Doyle-Fuller-Newman (DFN) Battery Model Initialization

These benchmarks compares the runtime and error for a range of nonlinear solvers. The solvers are implemented in NonlinearProblemLibrary.jl, where you can find the problem function declarations. We test the following solvers:

Setup

Fetch required packages.

using NonlinearSolve, LinearSolve, StaticArrays, Sundials, SpeedMapping,
    BenchmarkTools, LinearAlgebra, DiffEqDevTools, PolyesterForwardDiff, CairoMakie
import MINPACK, NLsolve
RUS = RadiusUpdateSchemes;

Declare the benchmarked solvers (and their names and plotting options).

DEFAULT_FORWARD_AD = AutoForwardDiff(; chunksize = 12)

solvers_all = [
    (; pkg = :nonlinearsolve,       name = "Default PolyAlgorithm",                                  solver = Dict(:alg => FastShortcutNonlinearPolyalg(; autodiff = DEFAULT_FORWARD_AD))),
    (; pkg = :nonlinearsolve,       name = "Newton Raphson",                                         solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD))),
    (; pkg = :nonlinearsolve,       name = "Newton Raphson (HagerZhang LineSearch)",                 solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, linesearch = HagerZhang()))),
    (; pkg = :nonlinearsolve,       name = "Newton Raphson (MoreThuente LineSearch)",                solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, linesearch = MoreThuente()))),
    (; pkg = :nonlinearsolve,       name = "Newton Raphson (BackTracking LineSearch)",               solver = Dict(:alg => NewtonRaphson(; linsolve = nothing, linesearch = BackTracking()))),
    (; pkg = :nonlinearsolve,       name = "Newton Krylov with GMRES",                               solver = Dict(:alg => NewtonRaphson(; linsolve = KrylovJL_GMRES()))),
    (; pkg = :nonlinearsolve,       name = "DFSane",                                                 solver = Dict(:alg => DFSane())),
    (; pkg = :nonlinearsolve,       name = "Trust Region",                                           solver = Dict(:alg => TrustRegion())),
    (; pkg = :nonlinearsolve,       name = "Trust Region (NLsolve Update)",                          solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.NLsolve))),
    (; pkg = :nonlinearsolve,       name = "Trust Region (Nocedal Wright)",                          solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.NocedalWright))),
    (; pkg = :nonlinearsolve,       name = "Trust Region (Hei)",                                     solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Hei))),
    (; pkg = :nonlinearsolve,       name = "Trust Region (Yuan)",                                    solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Yuan))),
    (; pkg = :nonlinearsolve,       name = "Trust Region (Bastin)",                                  solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Bastin))),
    (; pkg = :nonlinearsolve,       name = "Trust Region (Fan)",                                     solver = Dict(:alg => TrustRegion(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD, radius_update_scheme = RUS.Fan))),
    (; pkg = :nonlinearsolve,       name = "Levenberg-Marquardt",                                    solver = Dict(:alg => LevenbergMarquardt(; linsolve = nothing, autodiff = DEFAULT_FORWARD_AD))),
    (; pkg = :nonlinearsolve,       name = "Levenberg-Marquardt with Cholesky",                      solver = Dict(:alg => LevenbergMarquardt(; autodiff = DEFAULT_FORWARD_AD, linsolve = CholeskyFactorization()))),
    (; pkg = :nonlinearsolve,       name = "Levenberg-Marquardt (No Geodesic Accln.)",               solver = Dict(:alg => LevenbergMarquardt(; linsolve = nothing, disable_geodesic = Val(true), autodiff = DEFAULT_FORWARD_AD))),
    (; pkg = :nonlinearsolve,       name = "Levenberg-Marquardt (No Geodesic Accln.) with Cholesky", solver = Dict(:alg => LevenbergMarquardt(; disable_geodesic = Val(true), autodiff = DEFAULT_FORWARD_AD, linsolve = CholeskyFactorization()))),
    (; pkg = :wrapper,              name = "Modified Powell [MINPACK]",                              solver = Dict(:alg => CMINPACK(; method = :hybr))),
    (; pkg = :wrapper,              name = "Levenberg-Marquardt [MINPACK]",                          solver = Dict(:alg => CMINPACK(; method = :lm))),
    (; pkg = :wrapper,              name = "Newton Raphson [NLsolve.jl]",                            solver = Dict(:alg => NLsolveJL(; method = :newton, autodiff = :forward))),
    (; pkg = :wrapper,              name = "Trust Region [NLsolve.jl]",                              solver = Dict(:alg => NLsolveJL(; autodiff = :forward))),
    (; pkg = :wrapper,              name = "Mod. Newton Raphson [Sundials]",                         solver = Dict(:alg => KINSOL())),
    (; pkg = :wrapper,              name = "Newton Krylov [Sundials]",                               solver = Dict(:alg => KINSOL(; linear_solver = :GMRES))),
    (; pkg = :wrapper,              name = "Newton Raphson with LineSearch [Sundials]",              solver = Dict(:alg => KINSOL(; globalization_strategy = :LineSearch))),
    (; pkg = :wrapper,              name = "Speed Mapping [SpeedMapping.jl]",                        solver = Dict(:alg => SpeedMappingJL()))
];

Setup the problem

function f!(out, u, p = nothing)
    out[1] = -u[33]
    out[2] = -u[32]
    out[3] = -u[31]
    out[4] = 1.9876764062810574e10(u[1] + u[4]) - 1.9876764062810574e10u[23]
    out[5] = -u[2] + (-1.5546404484393263e-11exp(-19.460872248113507(-0.4 - u[10] + u[26])))
    out[6] = -1.9876764062810574e10u[14] + 1.9876764062810574e10(u[3] + u[6])
    out[7] = -1.9876764062810574e10u[4] +
             114676.11822324689(-exp(-19.460872248113507(-0.6608489145760508 + u[25])) +
                                exp(19.460872248113507(-0.6608489145760508 + u[25])))
    out[8] = -1.9876764062810574e10u[12] + 1.9876764062810574e10(u[2] + u[5])
    out[9] = -1.9876764062810574e10u[6] +
             114676.1182232469(-exp(-19.460872248113507(-0.6608489145760508 - u[11] +
                                                        u[27])) +
                               exp(19.460872248113507(-0.6608489145760508 - u[11] + u[27])))
    out[10] = -4.284490145672665e10u[19] + 4.284490145672665e10(u[31] + u[7])
    out[11] = -4.284490145672665e10u[21] + 4.284490145672665e10(u[32] + u[8])
    out[12] = -4.284490145672665e10u[22] + 4.284490145672665e10(u[33] + u[9])
    out[13] = 0.025692579121085843(7.680104664733624e7(u[10] - u[11]) +
                                   7.680104664733624e7u[10]) - 1.793773306620288e9u[12]
    out[14] = -u[3] +
              (-1.5546404484393263e-11exp(-19.460872248113507(-0.4 - u[11] + u[27])))
    out[15] = -1.9876764062810574e10u[5] +
              114676.1182232469(-exp(-19.460872248113507(-0.6608489145760506 - u[10] +
                                                         u[26])) +
                                exp(19.460872248113507(-0.6608489145760506 - u[10] +
                                                       u[26])))
    out[16] = 0.025692579121085843(7.680104664733624e7(-u[10] + u[11]) +
                                   1.4529008434739566e8(u[11] - u[13])) -
              1.793773306620288e9u[14]
    out[17] = -1.793773306620288e9u[14] - 1.4404300298567445e9(-u[26] + u[27])
    out[18] = 0.025692579121085843(5.1142109690283257e8(-u[11] + u[13]) +
                                   4.7254130462088e9(u[13] - u[15]))
    out[19] = 0.025692579121085843(4.7254130462088e9(-u[13] + u[15]) +
                                   4.7254130462088e9(u[15] - u[16]))
    out[20] = 0.025692579121085843(4.7254130462088e9(-u[15] + u[16]) +
                                   2.3040372207628164e8(u[16] - u[17]))
    out[21] = 0.025692579121085843(7.200116314883803e7(-u[16] + u[17]) +
                                   3.6900178974461965e7(u[17] - u[18])) -
              2.193876971198113e9u[19]
    out[22] = -4.284490145672665e10u[7] +
              147554.10828979727(-exp(-19.460872248113507(-3.3618450059739535 - u[17] +
                                                          u[28])) +
                                 exp(19.460872248113507(-3.3618450059739535 - u[17] +
                                                        u[28])))
    out[23] = 0.025692579121085843(3.6900178974461965e7(-u[17] + u[18]) +
                                   3.6900178974461965e7(u[18] - u[20])) -
              2.193876971198113e9u[21]
    out[24] = -4.284490145672665e10u[8] +
              147554.10828979727(-exp(-19.460872248113507(-3.3618450059739535 - u[18] +
                                                          u[29])) +
                                 exp(19.460872248113507(-3.3618450059739535 - u[18] +
                                                        u[29])))
    out[25] = 948060.7678835923(-u[18] + u[20]) - 2.193876971198113e9u[22]
    out[26] = -u[1] + (-1.5546404484393263e-11exp(-19.460872248113507(-0.4 + u[25])))
    out[27] = -2.193876971198113e9u[22] +
              0.025692579121085843(-37499.99999999999u[24] -
                                   8.296874999999998e10(-u[29] + u[30]))
    out[28] = -1.793773306620288e9u[23] +
              0.025692579121085843(34090.90909090909u[24] -
                                   5.6064049586776855e10(u[25] - u[26]))
    out[29] = -1.793773306620288e9u[12] +
              0.025692579121085843(-5.6064049586776855e10(-u[25] + u[26]) -
                                   5.6064049586776855e10(u[26] - u[27]))
    out[30] = -2.193876971198113e9u[19] - 2.1316811739525905e9(u[28] - u[29])
    out[31] = -2.193876971198113e9u[21] +
              0.025692579121085843(-8.296874999999998e10(-u[28] + u[29]) -
                                   8.296874999999998e10(u[29] - u[30]))
    out[32] = -4.284490145672665e10u[9] +
              147554.10828979727(-exp(-19.460872248113507(-3.3618450059739535 - u[20] +
                                                          u[30])) +
                                 exp(19.460872248113507(-3.3618450059739535 - u[20] +
                                                        u[30])))
    out[33] = 292.3000724036127 + u[24]
    nothing
end

n = 1
x_sol = [
    -3.889310081682032e-13,
    -5.690845522092043e-13,
    -1.4900105367898274e-12,
    -2.1680981422696e-5,
    -3.284624075480569e-5,
    -8.820027287447222e-5,
    9.53999632159426e-5,
    2.1138249693289567e-5,
    1.1829446876191545e-5,
    0.019709320908045884,
    0.06927785744111935,
    -3.2846241323890243e-5,
    0.13786323434647954,
    -8.820027436448276e-5,
    0.14528607936456214,
    0.15270892438264475,
    0.3049460860584471,
    0.3812355737657502,
    9.53999632159426e-5,
    0.40860971681949443,
    2.1138249693289567e-5,
    1.1829446876191545e-5,
    -2.1680981811627007e-5,
    -292.3000724036127,
    0.5895178515117894,
    0.5896685912243755,
    0.5897784273806014,
    3.837532182598256,
    3.8376303660343676,
    3.837750304468262,
    0.0,
    0.0,
    0.0,
]
x_start = zeros(length(x_sol))
x_start[25:27] .= 0.6608489145760508
x_start[28:30] .= 3.3618450059739433

dict = Dict("n" => n, "start" => x_start, "sol" => x_sol, "title" => "Doyle-Fuller-Newman (DFN) Battery Model Initialization")

testcase = (; prob = NonlinearProblem(f!, dict["start"]), true_sol = dict["sol"])
(prob = SciMLBase.NonlinearProblem{Vector{Float64}, true, SciMLBase.NullPar
ameters, SciMLBase.NonlinearFunction{true, SciMLBase.FullSpecialize, typeof
(Main.var"##WeaveSandBox#225".f!), LinearAlgebra.UniformScaling{Bool}, Noth
ing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing
, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing, Nothing, No
thing}, Base.Pairs{Symbol, Union{}, Tuple{}, @NamedTuple{}}, SciMLBase.Stan
dardNonlinearProblem}(SciMLBase.NonlinearFunction{true, SciMLBase.FullSpeci
alize, typeof(Main.var"##WeaveSandBox#225".f!), LinearAlgebra.UniformScalin
g{Bool}, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Nothing, Not
hing, Nothing, Nothing, typeof(SciMLBase.DEFAULT_OBSERVED_NO_TIME), Nothing
, Nothing, Nothing}(Main.var"##WeaveSandBox#225".f!, LinearAlgebra.UniformS
caling{Bool}(true), nothing, nothing, nothing, nothing, nothing, nothing, n
othing, nothing, nothing, nothing, SciMLBase.DEFAULT_OBSERVED_NO_TIME, noth
ing, nothing, nothing), [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  
…  0.0, 0.6608489145760508, 0.6608489145760508, 0.6608489145760508, 3.36184
50059739433, 3.3618450059739433, 3.3618450059739433, 0.0, 0.0, 0.0], SciMLB
ase.NullParameters(), SciMLBase.StandardNonlinearProblem(), Base.Pairs{Symb
ol, Union{}, Tuple{}, @NamedTuple{}}()), true_sol = [-3.889310081682032e-13
, -5.690845522092043e-13, -1.4900105367898274e-12, -2.1680981422696e-5, -3.
284624075480569e-5, -8.820027287447222e-5, 9.53999632159426e-5, 2.113824969
3289567e-5, 1.1829446876191545e-5, 0.019709320908045884  …  -292.3000724036
127, 0.5895178515117894, 0.5896685912243755, 0.5897784273806014, 3.83753218
2598256, 3.8376303660343676, 3.837750304468262, 0.0, 0.0, 0.0])

Sets tolerances.

abstols = 1.0 ./ 10.0 .^ (3:0.5:6)
reltols = 1.0 ./ 10.0 .^ (3:0.5:6);

Prepares various helper functions for benchmarking a specific problem.

function check_solver(prob, solver)
    try
        sol = solve(prob.prob, solver.solver[:alg]; abstol = 1e-4, reltol = 1e-4,
            maxiters = 10000)
        err = norm(sol.resid, Inf)
        if !SciMLBase.successful_retcode(sol.retcode)
            Base.printstyled("[Warn] Solver $(solver.name) returned retcode $(sol.retcode) with an residual norm = $(norm(sol.resid)).\n";
                color = :red)
            return false
        elseif err > 1e3
            Base.printstyled("[Warn] Solver $(solver.name) had a very large residual (norm = $(norm(sol.resid))).\n";
                color = :red)
            return false
        elseif isinf(err) || isnan(err)
            Base.printstyled("[Warn] Solver $(solver.name) had a residual of $(err).\n";
                color = :red)
            return false
        end
        Base.printstyled("[Info] Solver $(solver.name) successfully solved the problem (norm = $(norm(sol.resid))).\n";
            color = :green)
    catch e
        Base.printstyled("[Warn] Solver $(solver.name) threw an error: $e.\n"; color = :red)
        return false
    end
    return true
end

function generate_wpset(prob, solvers)
    # Finds the solvers that can solve the problem
    successful_solvers = filter(solver -> check_solver(prob, solver), solvers)

    return WorkPrecisionSet(prob.prob, abstols, reltols,
        getfield.(successful_solvers, :solver);
        names = getfield.(successful_solvers, :name), numruns = 50, error_estimate = :l∞,
        maxiters = 10000, verbose = true), successful_solvers
end
generate_wpset (generic function with 1 method)

Benchmarks

We here run benchmarks for each of the solvers.

Problem

wp_set, successful_solvers = generate_wpset(testcase, solvers_all);
[Info] Solver Default PolyAlgorithm successfully solved the problem (norm =
 1.5941038377860503e-6).
[Info] Solver Newton Raphson successfully solved the problem (norm = 1.5941
038377860503e-6).
[Warn] Solver Newton Raphson (HagerZhang LineSearch) returned retcode MaxIt
ers with an residual norm = 211.22117514557985.
[Warn] Solver Newton Raphson (MoreThuente LineSearch) returned retcode MaxI
ters with an residual norm = 215.32908275968444.
[Warn] Solver Newton Raphson (BackTracking LineSearch) returned retcode Int
ernalLineSearchFailed with an residual norm = 228.52744889002022.
[Warn] Solver Newton Krylov with GMRES returned retcode Unstable with an re
sidual norm = 292.3000724036127.
[Warn] Solver DFSane returned retcode Stalled with an residual norm = 292.3
000724036127.
[Info] Solver Trust Region successfully solved the problem (norm = 6.955145
971889403e-7).
[Info] Solver Trust Region (NLsolve Update) successfully solved the problem
 (norm = 6.87247134580685e-7).
[Info] Solver Trust Region (Nocedal Wright) successfully solved the problem
 (norm = 1.5941545843685634e-6).
[Info] Solver Trust Region (Hei) successfully solved the problem (norm = 7.
594866209720793e-7).
[Warn] Solver Trust Region (Yuan) returned retcode MaxIters with an residua
l norm = 159.7556690579833.
[Info] Solver Trust Region (Bastin) successfully solved the problem (norm =
 1.5942054286257434e-6).
[Info] Solver Trust Region (Fan) successfully solved the problem (norm = 7.
521466255487002e-7).
[Info] Solver Levenberg-Marquardt successfully solved the problem (norm = 7
.38426369554924e-5).
[Warn] Solver Levenberg-Marquardt with Cholesky returned retcode Stalled wi
th an residual norm = 0.00039458054329866794.
[Info] Solver Levenberg-Marquardt (No Geodesic Accln.) successfully solved 
the problem (norm = 5.246607252366464e-7).
[Warn] Solver Levenberg-Marquardt (No Geodesic Accln.) with Cholesky return
ed retcode Unstable with an residual norm = 0.0003015473498789062.
[Warn] Solver Modified Powell [MINPACK] returned retcode Failure with an re
sidual norm = 292.3000724036127.
[Warn] Solver Levenberg-Marquardt [MINPACK] returned retcode Failure with a
n residual norm = 292.3000724036127.
[Info] Solver Newton Raphson [NLsolve.jl] successfully solved the problem (
norm = 1.5941104186169045e-6).
[Info] Solver Trust Region [NLsolve.jl] successfully solved the problem (no
rm = 6.940612093440701e-7).
[Warn] Solver Mod. Newton Raphson [Sundials] had a residual of NaN.
[Warn] Solver Newton Krylov [Sundials] returned retcode Failure with an res
idual norm = 292.3000724036127.
[Warn] Solver Newton Raphson with LineSearch [Sundials] returned retcode Fa
ilure with an residual norm = 287.9954636633953.
[Warn] Solver Speed Mapping [SpeedMapping.jl] returned retcode Failure with
 an residual norm = 1.8355122321179187e92.

Plot and Save the Plot

fig = begin
    LINESTYLES = Dict(:nonlinearsolve => :solid, :simplenonlinearsolve => :dash,
        :wrapper => :dot)
    ASPECT_RATIO = 0.7
    WIDTH = 1200
    HEIGHT = round(Int, WIDTH * ASPECT_RATIO)
    STROKEWIDTH = 2.5

    colors = cgrad(:seaborn_bright, length(successful_solvers); categorical = true)
    cycle = Cycle([:marker], covary = true)
    plot_theme = Theme(Lines = (; cycle), Scatter = (; cycle))

    idxs = sortperm(median.(getfield.(wp_set.wps, :times)))

    with_theme(plot_theme) do 
        fig = Figure(; size = (WIDTH, HEIGHT))
        # `textbf` doesn't work
        ax = Axis(fig[1, 1], ylabel = L"Time $\mathbf{(s)}$",
            xlabelsize = 22, ylabelsize = 22,
            xlabel = L"Error: $\mathbf{||f(u^\ast)||_\infty}$",
            xscale = log10, yscale = log10, xtickwidth = STROKEWIDTH,
            ytickwidth = STROKEWIDTH, spinewidth = STROKEWIDTH,
            xticklabelsize = 20, yticklabelsize = 20)

        ls, scs = [], []

        for (i, (wp, solver)) in enumerate(zip(wp_set.wps[idxs], successful_solvers[idxs]))
            (; name, times, errors) = wp
            errors = [err.l∞ for err in errors]
            l = lines!(ax, errors, times; linestyle = LINESTYLES[solver.pkg], label = name,
                linewidth = 5, color = colors[i])
            sc = scatter!(ax, errors, times; label = name, markersize = 16, strokewidth = 3,
                color = colors[i])
            push!(ls, l)
            push!(scs, sc)
        end

        axislegend(ax, [[l, sc] for (l, sc) in zip(ls, scs)],
            [solver.name for solver in successful_solvers[idxs]], "Successful Solvers\n(Fastest to Slowest)";
            framevisible=true, framewidth = STROKEWIDTH, orientation = :vertical,
            titlesize = 20, nbanks = 1, labelsize = 16,#  margin = (0.0, 80.0, 0.0, 0.0),
            tellheight = false, tellwidth = true, patchsize = (40.0f0, 20.0f0),
            position = :rb)

        fig[0, :] = Label(fig, "Doyle-Fuller-Newman (DFN) Battery Model Initialization: Work Precision Diagram",
            fontsize = 24, tellwidth = false, font = :bold)

        fig
    end
end

save("battery_problem_work_precision.svg", fig)
CairoMakie.Screen{SVG}

Summary of successful solvers

Finally, we print a summary of which solvers successfully solved which problems.

solver_successes = [(solver in successful_solvers) ? "✔" : "✖" for solver in solvers_all];
using PrettyTables
io = IOBuffer()
println(io, "```@raw html")
pretty_table(io, reshape(solver_successes, 1, :); backend = Val(:html),
    header = getfield.(solvers_all, :name), alignment=:c)
println(io, "```")
Docs.Text(String(take!(io)))
Default PolyAlgorithmNewton RaphsonNewton Raphson (HagerZhang LineSearch)Newton Raphson (MoreThuente LineSearch)Newton Raphson (BackTracking LineSearch)Newton Krylov with GMRESDFSaneTrust RegionTrust Region (NLsolve Update)Trust Region (Nocedal Wright)Trust Region (Hei)Trust Region (Yuan)Trust Region (Bastin)Trust Region (Fan)Levenberg-MarquardtLevenberg-Marquardt with CholeskyLevenberg-Marquardt (No Geodesic Accln.)Levenberg-Marquardt (No Geodesic Accln.) with CholeskyModified Powell [MINPACK]Levenberg-Marquardt [MINPACK]Newton Raphson [NLsolve.jl]Trust Region [NLsolve.jl]Mod. Newton Raphson [Sundials]Newton Krylov [Sundials]Newton Raphson with LineSearch [Sundials]Speed Mapping [SpeedMapping.jl]

Appendix

These benchmarks are a part of the SciMLBenchmarks.jl repository, found at: https://github.com/SciML/SciMLBenchmarks.jl. For more information on high-performance scientific machine learning, check out the SciML Open Source Software Organization https://sciml.ai.

To locally run this benchmark, do the following commands:

using SciMLBenchmarks
SciMLBenchmarks.weave_file("benchmarks/NonlinearProblem","nonlinear_battery_problem.jmd")

Computer Information:

Julia Version 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 128 × AMD EPYC 7502 32-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
  JULIA_CPU_THREADS = 128
  JULIA_DEPOT_PATH = /cache/julia-buildkite-plugin/depots/5b300254-1738-4989-ae0a-f4d2d937f953

Package Information:

Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Project.toml`
  [2169fc97] AlgebraicMultigrid v0.6.0
  [6e4b80f9] BenchmarkTools v1.5.0
  [13f3f980] CairoMakie v0.11.9
  [2b5f629d] DiffEqBase v6.148.0
  [f3b72e0c] DiffEqDevTools v2.44.2
  [40713840] IncompleteLU v0.2.1
  [b964fa9f] LaTeXStrings v1.3.1
  [7ed4a6bd] LinearSolve v2.27.0
  [4854310b] MINPACK v1.2.0
  [2774e3e8] NLsolve v4.5.1
  [b7050fa9] NonlinearProblemLibrary v0.1.2
  [8913a72c] NonlinearSolve v3.8.0
  [98d1487c] PolyesterForwardDiff v0.1.1
  [08abe8d2] PrettyTables v2.3.1
  [31c91b34] SciMLBenchmarks v0.1.3
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.6.0
  [47a9eef4] SparseDiffTools v2.17.0
  [f1835b91] SpeedMapping v0.3.0
  [860ef19b] StableRNGs v1.0.1
  [90137ffa] StaticArrays v1.9.3
  [c3572dad] Sundials v4.24.0
⌃ [0c5d862f] Symbolics v5.23.0
Info Packages marked with ⌃ have new versions available and may be upgradable.

And the full manifest:

Status `/cache/build/exclusive-amdci3-0/julialang/scimlbenchmarks-dot-jl/benchmarks/NonlinearProblem/Manifest.toml`
⌃ [47edcb42] ADTypes v0.2.6
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  [79e6a3ab] Adapt v4.0.3
  [2169fc97] AlgebraicMultigrid v0.6.0
  [27a7e980] Animations v0.4.1
⌅ [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v7.9.0
  [4c555306] ArrayLayouts v1.6.1
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  [6e4b80f9] BenchmarkTools v1.5.0
  [e2ed5e7c] Bijections v0.1.6
  [d1d4a3ce] BitFlags v0.1.8
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
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  [5ae59095] Colors v0.12.10
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  [34da2185] Compat v4.14.0
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⌃ [f0e56b4a] ConcurrentUtilities v2.3.1
  [8f4d0f93] Conda v1.10.0
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⌃ [5b8099bc] DomainSets v0.7.9
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⌃ [f151be2c] EnzymeCore v0.6.5
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⌃ [d7ba0133] Git v1.3.0
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  [eafb193a] Highlights v0.5.2
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  [34004b35] HypergeometricFunctions v0.3.23
  [7073ff75] IJulia v1.24.2
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  [615f187c] IfElse v0.1.1
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  [40713840] IncompleteLU v0.2.1
  [9b13fd28] IndirectArrays v1.0.0
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  [d1acc4aa] IntervalArithmetic v0.22.8
  [8197267c] IntervalSets v0.7.10
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⌃ [0c5d862f] Symbolics v5.23.0
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⌅ [e9f186c6] Libffi_jll v3.2.2+1
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  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.2+1
  [14a3606d] MozillaCACerts_jll v2023.1.10
  [4536629a] OpenBLAS_jll v0.3.23+4
  [05823500] OpenLibm_jll v0.8.1+2
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.8.0+1
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.4.0+2
Info Packages marked with ⌃ and ⌅ have new versions available. Those with ⌃ may be upgradable, but those with ⌅ are restricted by compatibility constraints from upgrading. To see why use `status --outdated -m`