RADAR5 Robertson Work-Precision Diagrams

RADAR5 Robertson Chemical Reaction

This is a stiff delay differential equation model of a chemical reaction with a steady state solution, taken from the RADAR5 test suite by Guglielmi and Hairer. The system has dimension 3 with one constant delay.

\[u_1'(t) = -a \, u_1(t) + b \, u_2(t - \tau) \, u_3(t)\]

\[u_2'(t) = a \, u_1(t) - b \, u_2(t - \tau) \, u_3(t) - c \, u_2(t)^2\]

\[u_3'(t) = c \, u_2(t)^2\]

for $t \in [0, 1]$ with initial conditions $u_1(0) = 1$, $u_2(t) = 0$ for $t \in [-\tau, 0]$, and $u_3(0) = 0$, where $a = 0.04$, $b = 10000$, $c = 3 \times 10^7$, and $\tau = 0.01$.

This is the DDE analogue of the classic Robertson ODE problem. The extreme stiffness arises from the ratio $c/a = 7.5 \times 10^8$ between the fastest and slowest time scales. In the original RADAR5 formulation the problem is integrated up to $t = 10^{10}$, but this is currently not achievable with the method of steps approach in DelayDiffEq.jl. We benchmark on the interval $[0, 1]$ which already demonstrates the stiffness challenges.

References

Guglielmi, N. and Hairer, E. (2001). Implementing Radau IIA methods for stiff delay differential equations, Computing (67), pp. 1-12.

using DelayDiffEq, DiffEqDevTools, DDEProblemLibrary, Plots
using OrdinaryDiffEqCore: IController
using OrdinaryDiffEqLowOrderRK, OrdinaryDiffEqRosenbrock, OrdinaryDiffEqSDIRK,
    OrdinaryDiffEqTsit5
import DDEProblemLibrary: prob_dde_RADAR5_robertson
gr()

Plots.GRBackend()

Problem Setup

We use a truncated time span of $[0, 1]$ for benchmarking:

prob = remake(prob_dde_RADAR5_robertson; tspan = (0.0, 1.0))

DDEProblem with uType Vector{Float64} and tType Float64. In-place: true
Non-trivial mass matrix: false
timespan: (0.0, 1.0)
u0: 3-element Vector{Float64}:
 1.0
 0.0
 0.0

Reference Solution

Due to the extreme stiffness and the small scale of the second component ($u_2 \sim O(10^{-5})$), we use component-wise absolute tolerances to compute the reference solution:

sol = solve(
    prob, MethodOfSteps(Rodas5P());
    reltol = 1.0e-14, abstol = [1.0e-14, 1.0e-20, 1.0e-14], dt = 1.0e-6
)
test_sol = TestSolution(sol)
plot(sol; title = "Robertson DDE Solution (t ∈ [0, 1])")

High Tolerances

Rosenbrock methods

abstols = 1.0 ./ 10.0 .^ (4:7)
reltols = 1.0 ./ 10.0 .^ (1:4)

setups = [
    Dict(:alg => MethodOfSteps(Rosenbrock23())),
    Dict(:alg => MethodOfSteps(Rodas4())),
    Dict(:alg => MethodOfSteps(Rodas5())),
    Dict(:alg => MethodOfSteps(Rodas5P())),
]
names = ["Rosenbrock23", "Rodas4", "Rodas5", "Rodas5P"]
wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e5), error_estimate = :final,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: Rosenbrock Methods (final error)")

wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e5), error_estimate = :L2,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: Rosenbrock Methods (L2 error)")

SDIRK methods

setups = [
    Dict(:alg => MethodOfSteps(TRBDF2())),
    Dict(
        :alg => MethodOfSteps(SDIRK2()),
        :controller => IController(SDIRK2(); qmax = 10, qmax_first_step = 10)
    ),
    Dict(:alg => MethodOfSteps(KenCarp4())),
]
names = ["TRBDF2", "SDIRK2", "KenCarp4"]
wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e5), error_estimate = :final,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: SDIRK Methods (final error)")

wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e5), error_estimate = :L2,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: SDIRK Methods (L2 error)")

Stiff vs Non-Stiff Comparison

setups = [
    Dict(:alg => MethodOfSteps(Rodas5P())),
    Dict(:alg => MethodOfSteps(TRBDF2())),
    Dict(:alg => MethodOfSteps(KenCarp4())),
    Dict(:alg => MethodOfSteps(Tsit5())),
    Dict(:alg => MethodOfSteps(DP5())),
]
names = ["Rodas5P", "TRBDF2", "KenCarp4", "Tsit5", "DP5"]
wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e6), error_estimate = :final,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: Stiff vs Non-Stiff (final error)")

Low Tolerances

abstols = 1.0 ./ 10.0 .^ (8:11)
reltols = 1.0 ./ 10.0 .^ (5:8)

setups = [
    Dict(:alg => MethodOfSteps(Rosenbrock23())),
    Dict(:alg => MethodOfSteps(Rodas4())),
    Dict(:alg => MethodOfSteps(Rodas5())),
    Dict(:alg => MethodOfSteps(Rodas5P())),
    Dict(:alg => MethodOfSteps(TRBDF2())),
    Dict(:alg => MethodOfSteps(KenCarp4())),
]
names = ["Rosenbrock23", "Rodas4", "Rodas5", "Rodas5P", "TRBDF2", "KenCarp4"]
wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e5), error_estimate = :final,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: Low Tolerances (final error)")

wp = WorkPrecisionSet(
    prob, abstols, reltols, setups;
    names = names, appxsol = test_sol, maxiters = Int(1.0e5), error_estimate = :L2,
    dt = 1.0e-6
)
plot(wp; title = "Robertson: Low Tolerances (L2 error)")

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/StiffDDE","Robertson_wpd.jmd")

Computer Information:

Julia Version 1.11.9
Commit 53a02c0720c (2026-02-06 00:27 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
  LLVM: libLLVM-16.0.6 (ORCJIT, znver2)
Threads: 128 default, 0 interactive, 64 GC (on 128 virtual cores)
Environment:
  JULIA_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/StiffDDE/Project.toml`
⌃ [f42792ee] DDEProblemLibrary v0.1.5
⌃ [bcd4f6db] DelayDiffEq v6.0.0
⌃ [f3b72e0c] DiffEqDevTools v3.0.0
⌅ [bbf590c4] OrdinaryDiffEqCore v4.0.0
⌃ [d28bc4f8] OrdinaryDiffEqHighOrderRK v2.0.0
⌃ [1344f307] OrdinaryDiffEqLowOrderRK v2.0.0
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.0.0
⌅ [2d112036] OrdinaryDiffEqSDIRK v2.0.0
⌃ [b1df2697] OrdinaryDiffEqTsit5 v2.0.0
⌃ [79d7bb75] OrdinaryDiffEqVerner v2.0.0
⌃ [91a5bcdd] Plots v1.41.6
⌃ [31c91b34] SciMLBenchmarks v0.1.3
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`

And the full manifest:

Status `~/github-runners/amdci3-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/StiffDDE/Manifest.toml`
⌃ [47edcb42] ADTypes v1.22.0
⌃ [7d9f7c33] Accessors v0.1.44
⌃ [79e6a3ab] Adapt v4.5.2
  [66dad0bd] AliasTables v1.1.3
⌃ [4fba245c] ArrayInterface v7.24.0
⌃ [d1d4a3ce] BitFlags v0.1.9
⌃ [70df07ce] BracketingNonlinearSolve v1.12.1
⌃ [944b1d66] CodecZlib v0.7.8
  [35d6a980] ColorSchemes v3.31.0
  [3da002f7] ColorTypes v0.12.1
  [c3611d14] ColorVectorSpace v0.11.0
  [5ae59095] Colors v0.13.1
⌃ [38540f10] CommonSolve v0.2.6
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.18.1
  [a33af91c] CompositionsBase v0.1.2
⌃ [2569d6c7] ConcreteStructs v0.2.3
⌃ [f0e56b4a] ConcurrentUtilities v2.5.1
  [8f4d0f93] Conda v1.10.3
  [187b0558] ConstructionBase v1.6.0
  [d38c429a] Contour v0.6.3
⌃ [f42792ee] DDEProblemLibrary v0.1.5
  [9a962f9c] DataAPI v1.16.0
⌃ [864edb3b] DataStructures v0.19.4
  [e2d170a0] DataValueInterfaces v1.0.0
⌃ [bcd4f6db] DelayDiffEq v6.0.0
  [8bb1440f] DelimitedFiles v1.9.1
⌃ [2b5f629d] DiffEqBase v7.1.0
⌃ [f3b72e0c] DiffEqDevTools v3.0.0
⌃ [77a26b50] DiffEqNoiseProcess v5.31.0
  [163ba53b] DiffResults v1.1.0
⌃ [b552c78f] DiffRules v1.15.1
⌃ [a0c0ee7d] DifferentiationInterface v0.7.17
  [b4f34e82] Distances v0.10.12
⌃ [31c24e10] Distributions v0.25.125
  [ffbed154] DocStringExtensions v0.9.5
  [4e289a0a] EnumX v1.0.7
⌃ [f151be2c] EnzymeCore v0.8.20
  [460bff9d] ExceptionUnwrapping v0.1.11
⌃ [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.5
⌃ [7034ab61] FastBroadcast v1.3.2
  [9aa1b823] FastClosures v0.3.2
⌃ [a4df4552] FastPower v1.3.1
⌃ [1a297f60] FillArrays v1.16.0
⌃ [6a86dc24] FiniteDiff v2.31.0
⌅ [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
⌃ [f6369f11] ForwardDiff v1.3.3
  [069b7b12] FunctionWrappers v1.1.3
⌃ [77dc65aa] FunctionWrappersWrappers v1.8.0
  [46192b85] GPUArraysCore v0.2.0
⌃ [28b8d3ca] GR v0.73.24
  [d7ba0133] Git v1.5.0
  [42e2da0e] Grisu v1.0.2
⌅ [cd3eb016] HTTP v1.11.0
⌅ [eafb193a] Highlights v0.5.3
⌃ [34004b35] HypergeometricFunctions v0.3.28
  [7073ff75] IJulia v1.34.4
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.6
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.11
⌃ [692b3bcd] JLLWrappers v1.7.1
⌅ [682c06a0] JSON v0.21.4
⌃ [ba0b0d4f] Krylov v0.10.6
⌃ [b964fa9f] LaTeXStrings v1.4.0
⌃ [23fbe1c1] Latexify v0.16.10
⌃ [87fe0de2] LineSearch v0.1.9
⌃ [d3d80556] LineSearches v7.5.1
⌅ [7ed4a6bd] LinearSolve v3.75.0
⌅ [2ab3a3ac] LogExpFunctions v0.3.29
  [e6f89c97] LoggingExtras v1.2.0
  [1914dd2f] MacroTools v0.5.16
⌃ [bb5d69b7] MaybeInplace v0.1.4
  [739be429] MbedTLS v1.1.10
  [442fdcdd] Measures v0.3.3
  [e1d29d7a] Missings v1.2.0
⌃ [46d2c3a1] MuladdMacro v0.2.4
  [ffc61752] Mustache v1.0.21
⌅ [d41bc354] NLSolversBase v7.10.0
⌅ [2774e3e8] NLsolve v4.5.1
⌃ [77ba4419] NaNMath v1.1.3
⌃ [8913a72c] NonlinearSolve v4.19.0
⌅ [be0214bd] NonlinearSolveBase v2.25.0
⌃ [5959db7a] NonlinearSolveFirstOrder v2.1.1
⌃ [9a2c21bd] NonlinearSolveQuasiNewton v1.13.1
⌃ [26075421] NonlinearSolveSpectralMethods v1.7.1
  [4d8831e6] OpenSSL v1.6.1
⌅ [bac558e1] OrderedCollections v1.8.1
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.0.0
⌅ [bbf590c4] OrdinaryDiffEqCore v4.0.0
⌃ [50262376] OrdinaryDiffEqDefault v2.1.0
⌅ [4302a76b] OrdinaryDiffEqDifferentiation v3.0.0
⌃ [d3585ca7] OrdinaryDiffEqFunctionMap v2.0.0
⌃ [d28bc4f8] OrdinaryDiffEqHighOrderRK v2.0.0
⌃ [1344f307] OrdinaryDiffEqLowOrderRK v2.0.0
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.0.0
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.0.0
⌃ [b4bd8bb3] OrdinaryDiffEqRosenbrockTableaus v2.0.0
⌅ [2d112036] OrdinaryDiffEqSDIRK v2.0.0
⌃ [b1df2697] OrdinaryDiffEqTsit5 v2.0.0
⌃ [79d7bb75] OrdinaryDiffEqVerner v2.0.0
⌃ [90014a1f] PDMats v0.11.37
⌅ [69de0a69] Parsers v2.8.4
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
⌃ [91a5bcdd] Plots v1.41.6
⌃ [e409e4f3] PoissonRandom v0.4.7
⌃ [d236fae5] PreallocationTools v1.2.0
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.2
  [43287f4e] PtrArrays v1.4.0
  [1fd47b50] QuadGK v2.11.3
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌃ [731186ca] RecursiveArrayTools v4.3.0
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
⌃ [ae5879a3] ResettableStacks v1.2.0
  [79098fc4] Rmath v0.9.0
⌃ [47965b36] RootedTrees v2.25.0
⌃ [7e49a35a] RuntimeGeneratedFunctions v0.5.18
⌅ [0bca4576] SciMLBase v3.7.1
⌃ [31c91b34] SciMLBenchmarks v0.1.3
⌃ [19f34311] SciMLJacobianOperators v0.1.13
⌅ [a6db7da4] SciMLLogging v1.9.1
⌃ [c0aeaf25] SciMLOperators v1.17.0
⌃ [431bcebd] SciMLPublic v1.0.1
⌃ [53ae85a6] SciMLStructures v1.10.0
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
⌃ [727e6d20] SimpleNonlinearSolve v2.11.1
⌃ [a2af1166] SortingAlgorithms v1.2.2
  [0a514795] SparseMatrixColorings v0.4.27
⌃ [276daf66] SpecialFunctions v2.7.2
  [860ef19b] StableRNGs v1.0.4
⌃ [90137ffa] StaticArrays v1.9.18
  [1e83bf80] StaticArraysCore v1.4.4
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.8.0
⌃ [2913bbd2] StatsBase v0.34.10
⌅ [4c63d2b9] StatsFuns v1.5.2
  [69024149] StringEncodings v0.3.7
  [09ab397b] StructArrays v0.7.3
⌃ [2efcf032] SymbolicIndexingInterface v0.3.46
  [3783bdb8] TableTraits v1.0.1
⌃ [bd369af6] Tables v1.12.1
  [62fd8b95] TensorCore v0.1.1
⌅ [a759f4b9] TimerOutputs v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.3
  [781d530d] TruncatedStacktraces v1.4.0
⌃ [5c2747f8] URIs v1.6.1
  [1cfade01] UnicodeFun v0.4.1
  [41fe7b60] Unzip v0.2.0
  [81def892] VersionParsing v1.3.0
  [44d3d7a6] Weave v0.10.12
  [ddb6d928] YAML v0.4.16
  [c2297ded] ZMQ v1.5.1
  [6e34b625] Bzip2_jll v1.0.9+0
⌃ [83423d85] Cairo_jll v1.18.6+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
⌃ [2e619515] Expat_jll v2.8.0+0
⌅ [b22a6f82] FFMPEG_jll v8.1.0+0
  [a3f928ae] Fontconfig_jll v2.17.1+0
  [d7e528f0] FreeType2_jll v2.14.3+1
  [559328eb] FriBidi_jll v1.0.17+0
⌃ [0656b61e] GLFW_jll v3.4.1+1
⌅ [d2c73de3] GR_jll v0.73.24+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
⌃ [020c3dae] Git_LFS_jll v3.7.0+0
⌃ [f8c6e375] Git_jll v2.54.0+0
⌃ [7746bdde] Glib_jll v2.86.3+0
⌃ [3b182d85] Graphite2_jll v1.3.15+0
⌅ [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
⌃ [aacddb02] JpegTurbo_jll v3.1.5+0
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.1.0+0
⌃ [1d63c593] LLVMOpenMP_jll v18.1.8+0
⌅ [e9f186c6] Libffi_jll v3.4.7+0
  [7e76a0d4] Libglvnd_jll v1.7.1+1
  [94ce4f54] Libiconv_jll v1.18.0+0
  [4b2f31a3] Libmount_jll v2.42.0+0
⌃ [89763e89] Libtiff_jll v4.7.2+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [e7412a2a] Ogg_jll v1.3.6+0
⌃ [9bd350c2] OpenSSH_jll v10.3.1+0
⌃ [458c3c95] OpenSSL_jll v3.5.6+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
⌃ [36c8627f] Pango_jll v1.57.1+0
⌅ [30392449] Pixman_jll v0.44.2+0
⌃ [c0090381] Qt6Base_jll v6.10.2+1
⌃ [629bc702] Qt6Declarative_jll v6.10.2+1
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
⌃ [f50d1b31] Rmath_jll v0.5.1+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.24.0+0
  [ffd25f8a] XZ_jll v5.8.3+0
  [f67eecfb] Xorg_libICE_jll v1.1.2+0
  [c834827a] Xorg_libSM_jll v1.2.6+0
  [4f6342f7] Xorg_libX11_jll v1.8.13+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.13+0
  [935fb764] Xorg_libXcursor_jll v1.2.4+0
  [a3789734] Xorg_libXdmcp_jll v1.1.6+0
  [1082639a] Xorg_libXext_jll v1.3.8+0
  [d091e8ba] Xorg_libXfixes_jll v6.0.2+0
⌃ [a51aa0fd] Xorg_libXi_jll v1.8.3+0
  [d1454406] Xorg_libXinerama_jll v1.1.7+0
  [ec84b674] Xorg_libXrandr_jll v1.5.6+0
  [ea2f1a96] Xorg_libXrender_jll v0.9.12+0
  [a65dc6b1] Xorg_libpciaccess_jll v0.19.0+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.1+0
  [cc61e674] Xorg_libxkbfile_jll v1.2.0+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.6+0
  [12413925] Xorg_xcb_util_image_jll v0.4.1+0
  [2def613f] Xorg_xcb_util_jll v0.4.1+0
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.1+0
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.10+0
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.2+0
  [35661453] Xorg_xkbcomp_jll v1.4.7+0
⌃ [33bec58e] Xorg_xkeyboard_config_jll v2.47.0+0
  [c5fb5394] Xorg_xtrans_jll v1.6.0+0
  [8f1865be] ZeroMQ_jll v4.3.6+0
  [3161d3a3] Zstd_jll v1.5.7+1
  [35ca27e7] eudev_jll v3.2.14+0
⌅ [214eeab7] fzf_jll v0.61.1+0
⌃ [a4ae2306] libaom_jll v3.13.3+0
  [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
⌃ [8e53e030] libdrm_jll v2.4.125+1
  [2db6ffa8] libevdev_jll v1.13.4+0
  [f638f0a6] libfdk_aac_jll v2.0.4+0
  [36db933b] libinput_jll v1.28.1+0
  [b53b4c65] libpng_jll v1.6.58+0
  [a9144af2] libsodium_jll v1.0.21+0
  [9a156e7d] libva_jll v2.23.0+0
  [f27f6e37] libvorbis_jll v1.3.8+0
  [009596ad] mtdev_jll v1.1.7+0
⌃ [1317d2d5] oneTBB_jll v2022.0.0+1
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.2
  [56f22d72] Artifacts v1.11.0
  [2a0f44e3] Base64 v1.11.0
  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching v1.11.0
  [9fa8497b] Future v1.11.0
  [b77e0a4c] InteractiveUtils v1.11.0
  [4af54fe1] LazyArtifacts v1.11.0
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2 v1.11.0
  [8f399da3] Libdl v1.11.0
  [37e2e46d] LinearAlgebra v1.11.0
  [56ddb016] Logging v1.11.0
  [d6f4376e] Markdown v1.11.0
  [a63ad114] Mmap v1.11.0
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [3fa0cd96] REPL v1.11.0
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [f489334b] StyledStrings v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test v1.11.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.7.0+0
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.59.0+0
  [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`