ForwardDiff differentiates through solver

Describe the bug 🐞

ForwardDiff.jl differentiates through integral solver in the example below.

Expected behavior

In the example below, Integrals.jl should compute the integral without reaching the QuadGKJL algorithm. Instead, it hits the algorithm at kronrod where it returns a method error. Note that this example works correctly for Zygote.

Minimal Reproducible Example 👇

using BenchmarkTools
using Distributions
using Integrals
using ForwardDiff

integrand(x::T1, p::T2) where {T1<:Real,T2<:Real} = pdf(Normal(p, x), one(promote_type(T1, T2)))

function f(Θ)
    domain = (Θ[2], Θ[3])
    p = Θ[1]
    prob = IntegralProblem(integrand, domain, p)
    sol = solve(prob, QuadGKJL(); reltol=1e-3, abstol=1e-3)
    return sol.u
end

Θ = [0.0, 0.0, 2.0]
f(Θ)
ForwardDiff.gradient(f, Θ)[1]

Error & Stacktrace ⚠️

ERROR: MethodError: no method matching kronrod(::Type{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 3}}, ::Int64)

Closest candidates are:
  kronrod(::Any, ::Integer, ::Real, ::Real; rtol, quad)
   @ QuadGK ~/.julia/packages/QuadGK/OtnWt/src/weightedgauss.jl:90
  kronrod(::Type{T}, ::Integer) where T<:AbstractFloat
   @ QuadGK ~/.julia/packages/QuadGK/OtnWt/src/gausskronrod.jl:316
  kronrod(::AbstractMatrix{<:Real}, ::Integer, ::Real, ::Pair{<:Tuple{Real, Real}, <:Tuple{Real, Real}})
   @ QuadGK ~/.julia/packages/QuadGK/OtnWt/src/gausskronrod.jl:390
  ...

Stacktrace:
  [1] macro expansion
    @ ~/.julia/packages/QuadGK/OtnWt/src/gausskronrod.jl:564 [inlined]
  [2] _cachedrule
    @ ~/.julia/packages/QuadGK/OtnWt/src/gausskronrod.jl:564 [inlined]
  [3] cachedrule
    @ ~/.julia/packages/QuadGK/OtnWt/src/gausskronrod.jl:569 [inlined]
  [4] do_quadgk(f::Integrals.var"#53#59"{…}, s::Tuple{…}, n::Int64, atol::Float64, rtol::Float64, maxevals::Int64, nrm::typeof(LinearAlgebra.norm), segbuf::Vector{…})
    @ QuadGK ~/.julia/packages/QuadGK/OtnWt/src/adapt.jl:7
  [5] #50
    @ ~/.julia/packages/QuadGK/OtnWt/src/adapt.jl:253 [inlined]
  [6] handle_infinities(workfunc::QuadGK.var"#50#51"{…}, f::Integrals.var"#53#59"{…}, s::Tuple{…})
    @ QuadGK ~/.julia/packages/QuadGK/OtnWt/src/adapt.jl:145
  [7] #quadgk#49
    @ ~/.julia/packages/QuadGK/OtnWt/src/adapt.jl:252 [inlined]
  [8] quadgk
    @ ~/.julia/packages/QuadGK/OtnWt/src/adapt.jl:250 [inlined]
  [9] #__solvebp_call#47
    @ ~/.julia/packages/Integrals/tvunm/src/Integrals.jl:142 [inlined]
 [10] __solvebp_call
    @ ~/.julia/packages/Integrals/tvunm/src/Integrals.jl:88 [inlined]
 [11] #__solvebp#1
    @ ~/.julia/packages/Integrals/tvunm/ext/IntegralsForwardDiffExt.jl:27 [inlined]
 [12] __solvebp
    @ ~/.julia/packages/Integrals/tvunm/ext/IntegralsForwardDiffExt.jl:7 [inlined]
 [13] solve!(cache::Integrals.IntegralCache{…})
    @ Integrals ~/.julia/packages/Integrals/tvunm/src/common.jl:105
 [14] solve(prob::IntegralProblem{…}, alg::QuadGKJL{…}; kwargs::@Kwargs{…})
    @ Integrals ~/.julia/packages/Integrals/tvunm/src/common.jl:101
 [15] f(Θ::Vector{ForwardDiff.Dual{ForwardDiff.Tag{typeof(f), Float64}, Float64, 3}})
    @ Main ~/.julia/dev/sandbox/DDM/hcubature_turing/hcubature_turing.jl:102
 [16] vector_mode_dual_eval!
    @ ~/.julia/packages/ForwardDiff/PcZ48/src/apiutils.jl:24 [inlined]
 [17] vector_mode_gradient(f::typeof(f), x::Vector{…}, cfg::ForwardDiff.GradientConfig{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/gradient.jl:89
 [18] gradient(f::Function, x::Vector{…}, cfg::ForwardDiff.GradientConfig{…}, ::Val{…})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/gradient.jl:19
 [19] gradient(f::Function, x::Vector{Float64}, cfg::ForwardDiff.GradientConfig{ForwardDiff.Tag{…}, Float64, 3, Vector{…}})
    @ ForwardDiff ~/.julia/packages/ForwardDiff/PcZ48/src/gradient.jl:17
 [20] top-level scope
    @ ~/.julia/dev/sandbox/DDM/hcubature_turing/hcubature_turing.jl:108
Some type information was truncated. Use `show(err)` to see complete types.

Environment (please complete the following information):

Output of using Pkg; Pkg.status()

(hcubature_turing) pkg> st
Status `~/.julia/dev/sandbox/DDM/hcubature_turing/Project.toml`
  [31c24e10] Distributions v0.25.109
  [f6369f11] ForwardDiff v0.10.36
  [19dc6840] HCubature v1.6.0
  [de52edbc] Integrals v4.4.1
  [1fd47b50] QuadGK v2.9.4
  [f3b207a7] StatsPlots v0.15.7
  [fce5fe82] Turing v0.33.1

Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/.julia/dev/sandbox/DDM/hcubature_turing/Manifest.toml`
  [47edcb42] ADTypes v1.5.3
  [621f4979] AbstractFFTs v1.5.0
  [80f14c24] AbstractMCMC v5.2.0
  [7a57a42e] AbstractPPL v0.8.4
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.36
  [79e6a3ab] Adapt v4.0.4
  [0bf59076] AdvancedHMC v0.6.1
  [5b7e9947] AdvancedMH v0.8.2
  [576499cb] AdvancedPS v0.6.0
  [b5ca4192] AdvancedVI v0.2.6
  [66dad0bd] AliasTables v1.1.3
  [dce04be8] ArgCheck v2.3.0
  [ec485272] ArnoldiMethod v0.4.0
  [7d9fca2a] Arpack v0.5.4
  [4fba245c] ArrayInterface v7.12.0
  [a9b6321e] Atomix v0.1.0
  [13072b0f] AxisAlgorithms v1.1.0
  [39de3d68] AxisArrays v0.4.7
  [198e06fe] BangBang v0.4.2
  [9718e550] Baselet v0.1.1
  [e2ed5e7c] Bijections v0.1.7
  [76274a88] Bijectors v0.13.16
  [d1d4a3ce] BitFlags v0.1.9
  [fa961155] CEnum v0.5.0
  [49dc2e85] Calculus v0.5.1
  [082447d4] ChainRules v1.69.0
  [d360d2e6] ChainRulesCore v1.24.0
  [9e997f8a] ChangesOfVariables v0.1.8
  [aaaa29a8] Clustering v0.15.7
  [944b1d66] CodecZlib v0.7.5
  [35d6a980] ColorSchemes v3.25.0
  [3da002f7] ColorTypes v0.11.5
  [c3611d14] ColorVectorSpace v0.10.0
  [5ae59095] Colors v0.12.11
  [861a8166] Combinatorics v1.0.2
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.15.0
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [f0e56b4a] ConcurrentUtilities v2.4.2
  [88cd18e8] ConsoleProgressMonitor v0.1.2
  [187b0558] ConstructionBase v1.5.5
  [d38c429a] Contour v0.6.3
  [a8cc5b0e] Crayons v4.1.1
  [717857b8] DSP v0.7.9
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [244e2a9f] DefineSingletons v0.1.2
  [8bb1440f] DelimitedFiles v1.9.1
  [b429d917] DensityInterface v0.4.0
  [85a47980] Dictionaries v0.4.2
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [b4f34e82] Distances v0.10.11
  [31c24e10] Distributions v0.25.109
  [ced4e74d] DistributionsAD v0.6.55
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [fa6b7ba4] DualNumbers v0.6.8
  [366bfd00] DynamicPPL v0.28.0
⌅ [7c1d4256] DynamicPolynomials v0.5.7
  [b7d42ee7] Einsum v0.4.1
  [cad2338a] EllipticalSliceSampling v2.0.0
  [4e289a0a] EnumX v1.0.4
  [460bff9d] ExceptionUnwrapping v0.1.10
  [e2ba6199] ExprTools v0.1.10
  [c87230d0] FFMPEG v0.4.1
  [7a1cc6ca] FFTW v1.8.0
  [1a297f60] FillArrays v1.11.0
  [6a86dc24] FiniteDiff v2.23.1
  [53c48c17] FixedPointNumbers v0.8.5
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.11
  [46192b85] GPUArraysCore v0.1.6
  [28b8d3ca] GR v0.73.6
  [86223c79] Graphs v1.11.2
  [42e2da0e] Grisu v1.0.2
  [19dc6840] HCubature v1.6.0
  [cd3eb016] HTTP v1.10.8
  [1baab800] HybridArrays v0.4.16
  [34004b35] HypergeometricFunctions v0.3.23
  [615f187c] IfElse v0.1.1
  [313cdc1a] Indexing v1.1.1
  [d25df0c9] Inflate v0.1.5
  [22cec73e] InitialValues v0.3.1
  [505f98c9] InplaceOps v0.3.0
  [18e54dd8] IntegerMathUtils v0.1.2
  [de52edbc] Integrals v4.4.1
  [a98d9a8b] Interpolations v0.15.1
  [8197267c] IntervalSets v0.7.10
  [3587e190] InverseFunctions v0.1.14
  [41ab1584] InvertedIndices v1.3.0
  [92d709cd] IrrationalConstants v0.2.2
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [1019f520] JLFzf v0.1.7
  [692b3bcd] JLLWrappers v1.5.0
  [682c06a0] JSON v0.21.4
  [63c18a36] KernelAbstractions v0.9.22
  [5ab0869b] KernelDensity v0.6.9
  [2c470bb0] Kronecker v0.5.5
  [5be7bae1] LBFGSB v0.4.1
  [929cbde3] LLVM v8.0.0
  [8ac3fa9e] LRUCache v1.6.1
  [b964fa9f] LaTeXStrings v1.3.1
  [2ee39098] LabelledArrays v1.16.0
  [984bce1d] LambertW v0.4.6
  [23fbe1c1] Latexify v0.16.4
  [73f95e8e] LatticeRules v0.0.1
  [1d6d02ad] LeftChildRightSiblingTrees v0.2.0
  [6f1fad26] Libtask v0.8.7
  [d3d80556] LineSearches v7.2.0
  [7a12625a] LinearMaps v3.11.3
  [6fdf6af0] LogDensityProblems v2.1.1
  [996a588d] LogDensityProblemsAD v1.9.0
  [2ab3a3ac] LogExpFunctions v0.3.28
  [e6f89c97] LoggingExtras v1.0.3
  [c7f686f2] MCMCChains v6.0.6
  [be115224] MCMCDiagnosticTools v0.3.10
  [e80e1ace] MLJModelInterface v1.11.0
  [1914dd2f] MacroTools v0.5.13
  [af67fdf4] ManifoldDiff v0.3.10
  [1cead3c2] Manifolds v0.9.20
  [3362f125] ManifoldsBase v0.15.10
  [dbb5928d] MappedArrays v0.4.2
  [99c1a7ee] MatrixEquations v2.4.2
  [739be429] MbedTLS v1.1.9
  [442fdcdd] Measures v0.3.2
  [128add7d] MicroCollections v0.2.0
  [e1d29d7a] Missings v1.2.0
  [4886b29c] MonteCarloIntegration v0.2.0
  [102ac46a] MultivariatePolynomials v0.5.6
  [6f286f6a] MultivariateStats v0.10.3
  [d8a4904e] MutableArithmetics v1.4.5
  [d41bc354] NLSolversBase v7.8.3
  [872c559c] NNlib v0.9.20
  [77ba4419] NaNMath v1.0.2
  [86f7a689] NamedArrays v0.10.2
  [356022a1] NamedDims v1.2.2
  [c020b1a1] NaturalSort v1.0.0
  [b8a86587] NearestNeighbors v0.4.18
  [510215fc] Observables v0.5.5
  [6fe1bfb0] OffsetArrays v1.14.1
  [4d8831e6] OpenSSL v1.4.3
  [429524aa] Optim v1.9.4
  [3bd65402] Optimisers v0.3.3
  [7f7a1694] Optimization v3.27.0
  [bca83a33] OptimizationBase v1.3.3
  [36348300] OptimizationOptimJL v0.3.2
  [bac558e1] OrderedCollections v1.6.3
  [90014a1f] PDMats v0.11.31
  [d96e819e] Parameters v0.12.3
  [69de0a69] Parsers v2.8.1
  [b98c9c47] Pipe v1.3.0
  [ccf2f8ad] PlotThemes v3.2.0
  [995b91a9] PlotUtils v1.4.1
  [91a5bcdd] Plots v1.40.5
  [f27b6e38] Polynomials v4.0.11
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.22
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [08abe8d2] PrettyTables v2.3.2
  [27ebfcd6] Primes v0.5.6
  [33c8b6b6] ProgressLogging v0.1.4
  [92933f4c] ProgressMeter v1.10.0
  [43287f4e] PtrArrays v1.2.0
  [1fd47b50] QuadGK v2.9.4
  [8a4e6c94] QuasiMonteCarlo v0.3.3
  [94ee1d12] Quaternions v0.7.6
  [74087812] Random123 v1.7.0
  [e6cf234a] RandomNumbers v1.5.3
  [b3c3ace0] RangeArrays v0.3.2
  [c84ed2f1] Ratios v0.4.5
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [01d81517] RecipesPipeline v0.6.12
  [731186ca] RecursiveArrayTools v3.26.0
  [189a3867] Reexport v1.2.2
  [05181044] RelocatableFolders v1.0.1
  [ae029012] Requires v1.3.0
  [79098fc4] Rmath v0.7.1
  [f2b01f46] Roots v2.1.5
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [26aad666] SSMProblems v0.1.1
  [0bca4576] SciMLBase v2.42.0
  [c0aeaf25] SciMLOperators v0.3.8
  [53ae85a6] SciMLStructures v1.4.1
  [30f210dd] ScientificTypesBase v3.0.0
  [6c6a2e73] Scratch v1.2.1
  [91c51154] SentinelArrays v1.4.5
  [efcf1570] Setfield v1.1.1
  [992d4aef] Showoff v1.0.3
  [777ac1f9] SimpleBufferStream v1.1.0
  [699a6c99] SimpleTraits v0.9.4
  [ce78b400] SimpleUnPack v1.1.0
  [47aef6b3] SimpleWeightedGraphs v1.4.0
  [ed01d8cd] Sobol v1.5.0
  [a2af1166] SortingAlgorithms v1.2.1
  [dc90abb0] SparseInverseSubset v0.1.2
  [276daf66] SpecialFunctions v2.4.0
  [171d559e] SplittablesBase v0.1.15
  [90137ffa] StaticArrays v1.9.7
  [1e83bf80] StaticArraysCore v1.4.3
  [64bff920] StatisticalTraits v3.4.0
  [82ae8749] StatsAPI v1.7.0
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.1
  [f3b207a7] StatsPlots v0.15.7
  [892a3eda] StringManipulation v0.3.4
  [09ab397b] StructArrays v0.6.18
⌅ [4297ee4d] SymbolicAnalysis v0.1.0
  [2efcf032] SymbolicIndexingInterface v0.3.26
  [19f23fe9] SymbolicLimits v0.2.1
  [d1185830] SymbolicUtils v2.1.0
  [0c5d862f] Symbolics v5.33.0
  [ab02a1b2] TableOperations v1.2.0
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [62fd8b95] TensorCore v0.1.1
⌅ [8ea1fca8] TermInterface v0.4.1
  [5d786b92] TerminalLoggers v0.1.7
  [a759f4b9] TimerOutputs v0.5.24
  [9f7883ad] Tracker v0.2.34
  [3bb67fe8] TranscodingStreams v0.11.0
  [28d57a85] Transducers v0.4.82
  [fce5fe82] Turing v0.33.1
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1cfade01] UnicodeFun v0.4.1
  [1986cc42] Unitful v1.20.0
  [45397f5d] UnitfulLatexify v1.6.4
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [d80eeb9a] UnsafeAtomicsLLVM v0.1.5
  [41fe7b60] Unzip v0.2.0
  [cc8bc4a8] Widgets v0.6.6
  [efce3f68] WoodburyMatrices v1.0.0
  [700de1a5] ZygoteRules v0.2.5
⌅ [68821587] Arpack_jll v3.5.1+1
  [6e34b625] Bzip2_jll v1.0.8+1
  [83423d85] Cairo_jll v1.18.0+2
  [2702e6a9] EpollShim_jll v0.0.20230411+0
  [2e619515] Expat_jll v2.6.2+0
⌅ [b22a6f82] FFMPEG_jll v4.4.4+1
  [f5851436] FFTW_jll v3.3.10+0
  [a3f928ae] Fontconfig_jll v2.13.96+0
  [d7e528f0] FreeType2_jll v2.13.2+0
  [559328eb] FriBidi_jll v1.0.14+0
  [0656b61e] GLFW_jll v3.4.0+0
  [d2c73de3] GR_jll v0.73.6+0
  [78b55507] Gettext_jll v0.21.0+0
  [7746bdde] Glib_jll v2.80.2+0
  [3b182d85] Graphite2_jll v1.3.14+0
  [2e76f6c2] HarfBuzz_jll v2.8.1+1
  [1d5cc7b8] IntelOpenMP_jll v2024.2.0+0
  [aacddb02] JpegTurbo_jll v3.0.3+0
  [c1c5ebd0] LAME_jll v3.100.2+0
⌅ [88015f11] LERC_jll v3.0.0+1
  [dad2f222] LLVMExtra_jll v0.0.30+0
  [1d63c593] LLVMOpenMP_jll v15.0.7+0
  [dd4b983a] LZO_jll v2.10.2+0
  [81d17ec3] L_BFGS_B_jll v3.0.1+0
⌅ [e9f186c6] Libffi_jll v3.2.2+1
  [d4300ac3] Libgcrypt_jll v1.8.11+0
  [7e76a0d4] Libglvnd_jll v1.6.0+0
  [7add5ba3] Libgpg_error_jll v1.49.0+0
  [94ce4f54] Libiconv_jll v1.17.0+0
  [4b2f31a3] Libmount_jll v2.40.1+0
⌅ [89763e89] Libtiff_jll v4.5.1+1
  [38a345b3] Libuuid_jll v2.40.1+0
  [856f044c] MKL_jll v2024.2.0+0
  [e7412a2a] Ogg_jll v1.3.5+1
  [458c3c95] OpenSSL_jll v3.0.14+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [91d4177d] Opus_jll v1.3.2+0
  [30392449] Pixman_jll v0.43.4+0
  [c0090381] Qt6Base_jll v6.7.1+1
  [f50d1b31] Rmath_jll v0.4.2+0
  [a44049a8] Vulkan_Loader_jll v1.3.243+0
  [a2964d1f] Wayland_jll v1.21.0+1
  [2381bf8a] Wayland_protocols_jll v1.31.0+0
  [02c8fc9c] XML2_jll v2.13.1+0
  [aed1982a] XSLT_jll v1.1.41+0
  [ffd25f8a] XZ_jll v5.4.6+0
  [f67eecfb] Xorg_libICE_jll v1.1.1+0
  [c834827a] Xorg_libSM_jll v1.2.4+0
  [4f6342f7] Xorg_libX11_jll v1.8.6+0
  [0c0b7dd1] Xorg_libXau_jll v1.0.11+0
  [935fb764] Xorg_libXcursor_jll v1.2.0+4
  [a3789734] Xorg_libXdmcp_jll v1.1.4+0
  [1082639a] Xorg_libXext_jll v1.3.6+0
  [d091e8ba] Xorg_libXfixes_jll v5.0.3+4
  [a51aa0fd] Xorg_libXi_jll v1.7.10+4
  [d1454406] Xorg_libXinerama_jll v1.1.4+4
  [ec84b674] Xorg_libXrandr_jll v1.5.2+4
  [ea2f1a96] Xorg_libXrender_jll v0.9.11+0
  [14d82f49] Xorg_libpthread_stubs_jll v0.1.1+0
  [c7cfdc94] Xorg_libxcb_jll v1.17.0+0
  [cc61e674] Xorg_libxkbfile_jll v1.1.2+0
  [e920d4aa] Xorg_xcb_util_cursor_jll v0.1.4+0
  [12413925] Xorg_xcb_util_image_jll v0.4.0+1
  [2def613f] Xorg_xcb_util_jll v0.4.0+1
  [975044d2] Xorg_xcb_util_keysyms_jll v0.4.0+1
  [0d47668e] Xorg_xcb_util_renderutil_jll v0.3.9+1
  [c22f9ab0] Xorg_xcb_util_wm_jll v0.4.1+1
  [35661453] Xorg_xkbcomp_jll v1.4.6+0
  [33bec58e] Xorg_xkeyboard_config_jll v2.39.0+0
  [c5fb5394] Xorg_xtrans_jll v1.5.0+0
  [3161d3a3] Zstd_jll v1.5.6+0
  [35ca27e7] eudev_jll v3.2.9+0
⌅ [214eeab7] fzf_jll v0.43.0+0
  [1a1c6b14] gperf_jll v3.1.1+0
  [a4ae2306] libaom_jll v3.9.0+0
  [0ac62f75] libass_jll v0.15.1+0
  [2db6ffa8] libevdev_jll v1.11.0+0
  [f638f0a6] libfdk_aac_jll v2.0.2+0
  [36db933b] libinput_jll v1.18.0+0
  [b53b4c65] libpng_jll v1.6.43+1
  [f27f6e37] libvorbis_jll v1.3.7+1
  [009596ad] mtdev_jll v1.1.6+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
  [1270edf5] x264_jll v2021.5.5+0
  [dfaa095f] x265_jll v3.5.0+0
  [d8fb68d0] xkbcommon_jll v1.4.1+1
  [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
  [3fa0cd96] REPL
  [9a3f8284] Random
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization
  [1a1011a3] SharedArrays
  [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 v2.28.2+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 ⌅ have new versions available but compatibility constraints restrict them from upgrading. To see why use `status --outdated -m`

Output of versioninfo()

julia> versioninfo()
Julia Version 1.10.4
Commit 48d4fd48430 (2024-06-04 10:41 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 8 × Intel(R) Core(TM) i7-4790K CPU @ 4.00GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, haswell)
Threads: 4 default, 0 interactive, 2 GC (on 8 virtual cores)
Environment:
  JULIA_CMDSTAN_HOME = /home/dfish/cmdstan
  JULIA_NUM_THREADS = 4
  JULIA_EDITOR = code

Additional context

This error was discovered by @gdalle. Please ping him for technical details, as AD is not my expertise.

He notes that the issue might be a missing rule for integral bounds:

https://github.com/SciML/Integrals.jl/blob/26f0f739778b8a1256535acd14cc38c2a4e21e28/ext/IntegralsForwardDiffExt.jl#L45

SciML / Integrals.jl

ForwardDiff differentiates through solver #251