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benchmarks/DynamicalODE/Henon-Heiles_energy_conservation_benchmark.jmd

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```julia
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using OrdinaryDiffEq, Plots, DiffEqCallbacks
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using SciMLBenchmarks
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using ADTypes
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using DifferentialEquations
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using TaylorIntegration, LinearAlgebra, StaticArrays
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gr(fmt=:png)
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default(fmt=:png)

benchmarks/DynamicalODE/Manifest.toml

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julia_version = "1.10.5"
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manifest_format = "2.0"
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project_hash = "0606d91e8b8951374c26d5533f0b47f89fbee450"
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project_hash = "268db6928ccffd4d6f79409a36ddb0a44c29d12b"
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[[deps.ADTypes]]
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git-tree-sha1 = "eea5d80188827b35333801ef97a40c2ed653b081"
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[[deps.Artifacts]]
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uuid = "56f22d72-fd6d-98f1-02f0-08ddc0907c33"
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[[deps.BandedMatrices]]
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deps = ["ArrayLayouts", "FillArrays", "LinearAlgebra", "PrecompileTools"]
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git-tree-sha1 = "a2c85f53ddcb15b4099da59867868bd40f005579"
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version = "1.7.5"
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weakdeps = ["SparseArrays"]
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[deps.BandedMatrices.extensions]
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BandedMatricesSparseArraysExt = "SparseArrays"
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[[deps.Base64]]
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uuid = "2a0f44e3-6c83-55bd-87e4-b1978d98bd5f"
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git-tree-sha1 = "d434647f798823bcae510aee0bc0401927f64391"
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uuid = "8e7c35d0-a365-5155-bbbb-fb81a777f24e"
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version = "1.1.1"
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weakdeps = ["BandedMatrices"]
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[deps.BlockArrays.extensions]
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BlockArraysBandedMatricesExt = "BandedMatrices"
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[[deps.BoundaryValueDiffEq]]
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deps = ["ADTypes", "Adapt", "ArrayInterface", "BandedMatrices", "ConcreteStructs", "DiffEqBase", "FastAlmostBandedMatrices", "FastClosures", "ForwardDiff", "LineSearch", "LineSearches", "LinearAlgebra", "LinearSolve", "Logging", "NonlinearSolve", "OrdinaryDiffEq", "PreallocationTools", "PrecompileTools", "Preferences", "RecursiveArrayTools", "Reexport", "SciMLBase", "Setfield", "SparseArrays", "SparseDiffTools"]
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BoundaryValueDiffEqODEInterfaceExt = "ODEInterface"
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ODEInterface = "54ca160b-1b9f-5127-a996-1867f4bc2a2c"
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[deps.BlockArrays.weakdeps]
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BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
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[[deps.Bzip2_jll]]
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deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg"]
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git-tree-sha1 = "8873e196c2eb87962a2048b3b8e08946535864a1"
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version = "1.0.8+2"
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version = "0.5.0"
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[[deps.CPUSummary]]
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deps = ["CpuId", "IfElse", "PrecompileTools", "Static"]
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git-tree-sha1 = "5a97e67919535d6841172016c9530fd69494e5ec"
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uuid = "ee1fde0b-3d02-5ea6-8484-8dfef6360eab"
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version = "1.14.10+0"
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[[deps.DelayDiffEq]]
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deps = ["ArrayInterface", "DataStructures", "DiffEqBase", "LinearAlgebra", "Logging", "OrdinaryDiffEq", "Printf", "RecursiveArrayTools", "Reexport", "SciMLBase", "SimpleNonlinearSolve", "SimpleUnPack"]
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git-tree-sha1 = "066f60231c1b0ae2905ffd2651e207accd91f627"
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deps = ["Mmap"]
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git-tree-sha1 = "9e2f36d3c96a820c678f2f1f1782582fcf685bae"
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git-tree-sha1 = "19dbd44d18bbfdfcf5e56c99cea9b0ed23df350a"
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uuid = "459566f4-90b8-5000-8ac3-15dfb0a30def"
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version = "3.9.1"
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weakdeps = ["OrdinaryDiffEq", "OrdinaryDiffEqCore", "Sundials"]
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[deps.DiffEqCallbacks.weakdeps]
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OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
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OrdinaryDiffEqCore = "bbf590c4-e513-4bbe-9b18-05decba2e5d8"
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Sundials = "c3572dad-4567-51f8-b174-8c6c989267f4"
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[[deps.DiffEqNoiseProcess]]
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deps = ["DiffEqBase", "Distributions", "GPUArraysCore", "LinearAlgebra", "Markdown", "Optim", "PoissonRandom", "QuadGK", "Random", "Random123", "RandomNumbers", "RecipesBase", "RecursiveArrayTools", "ResettableStacks", "SciMLBase", "StaticArraysCore", "Statistics"]
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uuid = "b552c78f-8df3-52c6-915a-8e097449b14b"
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version = "1.15.1"
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[[deps.DifferentialEquations]]
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deps = ["BoundaryValueDiffEq", "DelayDiffEq", "DiffEqBase", "DiffEqCallbacks", "DiffEqNoiseProcess", "JumpProcesses", "LinearAlgebra", "LinearSolve", "NonlinearSolve", "OrdinaryDiffEq", "Random", "RecursiveArrayTools", "Reexport", "SciMLBase", "SteadyStateDiffEq", "StochasticDiffEq", "Sundials"]
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git-tree-sha1 = "d851f2ca05f3cec9988f081b047a778a58b48aaf"
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deps = ["ADTypes", "LinearAlgebra"]
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git-tree-sha1 = "16611777adf4a818f18c33210895947814180964"
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DispatchDoctorChainRulesCoreExt = "ChainRulesCore"
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DispatchDoctorEnzymeCoreExt = "EnzymeCore"
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[[deps.Distances]]
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deps = ["LinearAlgebra", "Statistics", "StatsAPI"]
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DistancesChainRulesCoreExt = "ChainRulesCore"
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DistancesSparseArraysExt = "SparseArrays"
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deps = ["ArrayInterface", "LinearAlgebra", "Polyester", "Static", "StaticArrayInterface", "StrideArraysCore"]
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git-tree-sha1 = "ab1b34570bcdf272899062e1a56285a53ecaae08"
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deps = ["Artifacts", "Pkg"]
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[[deps.LibCURL]]
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deps = ["LibCURL_jll", "MozillaCACerts_jll"]
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deps = ["Base64"]
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[[deps.MatrixFactorizations]]
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weakdeps = ["BandedMatrices"]
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MatrixFactorizationsBandedMatricesExt = "BandedMatrices"
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deps = ["ArrayInterface", "LinearAlgebra", "MacroTools"]
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git-tree-sha1 = "54e2fdc38130c05b42be423e90da3bade29b74bd"
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uuid = "d41bc354-129a-5804-8e4c-c37616107c6c"
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version = "7.8.3"
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deps = ["Distances", "LineSearches", "LinearAlgebra", "NLSolversBase", "Printf", "Reexport"]
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git-tree-sha1 = "019f12e9a1a7880459d0173c182e6a99365d7ac1"
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deps = ["Adapt", "ArrayInterface", "DataStructures", "DiffEqBase", "DiffEqNoiseProcess", "DocStringExtensions", "FastPower", "FiniteDiff", "ForwardDiff", "JumpProcesses", "LevyArea", "LinearAlgebra", "Logging", "MuladdMacro", "NLsolve", "OrdinaryDiffEq", "Random", "RandomNumbers", "RecursiveArrayTools", "Reexport", "SciMLBase", "SciMLOperators", "SparseArrays", "SparseDiffTools", "StaticArrays", "UnPack"]
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benchmarks/DynamicalODE/Project.toml

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[deps]
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ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
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DiffEqCallbacks = "459566f4-90b8-5000-8ac3-15dfb0a30def"
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DiffEqPhysics = "055956cb-9e8b-5191-98cc-73ae4a59e68a"
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DifferentialEquations = "0c46a032-eb83-5123-abaf-570d42b7fbaa"
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Elliptic = "b305315f-e792-5b7a-8f41-49f472929428"
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LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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benchmarks/DynamicalODE/Quadrupole_boson_Hamiltonian_energy_conservation_benchmark.jmd

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```julia
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using TaylorIntegration
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using DifferentialEquations
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using ParameterizedFunctions
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using StaticArrays
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gr()

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