GitHub

Multistate Work-Precision Diagrams

The following benchmark is of 9 ODEs with 18 terms that describe a chemical reaction network. This multistate model was used as a benchmark model in Gupta et al.. We use ReactionNetworkImporters to load the BioNetGen model files as a Catalyst model, and then use ModelingToolkit to convert the Catalyst network model to ODEs.

using DiffEqBase, OrdinaryDiffEq, Catalyst, ReactionNetworkImporters,
      Sundials, Plots, DiffEqDevTools, ODEInterface, ODEInterfaceDiffEq,
      LSODA, TimerOutputs, LinearAlgebra, ModelingToolkit, BenchmarkTools,
      RecursiveFactorization
using OrdinaryDiffEqAdamsBashforthMoulton, OrdinaryDiffEqBDF, OrdinaryDiffEqRosenbrock, OrdinaryDiffEqSDIRK, OrdinaryDiffEqStabilizedRK, OrdinaryDiffEqVerner, OrdinaryDiffEqLowOrderRK

gr()
const to = TimerOutput()
tf = 20.0

# generate ModelingToolkit ODEs
@timeit to "Parse Network" prnbng = loadrxnetwork(BNGNetwork(), joinpath(@__DIR__, "Models/multistate.net"))
show(to)
rn = complete(prnbng)
obs = [eq.lhs for eq in observed(rn)]

@timeit to "Create ODESys" osys = complete(Catalyst.ode_model(rn))
show(to)

tspan = (0.0, tf)
@timeit to "ODEProb No Jac" oprob = ODEProblem{true, SciMLBase.FullSpecialize}(
    osys, Float64[], tspan, Float64[])
show(to);
Scanning blocks...done
Parsing parameters...done
Creating parameters...done
Parsing species...done
Creating variables...done
Setting up expression bindings...done
Parsing groups...done
Parsing functions...done
Parsing and adding reactions...done
──────────────────────────────────────────────────────────────────────────
                                 Time                    Allocations      
                        ───────────────────────   ────────────────────────
   Tot / % measured:         3.80s /  99.4%            317MiB / 100.0%    

Section         ncalls     time    %tot     avg     alloc    %tot      avg
──────────────────────────────────────────────────────────────────────────
Parse Network        1    3.78s  100.0%   3.78s    317MiB  100.0%   317MiB
───────────────────────────────────────────────────────────────────────────
─────────────────────────────────────────────────────────────────────────
                                 Time                    Allocations      
                        ───────────────────────   ────────────────────────
   Tot / % measured:         13.0s /  84.1%           1.24GiB /  72.5%    

Section         ncalls     time    %tot     avg     alloc    %tot      avg
──────────────────────────────────────────────────────────────────────────
Create ODESys        1    7.14s   65.4%   7.14s    601MiB   65.5%   601MiB
Parse Network        1    3.78s   34.6%   3.78s    317MiB   34.5%   317MiB
───────────────────────────────────────────────────────────────────────────
──────────────────────────────────────────────────────────────────────────
                                  Time                    Allocations      
                         ───────────────────────   ────────────────────────
    Tot / % measured:         39.5s /  94.8%           2.85GiB /  88.1%    

Section          ncalls     time    %tot     avg     alloc    %tot      avg
───────────────────────────────────────────────────────────────────────────
ODEProb No Jac        1    26.5s   70.8%   26.5s   1.61GiB   64.3%  1.61GiB
Create ODESys         1    7.14s   19.1%   7.14s    601MiB   23.4%   601MiB
Parse Network         1    3.78s   10.1%   3.78s    317MiB   12.3%   317MiB
───────────────────────────────────────────────────────────────────────────
@timeit to "ODEProb SparseJac" sparsejacprob = ODEProblem{true, SciMLBase.FullSpecialize}(
    osys, Float64[], tspan, Float64[], jac = true, sparse = true)
show(to)
───────────────────────────────────────────────────────────────────────────
───
                                     Time                    Allocations   
   
                            ───────────────────────   ─────────────────────
───
     Tot / % measured:           44.9s /  95.1%           3.30GiB /  89.2% 
   

Section             ncalls     time    %tot     avg     alloc    %tot      
avg
───────────────────────────────────────────────────────────────────────────
───
ODEProb No Jac           1    26.5s   62.0%   26.5s   1.61GiB   54.9%  1.61
GiB
Create ODESys            1    7.14s   16.7%   7.14s    601MiB   20.0%   601
MiB
ODEProb SparseJac        1    5.31s   12.4%   5.31s    441MiB   14.6%   441
MiB
Parse Network            1    3.78s    8.8%   3.78s    317MiB   10.5%   317
MiB
───────────────────────────────────────────────────────────────────────────
───
@show numspecies(rn) # Number of ODEs
@show numreactions(rn) # Approx. number of terms in the ODE
@show length(parameters(rn)); # Number of Parameters
numspecies(rn) = 9
numreactions(rn) = 18
length(parameters(rn)) = 9

Time ODE derivative function compilation

As compiling the ODE derivative functions has in the past taken longer than running a simulation, we first force compilation by evaluating these functions one time.

u = oprob.u0
du = copy(u)
p = oprob.p
@timeit to "ODE rhs Eval1" oprob.f(du, u, p, 0.0)
@timeit to "ODE rhs Eval2" oprob.f(du, u, p, 0.0)
sparsejacprob.f(du, u, p, 0.0)
9-element Vector{Float64}:
 -349472.0
  -62176.0
 -287296.0
   62176.0
  287296.0
       0.0
       0.0
       0.0
       0.0

We also time the ODE rhs function with BenchmarkTools as it is more accurate given how fast evaluating f is:

@btime oprob.f($du, $u, $p, 0.0)
88.548 ns (2 allocations: 368 bytes)
9-element Vector{Float64}:
 -349472.0
  -62176.0
 -287296.0
   62176.0
  287296.0
       0.0
       0.0
       0.0
       0.0

Picture of the solution

sol = solve(oprob, CVODE_BDF(), saveat = tf/1000.0, reltol = 1e-5, abstol = 1e-5)
plot(sol; idxs = obs, legend = false, fmt = :png)

For these benchmarks we will be using the time-series error with these saving points.

Generate Test Solution

@time sol = solve(oprob, CVODE_BDF(), reltol = 1e-15, abstol = 1e-15)
test_sol = TestSolution(sol);
0.634720 seconds (509.16 k allocations: 34.988 MiB, 9.11% gc time, 98.16%
 compilation time)

Setups

Sets plotting defaults

default(legendfontsize = 7, framestyle = :box, gridalpha = 0.3, gridlinewidth = 2.5)

Sets tolerances

abstols = 1.0 ./ 10.0 .^ (6:10)
reltols = 1.0 ./ 10.0 .^ (6:10);

Work-Precision Diagram

We start by trying lsoda and CVODE solvers.

Declare solvers

We designate the solvers (and options) we wish to use.

setups = [
    Dict(:alg=>lsoda()),
    Dict(:alg=>CVODE_BDF()),
    Dict(:alg=>CVODE_BDF(linear_solver = :LapackDense)),
    Dict(:alg=>CVODE_BDF(linear_solver = :GMRES))
];

Plot Work-Precision Diagram

Finally, we generate a work-precision diagram for the selection of solvers.

wp = WorkPrecisionSet(oprob, abstols, reltols, setups; error_estimate = :l2,
    saveat = tf/10000.0, appxsol = test_sol, maxiters = Int(1e9), numruns = 200)

names = ["lsoda" "CVODE_BDF" "CVODE_BDF (LapackDense)" "CVODE_BDF (GMRES)"]
plot(wp; label = names)

Implicit Work-Precision Diagram

Next, we try a couple of implicit Julia solvers.

Declare solvers

We designate the solvers we wish to use.

setups = [
    Dict(:alg=>TRBDF2()),
    Dict(:alg=>QNDF()),
    Dict(:alg=>FBDF()),
    Dict(:alg=>NordsieckBDF()),
    Dict(:alg=>KenCarp4()),
    Dict(:alg=>Rosenbrock23()),
    Dict(:alg=>Rodas4()),
    Dict(:alg=>Rodas5P())
];

Plot Work-Precision Diagram

Finally, we generate a work-precision diagram for the selection of solvers.

wp = WorkPrecisionSet(oprob, abstols, reltols, setups; error_estimate = :l2,
    saveat = tf/10000.0, appxsol = test_sol, maxiters = Int(1e12), dtmin = 1e-18, numruns = 200)

names = ["TRBDF2" "QNDF" "FBDF" "NordsieckBDF" "KenCarp4" "Rosenbrock23" "Rodas4" "Rodas5P"]
plot(wp; label = names)

Implicit methods doing poorly suggests it's non-stiff.

Explicit Work-Precision Diagram

Benchmarks for explicit solvers.

Declare solvers

We designate the solvers we wish to use, this also includes lsoda and CVODE.

setups = [
    Dict(:alg=>lsoda()),
    Dict(:alg=>Tsit5()),
    Dict(:alg=>BS5()),
    Dict(:alg=>VCABM()),
    Dict(:alg=>Vern6()),
    Dict(:alg=>Vern7()),
    Dict(:alg=>Vern8()),
    Dict(:alg=>Vern9()),
    Dict(:alg=>ROCK4())
];

Plot Work-Precision Diagram

wp = WorkPrecisionSet(oprob, abstols, reltols, setups; error_estimate = :l2,
    saveat = tf/10000.0, appxsol = test_sol, maxiters = Int(1e9), numruns = 200)

names = ["lsoda" "Tsit5" "BS5" "VCABM" "Vern6" "Vern7" "Vern8" "Vern9" "ROCK4"]
plot(wp; label = names)

Loser methods (large cost in isolation)

CVODE_Adams and ROCK2 are not competitive with the explicit set above. They are not folded into the multi-tolerance / multi-run work-precision suites; a single-tolerance isolation timing against a competitive explicit (Vern7) shows the wall-time gap.

const _loser_tol = 1e-6
const _loser_maxiters = Int(1e7)
_solve_kwargs = (; abstol = _loser_tol, reltol = _loser_tol, maxiters = _loser_maxiters,
    save_everystep = false)

loser_labels = String[]
loser_elapsed = Float64[]

function _time_loser!(label, alg)
    println("--- $label ---")
    t = @elapsed sol = solve(oprob, alg; _solve_kwargs...)
    @show sol.retcode
    println("elapsed = ", t, " s")
    push!(loser_labels, label)
    push!(loser_elapsed, t)
    return sol
end

_time_loser!("Vern7 (reference)", Vern7())
_time_loser!("CVODE_Adams (loser)", CVODE_Adams())
_time_loser!("ROCK2 (loser)", ROCK2())
--- Vern7 (reference) ---
sol.retcode = SciMLBase.ReturnCode.Success
elapsed = 1.685565136 s
--- CVODE_Adams (loser) ---
sol.retcode = SciMLBase.ReturnCode.Success
elapsed = 0.55766461 s
--- ROCK2 (loser) ---
sol.retcode = SciMLBase.ReturnCode.Success
elapsed = 2.715707341 s
retcode: Success
Interpolation: 1st order linear
t: 2-element Vector{Float64}:
  0.0
 20.0
u: 2-element Vector{Vector{Float64}}:
 [5360.0, 1160.0, 5360.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
 [177.65315507390076, 2.7535434675468977, 222.84890705209517, 48.9175684642
8348, 3981.0593991339315, 1063.7298145736306, 44.59907349453874, 44.0409892
5967407, 3.7218164860954883]
ref_t = loser_elapsed[1]
bar(loser_labels, loser_elapsed ./ ref_t; legend = false, xrotation = 20,
    ylabel = "wall time / Vern7 reference",
    title = "multistate loser isolation (tol=$_loser_tol, one solve each)",
    size = (700, 400), bottom_margin = 8Plots.mm)

Summary of results

Finally, we compute a single diagram comparing the various solvers used.

Declare solvers

We designate the solvers we wish to compare.

setups = [
    Dict(:alg=>lsoda()),
    Dict(:alg=>CVODE_BDF()),
    Dict(:alg=>QNDF()),
    Dict(:alg=>NordsieckBDF()),
    Dict(:alg=>KenCarp4()),
    Dict(:alg=>Rodas5P()),
    Dict(:alg=>Tsit5()),
    Dict(:alg=>BS5()),
    Dict(:alg=>VCABM()),
    Dict(:alg=>Vern7())
];

Plot Work-Precision Diagram

For these, we generate a work-precision diagram for the selection of solvers.

wp = WorkPrecisionSet(oprob, abstols, reltols, setups; error_estimate = :l2,
    saveat = tf/10000.0, appxsol = test_sol, maxiters = Int(1e9), numruns = 200)

names = ["lsoda" "CVODE_BDF" "QNDF" "NordsieckBDF" "KenCarp4" "Rodas5P" "Tsit5" "BS5" "VCABM" "Vern7"]
colors = [:seagreen1 :chartreuse1 :deepskyblue1 :mediumorchid :lightskyblue :blue :orchid2 :thistle2 :lightsteelblue2 :mediumpurple1]
markershapes = [:star4 :circle :hexagon :diamond :star5 :heptagon :ltriangle :star8 :heptagon :star6]
plot(wp; label = names, left_margin = 10Plots.mm, right_margin = 10Plots.mm,
    xticks = [1e-12, 1e-11, 1e-10, 1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2],
    yticks = [1e-3, 1e-2], color = colors, markershape = markershapes,
    legendfontsize = 15, tickfontsize = 15, guidefontsize = 15, legend = :topright,
    lw = 20, la = 0.8, markersize = 20, markerstrokealpha = 1.0,
    markerstrokewidth = 1.5, gridalpha = 0.3, gridlinewidth = 7.5, size = (1100, 1000))

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/Bio","multistate.jmd")

Computer Information:

Julia Version 1.10.12
Commit d93beab124c (2026-08-15 10:29 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_DEPOT_PATH = /home/crackauc/github-runners/amdci8-1/.julia
  JULIA_NUM_THREADS = auto

Package Information:

Status `~/github-runners/amdci8-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Bio/Project.toml`
  [47edcb42] ADTypes v1.24.0
  [6e4b80f9] BenchmarkTools v1.8.0
⌃ [479239e8] Catalyst v16.3.0
  [d360d2e6] ChainRulesCore v1.26.1
⌃ [2b5f629d] DiffEqBase v7.18.2
⌃ [f3b72e0c] DiffEqDevTools v3.4.0
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⌃ [7f56f5a3] LSODA v1.1.0
⌃ [7ed4a6bd] LinearSolve v5.13.0
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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/amdci8-1/_work/SciMLBenchmarks.jl/SciMLBenchmarks.jl/benchmarks/Bio/Manifest.toml`
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⌃ [26075421] NonlinearSolveSpectralMethods v1.8.0
  [54ca160b] ODEInterface v0.5.2
⌅ [09606e27] ODEInterfaceDiffEq v4.1.0
  [6fe1bfb0] OffsetArrays v1.17.0
  [4d8831e6] OpenSSL v1.6.1
⌅ [bac558e1] OrderedCollections v1.8.2
⌃ [1dea7af3] OrdinaryDiffEq v7.7.0
  [89bda076] OrdinaryDiffEqAdamsBashforthMoulton v2.2.0
⌃ [6ad6398a] OrdinaryDiffEqBDF v2.4.4
⌃ [bbf590c4] OrdinaryDiffEqCore v4.15.0
⌃ [50262376] OrdinaryDiffEqDefault v2.5.0
⌃ [4302a76b] OrdinaryDiffEqDifferentiation v3.10.0
⌃ [becaefa8] OrdinaryDiffEqExtrapolation v2.5.0
⌃ [1344f307] OrdinaryDiffEqLowOrderRK v2.2.3
⌃ [127b3ac7] OrdinaryDiffEqNonlinearSolve v2.9.0
⌃ [43230ef6] OrdinaryDiffEqRosenbrock v2.7.0
⌃ [b4bd8bb3] OrdinaryDiffEqRosenbrockTableaus v2.4.1
⌃ [2d112036] OrdinaryDiffEqSDIRK v2.9.0
  [358294b1] OrdinaryDiffEqStabilizedRK v2.6.0
⌃ [b1df2697] OrdinaryDiffEqTsit5 v2.1.3
⌃ [79d7bb75] OrdinaryDiffEqVerner v2.4.0
  [90014a1f] PDMats v0.11.41
⌅ [d96e819e] Parameters v0.12.3
⌅ [69de0a69] Parsers v2.8.7
  [ccf2f8ad] PlotThemes v3.3.0
  [995b91a9] PlotUtils v1.4.4
  [91a5bcdd] Plots v1.41.7
  [e409e4f3] PoissonRandom v0.4.13
  [f517fe37] Polyester v0.7.19
  [1d0040c9] PolyesterWeave v0.2.2
⌃ [d236fae5] PreallocationTools v1.6.0
⌅ [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.5.2
  [27ebfcd6] Primes v0.5.7
  [43287f4e] PtrArrays v1.4.0
  [0c0d3e7f] PureKLU v1.4.1
  [1fd47b50] QuadGK v2.11.3
  [b4db0fb7] ReactionNetworkImporters v1.5.0
  [988b38a3] ReadOnlyArrays v0.2.0
  [795d4caa] ReadOnlyDicts v1.0.1
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
⌃ [731186ca] RecursiveArrayTools v4.5.0
  [f2c3362d] RecursiveFactorization v0.2.30
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.1
  [ae5879a3] ResettableStacks v1.4.0
  [9fe22ead] RespecializeParams v1.3.0
  [79098fc4] Rmath v0.9.0
  [47965b36] RootedTrees v2.27.0
  [f2b01f46] Roots v3.0.7
  [7e49a35a] RuntimeGeneratedFunctions v0.5.25
⌃ [9dfe8606] SCCNonlinearSolve v1.15.0
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.46
⌃ [0bca4576] SciMLBase v3.49.2
⌃ [31c91b34] SciMLBenchmarks v0.1.3
⌃ [19f34311] SciMLJacobianOperators v0.1.17
  [a6db7da4] SciMLLogging v2.1.0
⌃ [c0aeaf25] SciMLOperators v1.29.0
  [431bcebd] SciMLPublic v1.3.0
⌃ [53ae85a6] SciMLStructures v1.10.4
  [7e506255] ScopedValues v1.6.2
  [6c6a2e73] Scratch v1.3.0
  [efcf1570] Setfield v1.1.2
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.2.0
⌃ [727e6d20] SimpleNonlinearSolve v2.14.0
  [699a6c99] SimpleTraits v0.9.6
  [a2af1166] SortingAlgorithms v1.2.3
  [bd59d7e1] SparseBandedMatrices v1.4.0
  [a57abbd0] SparseColumnPivotedQR v2.1.7
  [0a514795] SparseMatrixColorings v0.4.27
  [276daf66] SpecialFunctions v2.9.0
  [860ef19b] StableRNGs v1.0.4
  [0c0c59c1] StarAlgebras v0.3.0
⌃ [64909d44] StateSelection v1.11.0
  [aedffcd0] Static v1.4.6
  [0d7ed370] StaticArrayInterface v1.10.0
  [90137ffa] StaticArrays v1.9.19
  [1e83bf80] StaticArraysCore v1.4.4
  [82ae8749] StatsAPI v1.8.0
  [2913bbd2] StatsBase v0.34.13
  [4c63d2b9] StatsFuns v2.2.1
  [7792a7ef] StrideArraysCore v0.5.9
  [69024149] StringEncodings v0.3.7
  [09ab397b] StructArrays v0.7.3
  [c3572dad] Sundials v6.6.0
  [2efcf032] SymbolicIndexingInterface v0.3.55
  [19f23fe9] SymbolicLimits v1.2.0
⌅ [d1185830] SymbolicUtils v4.45.0
⌃ [0c5d862f] Symbolics v7.36.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.14.0
  [ed4db957] TaskLocalValues v0.1.3
  [62fd8b95] TensorCore v0.1.1
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.1.0
  [8290d209] ThreadingUtilities v0.5.6
⌅ [a759f4b9] TimerOutputs v0.5.29
  [3bb67fe8] TranscodingStreams v0.11.3
  [d5829a12] TriangularSolve v0.2.6
  [410a4b4d] Tricks v0.1.13
  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.7.0
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [41fe7b60] Unzip v0.2.0
  [3d5dd08c] VectorizationBase v0.21.74
  [33b4df10] VectorizedRNG v0.2.26
  [81def892] VersionParsing v1.3.0
  [d30d5f5c] WeakCacheSets v0.1.0
  [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 v1.18.7+0
  [ee1fde0b] Dbus_jll v1.16.2+0
  [2702e6a9] EpollShim_jll v0.0.20230411+1
  [2e619515] Expat_jll v2.8.3+0
⌅ [b22a6f82] FFMPEG_jll v8.1.2+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 v0.73.26+0
⌅ [b0724c58] GettextRuntime_jll v0.22.4+0
  [61579ee1] Ghostscript_jll v9.55.1+0
  [020c3dae] Git_LFS_jll v3.7.1+0
  [f8c6e375] Git_jll v2.55.0+0
  [7746bdde] Glib_jll v2.88.3+0
  [3b182d85] Graphite2_jll v1.3.16+0
⌅ [2e76f6c2] HarfBuzz_jll v8.5.1+0
  [1d5cc7b8] IntelOpenMP_jll v2025.2.0+0
  [aacddb02] JpegTurbo_jll v3.2.0+1
  [c1c5ebd0] LAME_jll v3.100.3+0
  [88015f11] LERC_jll v4.1.0+0
  [1d63c593] LLVMOpenMP_jll v22.1.7+0
  [aae0fff6] LSODA_jll v0.1.2+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 v4.7.3+0
  [38a345b3] Libuuid_jll v2.42.0+0
  [856f044c] MKL_jll v2025.2.0+0
  [c771fb93] ODEInterface_jll v0.0.2+0
  [e7412a2a] Ogg_jll v1.3.6+0
⌅ [656ef2d0] OpenBLAS32_jll v0.3.24+0
  [9bd350c2] OpenSSH_jll v10.5.1+0
⌃ [458c3c95] OpenSSL_jll v3.5.7+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+0
  [91d4177d] Opus_jll v1.6.1+0
⌃ [36c8627f] Pango_jll v1.58.0+0
  [30392449] Pixman_jll v0.46.4+0
  [c0090381] Qt6Base_jll v6.10.2+2
  [629bc702] Qt6Declarative_jll v6.10.2+2
  [ce943373] Qt6ShaderTools_jll v6.10.2+1
  [6de9746b] Qt6Svg_jll v6.10.2+0
  [e99dba38] Qt6Wayland_jll v6.10.2+1
  [f50d1b31] Rmath_jll v0.5.2+0
⌅ [ca45d3f4] SuiteSparse32_jll v5.10.1+0
  [fb77eaff] Sundials_jll v7.5.0+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 v1.8.4+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+2
  [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 v3.14.1+0
⌃ [0ac62f75] libass_jll v0.17.4+0
  [1183f4f0] libdecor_jll v0.2.2+0
  [8e53e030] libdrm_jll v2.4.134+0
  [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 v2022.3.0+0
⌅ [1270edf5] x264_jll v10164.0.1+0
  [dfaa095f] x265_jll v4.1.0+0
  [d8fb68d0] xkbcommon_jll v1.13.0+0
  [0dad84c5] ArgTools v1.1.1
  [56f22d72] Artifacts
  [2a0f44e3] Base64
  [ade2ca70] Dates
  [8ba89e20] Distributed
  [f43a241f] Downloads v1.6.0
  [7b1f6079] FileWatching
  [9fa8497b] Future
  [b77e0a4c] InteractiveUtils
  [4af54fe1] LazyArtifacts
  [b27032c2] LibCURL v0.6.4
  [76f85450] LibGit2
  [8f399da3] Libdl
  [37e2e46d] LinearAlgebra
  [56ddb016] Logging
  [d6f4376e] Markdown
  [a63ad114] Mmap
  [ca575930] NetworkOptions v1.2.0
  [44cfe95a] Pkg v1.10.0
  [de0858da] Printf
  [9abbd945] Profile
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [6462fe0b] Sockets
  [2f01184e] SparseArrays v1.10.0
  [10745b16] Statistics v1.10.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [8dfed614] Test
  [cf7118a7] UUIDs
  [4ec0a83e] Unicode
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.4.0+0
  [e37daf67] LibGit2_jll v1.6.4+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [c8ffd9c3] MbedTLS_jll v2.28.1010+0
  [14a3606d] MozillaCACerts_jll v2025.12.2
  [4536629a] OpenBLAS_jll v0.3.23+5
  [05823500] OpenLibm_jll v0.8.5+0
  [efcefdf7] PCRE2_jll v10.42.0+1
  [bea87d4a] SuiteSparse_jll v7.2.1+1
  [83775a58] Zlib_jll v1.2.13+1
  [8e850b90] libblastrampoline_jll v5.11.0+0
  [8e850ede] nghttp2_jll v1.52.0+1
  [3f19e933] p7zip_jll v17.6.1+0
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`