltonian_energy_error = 0.5105161365889161, max_hamiltonian_energy_error = 0.6358061142301716, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 1.0, log_density = 8.015661510273958, hamiltonian_energy = -5.639315896265789, hamiltonian_energy_error = -0.6137869813931891, max_hamiltonian_energy_error = -0.6137869813931891, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7201924152718586, log_density = 8.82900829080957, hamiltonian_energy = -6.654524936483804, hamiltonian_energy_error = 0.15601863535840454, max_hamiltonian_energy_error = 0.6582303815157484, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9550701226599045, log_density = 7.930063441608935, hamiltonian_energy = -7.226861612669089, hamiltonian_energy_error = 0.10069273831030756, max_hamiltonian_energy_error = 0.10069273831030756, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9839864342069488, log_density = 8.163537755777611, hamiltonian_energy = -5.557306449506425, hamiltonian_energy_error = -0.07376556448351401, max_hamiltonian_energy_error = 0.074075525499115, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.6337746149169318, log_density = 2.6265775952899997, hamiltonian_energy = -0.3603730950924935, hamiltonian_energy_error = 0.027583559073136588, max_hamiltonian_energy_error = 1.1116239192079953, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9864539434303244, log_density = 4.774205036746407, hamiltonian_energy = -0.3589602016186264, hamiltonian_energy_error = -0.017436348522494427, max_hamiltonian_energy_error = -0.25743131756210147, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.890453371887913, log_density = 8.393665383501908, hamiltonian_energy = -3.1762073230906935, hamiltonian_energy_error = -0.2777405524524852, max_hamiltonian_energy_error = 0.39150493738936776, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9919061057793707, log_density = 9.137847148302882, hamiltonian_energy = -7.795655772848937, hamiltonian_energy_error = -0.08024056929725099, max_hamiltonian_energy_error = -0.08886743594510449, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.899498058460779, log_density = 8.395741460840533, hamiltonian_energy = -7.201886728115351, hamiltonian_energy_error = 0.1285801825185935, max_hamiltonian_energy_error = 0.22639426756092185, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9379149244104009, log_density = 6.873429049860244, hamiltonian_energy = -5.862168342313694, hamiltonian_energy_error = 0.11225032141559144, max_hamiltonian_energy_error = 0.13425605383407735, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6775608493217751, log_density = 8.568579059297962, hamiltonian_energy = -3.6665459253110386, hamiltonian_energy_error = -0.0554342155833778, max_hamiltonian_energy_error = 1.0440127112670021, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9940618876274094, log_density = 7.544045290809706, hamiltonian_energy = -6.846019177289583, hamiltonian_energy_error = -0.03668355984828775, max_hamiltonian_energy_error = -0.14301724592965925, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9950133021588147, log_density = 7.77353627831549, hamiltonian_energy = -6.145499598072227, hamiltonian_energy_error = 0.00464604125533441, max_hamiltonian_energy_error = -0.08827401674566815, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8523112712328064, log_density = 8.35668184727038, hamiltonian_energy = -6.038572119584926, hamiltonian_energy_error = 0.1357603210978935, max_hamiltonian_energy_error = 0.3301560833923567, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9893533882971468, log_density = 9.238355649147607, hamiltonian_energy = -8.128293063910583, hamiltonian_energy_error = -0.18961569582694615, max_hamiltonian_energy_error = -0.22564922137245347, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8888635315126044, log_density = 9.117749360581003, hamiltonian_energy = -8.155879196347524, hamiltonian_energy_error = 0.06881448731819262, max_hamiltonian_energy_error = 0.20807962710427752, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8696726716434373, log_density = 8.820690699066478, hamiltonian_energy = -6.587805394471857, hamiltonian_energy_error = 0.12495083804459206, max_hamiltonian_energy_error = 0.24822396933556856, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7368183304952931, log_density = 8.960498227869675, hamiltonian_energy = -5.5275324228134295, hamiltonian_energy_error = -0.23967711913844347, max_hamiltonian_energy_error = 0.7764072165501812, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9632165516052117, log_density = 9.441494390561777, hamiltonian_energy = -8.535667085437346, hamiltonian_energy_error = -0.005821379202831878, max_hamiltonian_energy_error = 0.0720245982356893, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9778280113453381, log_density = 7.679618214165682, hamiltonian_energy = -6.911115663065131, hamiltonian_energy_error = 0.005918871280077731, max_hamiltonian_energy_error = 0.042854032946945786, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9257718286151727, log_density = 9.572814254291206, hamiltonian_energy = -6.577489828945487, hamiltonian_energy_error = -0.053857422941937294, max_hamiltonian_energy_error = 0.10290363311385864, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8613519521404909, log_density = 7.4705174347104855, hamiltonian_energy = -7.113560543453405, hamiltonian_energy_error = 0.19934003655045274, max_hamiltonian_energy_error = 0.19934003655045274, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9410059102002383, log_density = 9.08520692868943, hamiltonian_energy = -5.3024604427142865, hamiltonian_energy_error = -0.09287175064708553, max_hamiltonian_energy_error = 0.22526942771686898, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.9143361133139664, log_density = 7.107084594582689, hamiltonian_energy = -5.14641847859189, hamiltonian_energy_error = 0.03777232662210128, max_hamiltonian_energy_error = 0.2000694562058607, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9165972551945808, log_density = 7.226231630973826, hamiltonian_energy = -5.806344911933662, hamiltonian_energy_error = 0.018930898811066577, max_hamiltonian_energy_error = 0.18073014503402351, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8026950442833568, log_density = 7.019814015324446, hamiltonian_energy = -5.873250565081715, hamiltonian_energy_error = -0.04260004745492729, max_hamiltonian_energy_error = 0.441384453109106, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9021407185841017, log_density = 8.210327053346775, hamiltonian_energy = -6.217910976312508, hamiltonian_energy_error = -0.016828455416963095, max_hamiltonian_energy_error = 0.21547406715917017, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8875446605772087, log_density = 7.479035832599505, hamiltonian_energy = -6.2719352033247375, hamiltonian_energy_error = 0.1288799723277787, max_hamiltonian_energy_error = 0.20143179199748573, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.915922561259923, log_density = 7.35488779913098, hamiltonian_energy = -4.705075574032229, hamiltonian_energy_error = -0.22327666188467532, max_hamiltonian_energy_error = 0.33427832157646087, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9041237214023679, log_density = 5.654332074760738, hamiltonian_energy = -3.143826275418225, hamiltonian_energy_error = 0.07147209480083294, max_hamiltonian_energy_error = 0.224166661872498, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8328009026964691, log_density = 3.6571685982962094, hamiltonian_energy = -2.7280213338030768, hamiltonian_energy_error = 0.35724819326554824, max_hamiltonian_energy_error = 0.35724819326554824, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9966687731629982, log_density = 5.55465274920134, hamiltonian_energy = -2.5446496842349884, hamiltonian_energy_error = -0.3246524745207271, max_hamiltonian_energy_error = -0.37254613062236297, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.965992097490641, log_density = 7.435125515823442, hamiltonian_energy = -1.8719183763421325, hamiltonian_energy_error = -0.02600132855296522, max_hamiltonian_energy_error = 0.1495300475158423, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9898456917642203, log_density = 6.356700301485066, hamiltonian_energy = -4.334441869902314, hamiltonian_energy_error = -0.01771818217695209, max_hamiltonian_energy_error = -0.15167837011388663, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9886054095399626, log_density = 6.9208635432941, hamiltonian_energy = -5.5235515601348615, hamiltonian_energy_error = -0.052841676861999254, max_hamiltonian_energy_error = -0.18480254055103096, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9882378587348439, log_density = 8.351831944138262, hamiltonian_energy = -5.187356964495653, hamiltonian_energy_error = -0.07324682308623398, max_hamiltonian_energy_error = -0.10309482888878208, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8901739744740943, log_density = 8.36114944197872, hamiltonian_energy = -4.558013052563163, hamiltonian_energy_error = 0.023437053931369967, max_hamiltonian_energy_error = 0.2507180849568602, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9950222152997338, log_density = 9.047851793337811, hamiltonian_energy = -8.141681989340203, hamiltonian_energy_error = -0.05650782167064783, max_hamiltonian_energy_error = -0.11589481342697994, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9169650672988506, log_density = 8.957237142924045, hamiltonian_energy = -7.927122048437718, hamiltonian_energy_error = 0.10801731756962685, max_hamiltonian_energy_error = 0.15669474457238586, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7768408397639514, log_density = 6.7782461969796675, hamiltonian_energy = -5.342331510159219, hamiltonian_energy_error = 0.15365694591879375, max_hamiltonian_energy_error = 0.46148184455326824, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.947060515662501, log_density = 7.4894984503890285, hamiltonian_energy = -5.5440089092062035, hamiltonian_energy_error = -0.0032743882484460585, max_hamiltonian_energy_error = -0.2806800710445696, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9921895122017312, log_density = 7.916260537441719, hamiltonian_energy = -4.717863919849499, hamiltonian_energy_error = -0.19506928648724653, max_hamiltonian_energy_error = -0.2964178862762106, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9976970995303269, log_density = 8.110664250580516, hamiltonian_energy = -6.6121667509730875, hamiltonian_energy_error = -0.023348040502859213, max_hamiltonian_energy_error = -0.057919467412434145, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.5601600744636396, log_density = 8.396605899391728, hamiltonian_energy = -3.7498331170314074, hamiltonian_energy_error = 0.23594444905632717, max_hamiltonian_energy_error = 1.0442934077691026, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.874067870508482, log_density = 7.6165655799086345, hamiltonian_energy = -5.74503961430684, hamiltonian_energy_error = -0.2090187706185862, max_hamiltonian_energy_error = 0.4369832891827512, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7522653165546807, log_density = 5.872996591804078, hamiltonian_energy = -2.8399968784859633, hamiltonian_energy_error = 0.4341362096142598, max_hamiltonian_energy_error = 0.7298663755635877, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9894497135480635, log_density = 7.50175879410901, hamiltonian_energy = -4.699891763324878, hamiltonian_energy_error = -0.056825532508106846, max_hamiltonian_energy_error = -0.2246342295008361, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9889980605084564, log_density = 7.927732899962692, hamiltonian_energy = -6.329226197421521, hamiltonian_energy_error = -0.08320967752918929, max_hamiltonian_energy_error = -0.20261449775251794, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8330315209109783, log_density = 7.168870938548604, hamiltonian_energy = -3.677782939872813, hamiltonian_energy_error = -0.027042806801429897, max_hamiltonian_energy_error = 0.35477382615126274, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7119562497549761, log_density = 7.908434440279146, hamiltonian_energy = -4.034085717690387, hamiltonian_energy_error = 0.35021911228742564, max_hamiltonian_energy_error = 0.8408778237762751, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9537657734167455, log_density = 7.087092631472162, hamiltonian_energy = -6.090082181706291, hamiltonian_energy_error = -0.15852193518473534, max_hamiltonian_energy_error = -0.15852193518473534, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8327109961910738, log_density = 5.6397134753659905, hamiltonian_energy = 1.9302576327932064, hamiltonian_energy_error = -0.229848657518132, max_hamiltonian_energy_error = 0.3875141867155101, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8577257928934529, log_density = 3.8417632566210376, hamiltonian_energy = -3.4906900279391624, hamiltonian_energy_error = 0.1921801054822745, max_hamiltonian_energy_error = 0.23241081548427456, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.6955576356666202, log_density = 4.166695302089932, hamiltonian_energy = 3.011735984998796, hamiltonian_energy_error = 0.9256586427386146, max_hamiltonian_energy_error = 1.236739177997637, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9512724802839235, log_density = 8.129878381990775, hamiltonian_energy = -3.69398801860756, hamiltonian_energy_error = -1.465173590627169, max_hamiltonian_energy_error = -1.465173590627169, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7479720862036733, log_density = 8.26835180541962, hamiltonian_energy = -6.318810911179896, hamiltonian_energy_error = -0.045254916592830874, max_hamiltonian_energy_error = 0.7945103504231916, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8405130654316701, log_density = 7.93352006470592, hamiltonian_energy = 0.030876053895168454, hamiltonian_energy_error = -0.1718285968189388, max_hamiltonian_energy_error = 0.5403947003138381, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8920313796582416, log_density = 6.817550656809951, hamiltonian_energy = -5.77177284009985, hamiltonian_energy_error = 0.21226264353246904, max_hamiltonian_energy_error = 0.2352700452048211, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9444465921084618, log_density = 6.59724556427507, hamiltonian_energy = -5.059527447572189, hamiltonian_energy_error = -0.36542884295235467, max_hamiltonian_energy_error = -0.37956555854396523, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.909207208027954, log_density = 6.685111898058176, hamiltonian_energy = -5.45704543626974, hamiltonian_energy_error = 0.017413317240655424, max_hamiltonian_energy_error = 0.22668768828756392, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7829581157733052, log_density = 5.621693260382358, hamiltonian_energy = -3.4863217315682355, hamiltonian_energy_error = 0.33781699193867487, max_hamiltonian_energy_error = 0.44013451718093055, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.8910802971515487, log_density = 8.916829902181632, hamiltonian_energy = -4.1452038485838445, hamiltonian_energy_error = -0.3232613949361358, max_hamiltonian_energy_error = -0.3232613949361358, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.7332759437182104, log_density = 8.292704698504163, hamiltonian_energy = -6.457570453430319, hamiltonian_energy_error = 0.14143488068232735, max_hamiltonian_energy_error = 0.666366521748853, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 0.9837964185189394, log_density = 6.827161067713549, hamiltonian_energy = -6.360362437014859, hamiltonian_energy_error = 0.04717633067409999, max_hamiltonian_energy_error = -0.10697598605038561, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7372532170912514, log_density = 8.257140967192425, hamiltonian_energy = -3.953187949349953, hamiltonian_energy_error = -0.3845351509872592, max_hamiltonian_energy_error = 1.2107425344663234, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7873847210195162, log_density = 8.748142390529363, hamiltonian_energy = -6.630973971884383, hamiltonian_energy_error = 0.09751945585582078, max_hamiltonian_energy_error = 0.5470767247826744, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9585413730111717, log_density = 8.37756467024884, hamiltonian_energy = -7.138744177341355, hamiltonian_energy_error = -0.015689962456360895, max_hamiltonian_energy_error = 0.14898387429239435, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9967785394932981, log_density = 8.576898008629449, hamiltonian_energy = -7.685336683163524, hamiltonian_energy_error = -0.03371316674128977, max_hamiltonian_energy_error = -0.06603020405718407, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8427556947748537, log_density = 5.331611940914062, hamiltonian_energy = -4.4806423986881025, hamiltonian_energy_error = 0.31490135759490734, max_hamiltonian_energy_error = 0.3849277302850185, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9685084287797812, log_density = 8.371606033809226, hamiltonian_energy = -3.60441791586533, hamiltonian_energy_error = -0.2971947102287529, max_hamiltonian_energy_error = -0.2971947102287529, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.7341962523535214, log_density = 6.483908628682167, hamiltonian_energy = -3.239925803288579, hamiltonian_energy_error = 0.3710548366594928, max_hamiltonian_energy_error = 0.5276543282833117, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9742170234039754, log_density = 7.114990603285888, hamiltonian_energy = -2.605362353664775, hamiltonian_energy_error = -0.4145576190607967, max_hamiltonian_energy_error = -0.4145576190607967, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8333058389124101, log_density = 6.391115791825396, hamiltonian_energy = -2.0105526053439657, hamiltonian_energy_error = 0.24445932682996663, max_hamiltonian_energy_error = 0.4443249517790284, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9086054720816693, log_density = 6.522156631811184, hamiltonian_energy = -2.995006425545415, hamiltonian_energy_error = -0.10583554372255977, max_hamiltonian_energy_error = 0.27765828977712115, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9125382949445974, log_density = 6.252342122924826, hamiltonian_energy = -3.2357351425190366, hamiltonian_energy_error = 0.06825439600828087, max_hamiltonian_energy_error = 0.28172560048108064, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.5671612505477462, log_density = 5.770780323795872, hamiltonian_energy = -3.0970442573738115, hamiltonian_energy_error = 0.4421827388233286, max_hamiltonian_energy_error = 1.4312552125534301, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9890178792140036, log_density = 4.049870980662746, hamiltonian_energy = -2.5636494805896124, hamiltonian_energy_error = 0.07999045833236318, max_hamiltonian_energy_error = -0.4595301640320719, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 4.972952469795185, hamiltonian_energy = -4.106666300030879, hamiltonian_energy_error = -0.6252290646796403, max_hamiltonian_energy_error = -0.628378898537294, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8607482179623124, log_density = 7.299312945621827, hamiltonian_energy = -1.5775285287463259, hamiltonian_energy_error = 0.005226171879316066, max_hamiltonian_energy_error = 0.3026906869139405, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.983644863198599, log_density = 9.021597217393841, hamiltonian_energy = -6.20495624575921, hamiltonian_energy_error = -0.2048565746372395, max_hamiltonian_energy_error = -0.2048565746372395, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8010894044548166, log_density = 6.97828335598944, hamiltonian_energy = -4.423542599816992, hamiltonian_energy_error = 0.25798417408281527, max_hamiltonian_energy_error = 0.5133449742830285, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8262149433611842, log_density = 5.8384209623913055, hamiltonian_energy = -4.434782139093235, hamiltonian_energy_error = 0.09000129482365615, max_hamiltonian_energy_error = 0.3781794085675658, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9682268458026494, log_density = 4.699378055613893, hamiltonian_energy = -2.3207210136479706, hamiltonian_energy_error = 0.016997058214821337, max_hamiltonian_energy_error = 0.11394870508279453, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9097553045972187, log_density = 8.296008991044506, hamiltonian_energy = -2.035180876809253, hamiltonian_energy_error = -0.12798689845914168, max_hamiltonian_energy_error = 0.21804565842793844, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8873659781269575, log_density = 8.389970020702314, hamiltonian_energy = -6.905205081741368, hamiltonian_energy_error = 0.026853301951232922, max_hamiltonian_energy_error = 0.23123507014506028, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.9860391878858489, log_density = 5.945549505266936, hamiltonian_energy = -5.208995826716329, hamiltonian_energy_error = 0.09770189459729384, max_hamiltonian_energy_error = -0.13338548960625296, tree_depth = 4, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 3, is_accept = true, acceptance_rate = 1.0, log_density = 7.13976741016959, hamiltonian_energy = -5.6862931672506365, hamiltonian_energy_error = -0.1300092984477903, max_hamiltonian_energy_error = -0.202494556047367, tree_depth = 2, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 15, is_accept = true, acceptance_rate = 0.8658072600779275, log_density = 8.935104147355267, hamiltonian_energy = -4.856335051663316, hamiltonian_energy_error = -0.18043043934932346, max_hamiltonian_energy_error = 0.3361538797070729, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9995159258043689, log_density = 8.898427171112381, hamiltonian_energy = -8.289773873440051, hamiltonian_energy_error = -0.009910651668107562, max_hamiltonian_energy_error = -0.019251451581048684, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9612535844897676, log_density = 8.850840500098169, hamiltonian_energy = -6.931401834184026, hamiltonian_energy_error = 0.03656926098655067, max_hamiltonian_energy_error = 0.0902314303199816, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 11, is_accept = true, acceptance_rate = 0.7596709402945101, log_density = 8.748048737889462, hamiltonian_energy = -6.393844025871126, hamiltonian_energy_error = 0.12433274545890871, max_hamiltonian_energy_error = 0.6507652835356659, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.8969453024767892, log_density = 6.652882561777766, hamiltonian_energy = -5.68485061166689, hamiltonian_energy_error = 0.14860449464697112, max_hamiltonian_energy_error = 0.3108167632220553, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, is_adapt = false), (n_steps = 7, is_accept = true, acceptance_rate = 0.9754354427289662, log_density = 8.20968656462486, hamiltonian_energy = -4.790662990100261, hamiltonian_energy_error = -0.12262556463237484, max_hamiltonian_energy_error = -0.22598277848720283, tree_depth = 3, numerical_error = false, step_size = 0.12681452541913416, nom_step_size = 0.12681452541913416, 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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