Unexpected MaxIters retcode

[AayushSabharwal]

Describe the bug 🐞

The following NonlinearProblem (which is actually just a linear system) retcodes with MaxIters despite having an almost-zero residual:

julia> rhs = (out, var"##arg#9935777206874629696", var"##arg#5772744033551999711")->begin
                 #= /Users/aayush/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:385 =#
                 #= /Users/aayush/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:386 =#
                 #= /Users/aayush/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:387 =#
                 begin
                     var"b[1]" = var"##arg#9935777206874629696"[1]
                     var"b[3]" = var"##arg#9935777206874629696"[2]
                     var"b[4]" = var"##arg#9935777206874629696"[3]
                     var"b[5]" = var"##arg#9935777206874629696"[4]
                     var"b[6]" = var"##arg#9935777206874629696"[5]
                     var"a[3, 2]" = var"##arg#5772744033551999711"[1]
                     var"a[4, 2]" = var"##arg#5772744033551999711"[2]
                     var"a[5, 2]" = var"##arg#5772744033551999711"[3]
                     var"a[6, 2]" = var"##arg#5772744033551999711"[4]
                     var"a[4, 3]" = var"##arg#5772744033551999711"[5]
                     var"a[5, 3]" = var"##arg#5772744033551999711"[6]
                     var"a[6, 3]" = var"##arg#5772744033551999711"[7]
                     var"a[5, 4]" = var"##arg#5772744033551999711"[8]
                     var"a[6, 4]" = var"##arg#5772744033551999711"[9]
                     var"a[6, 5]" = var"##arg#5772744033551999711"[10]
                     DEF = var"##arg#5772744033551999711"[11]
                     var"b[2]" = var"##arg#5772744033551999711"[12]
                     DEF = var"##arg#5772744033551999711"[13]
                     DEF = var"##arg#5772744033551999711"[14]
                     DEF = var"##arg#5772744033551999711"[15]
                     DEF = var"##arg#5772744033551999711"[16]
                     var"bh[1]" = var"##arg#5772744033551999711"[17]
                     var"bh[2]" = var"##arg#5772744033551999711"[18]
                     var"bh[3]" = var"##arg#5772744033551999711"[19]
                     var"bh[4]" = var"##arg#5772744033551999711"[20]
                     var"bh[5]" = var"##arg#5772744033551999711"[21]
                     var"bh[6]" = var"##arg#5772744033551999711"[22]
                     var"c[2]" = var"##arg#5772744033551999711"[23]
                     var"c[3]" = var"##arg#5772744033551999711"[24]
                     var"c[4]" = var"##arg#5772744033551999711"[25]
                     var"c[5]" = var"##arg#5772744033551999711"[26]
                     begin
                         #= /Users/aayush/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:430 =#
                         out[1] = (+)((+)((+)((+)((+)((+)(-1, var"b[1]"), var"b[2]"), var"b[3]"), var"b[4]"), var"b[5]"), var"b[6]")
                         out[2] = (+)((+)((+)((+)((+)(-1//2, var"b[6]"), (*)(var"b[2]", var"c[2]")), (*)(var"b[3]", var"c[3]")), (*)(var"b[4]", var"c[4]")), (*)(var"b[5]", var"c[5]"))
                         out[3] = (+)((+)((+)((+)((+)(-1//3, var"b[6]"), (*)(var"b[2]", (^)(var"c[2]", 2))), (*)(var"b[3]", (^)(var"c[3]", 2))), (*)(var"b[4]", (^)(var"c[4]", 2))), (*)(var"b[5]", (^)(var"c[5]", 2)))
                         out[4] = (+)((+)((+)((+)((+)(-1//4, var"b[6]"), (*)(var"b[2]", (^)(var"c[2]", 3))), (*)(var"b[3]", (^)(var"c[3]", 3))), (*)(var"b[4]", (^)(var"c[4]", 3))), (*)(var"b[5]", (^)(var"c[5]", 3)))
                         out[5] = (+)((+)((+)((+)((+)(-1//5, var"b[6]"), (*)(var"b[2]", (^)(var"c[2]", 4))), (*)(var"b[3]", (^)(var"c[3]", 4))), (*)(var"b[4]", (^)(var"c[4]", 4))), (*)(var"b[5]", (^)(var"c[5]", 4)))
                         #= /Users/aayush/.julia/packages/SymbolicUtils/jf8aQ/src/code.jl:432 =#
                         nothing
                     end
                 end
             end
julia> buf = [-3.9832922616275948, -4.897257424419193, 0.09342981865962026, 0.012311116055817766, -0.8184897230589248, 0.03567038175398558, 0.007904372737270881, -0.023021565778278998, -0.004547784942303123, -0.08604742939071738, 0.3222220453337315, 4.0, 14.510754334138149, -0.06388830199314302, -14.877423429110568, -2.8916646483591006, 0.7838826954260111, 3.558969354280331, 0.5437040690837686, -0.20242602909940763, -0.26057184466461175, -3.4485994161224918, 1.0, 2.0, 3.0, 2.000017523009925]
julia> idxs = [11, 13, 14, 15, 16]
julia> nlp2 = NonlinearProblem(rhs, buf[idxs], buf)
julia> sol = solve(nlp2)
retcode: MaxIters
u: 5-element Vector{Float64}:
      0.3222226846094242
 -18071.685098970098
     -0.06389073858644431
  18071.31843923952
     -2.8916722154444034
julia> sol.resid
5-element Vector{Float64}:
 -1.7355006320940447e-12
  0.0
  0.0
  0.0
  0.0

Expected behavior

It returns successfully

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

  [47edcb42] ADTypes v1.9.0
⌃ [7da242da] Enzyme v0.13.11
  [6a86dc24] FiniteDiff v2.26.0
  [f6369f11] ForwardDiff v0.10.36
  [14197337] GenericLinearAlgebra v0.3.14
  [86223c79] Graphs v1.12.0
⌃ [0b43b601] Groebner v0.7.5
  [f213a82b] HomotopyContinuation v2.11.1
  [7ed4a6bd] LinearSolve v2.36.1
⌃ [961ee093] ModelingToolkit v9.46.1
  [bdf0d083] MultiFloats v2.3.0
⌅ [2edaba10] Nemo v0.45.7
  [8913a72c] NonlinearSolve v3.15.1
  [d236fae5] PreallocationTools v0.4.24
  [47965b36] RootedTrees v2.23.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [d1185830] SymbolicUtils v3.7.2
⌃ [0c5d862f] Symbolics v6.15.3

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

  [47edcb42] ADTypes v1.9.0
⌅ [c3fe647b] AbstractAlgebra v0.41.11
  [398f06c4] AbstractLattices v0.3.1
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  [ec485272] ArnoldiMethod v0.4.0
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⌃ [4c555306] ArrayLayouts v1.10.3
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  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.1.1
  [fa961155] CEnum v0.5.0
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  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.25.0
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  [861a8166] Combinatorics v1.0.2
  [a80b9123] CommonMark v0.8.15
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [f70d9fcc] CommonWorldInvalidations v1.0.0
  [34da2185] Compat v4.16.0
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  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
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⌃ [a0c0ee7d] DifferentiationInterface v0.6.16
⌃ [8d63f2c5] DispatchDoctor v0.4.16
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⌃ [7da242da] Enzyme v0.13.11
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⌅ [46192b85] GPUArraysCore v0.1.6
⌃ [61eb1bfa] GPUCompiler v1.0.0
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⌃ [0b43b601] Groebner v0.7.5
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  [ef3ab10e] KLU v0.6.0
⌃ [ba0b0d4f] Krylov v0.9.7
⌃ [929cbde3] LLVM v9.1.2
  [8ac3fa9e] LRUCache v1.6.1
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⌃ [961ee093] ModelingToolkit v9.46.1
⌃ [7475f97c] Mods v2.2.5
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  [8913a72c] NonlinearSolve v3.15.1
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  [429524aa] Optim v1.9.4
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  [65ce6f38] PackageExtensionCompat v1.0.2
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  [2ae35dd2] Permutations v0.4.22
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  [f517fe37] Polyester v0.7.16
  [1d0040c9] PolyesterWeave v0.2.2
  [f27b6e38] Polynomials v4.0.11
  [85a6dd25] PositiveFactorizations v0.2.4
  [d236fae5] PreallocationTools v0.4.24
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
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  [92933f4c] ProgressMeter v1.10.2
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  [e6cf234a] RandomNumbers v1.6.0
  [3cdcf5f2] RecipesBase v1.3.4
⌃ [731186ca] RecursiveArrayTools v3.27.0
  [f2c3362d] RecursiveFactorization v0.2.23
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [ae5879a3] ResettableStacks v1.1.1
  [286e9d63] RingLists v0.2.9
  [79098fc4] Rmath v0.8.0
  [47965b36] RootedTrees v2.23.1
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [fdea26ae] SIMD v3.6.0
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  [476501e8] SLEEFPirates v0.6.43
⌃ [0bca4576] SciMLBase v2.56.4
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  [727e6d20] SimpleNonlinearSolve v1.12.3
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  [cc47b68c] SimplePolynomials v0.2.18
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  [a2af1166] SortingAlgorithms v1.2.1
  [9f842d2f] SparseConnectivityTracer v0.6.8
⌃ [0a514795] SparseMatrixColorings v0.4.7
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.4.0
  [aedffcd0] Static v1.1.1
  [0d7ed370] StaticArrayInterface v1.8.0
  [90137ffa] StaticArrays v1.9.8
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [82ae8749] StatsAPI v1.7.0
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  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
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  [09ab397b] StructArrays v0.6.18
  [53d494c1] StructIO v0.3.1
⌃ [2efcf032] SymbolicIndexingInterface v0.3.33
  [19f23fe9] SymbolicLimits v0.2.2
  [d1185830] SymbolicUtils v3.7.2
⌃ [0c5d862f] Symbolics v6.15.3
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [8ea1fca8] TermInterface v2.0.0
  [1c621080] TestItems v1.0.0
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.25
  [0796e94c] Tokenize v0.5.29
  [a2a6695c] TreeViews v0.3.0
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  [781d530d] TruncatedStacktraces v1.4.0
  [5c2747f8] URIs v1.5.1
  [3a884ed6] UnPack v1.0.2
  [1986cc42] Unitful v1.21.0
  [a7c27f48] Unityper v0.1.6
  [013be700] UnsafeAtomics v0.2.1
  [3d5dd08c] VectorizationBase v0.21.70
⌅ [7cc45869] Enzyme_jll v0.0.154+0
  [e134572f] FLINT_jll v300.100.300+0
  [1d5cc7b8] IntelOpenMP_jll v2024.2.1+0
  [dad2f222] LLVMExtra_jll v0.0.34+0
⌃ [94ce4f54] Libiconv_jll v1.17.0+0
  [856f044c] MKL_jll v2024.2.0+0
  [2ce0c516] MPC_jll v1.2.1+0
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⌅ [3428059b] SymEngine_jll v0.9.0+1
⌃ [02c8fc9c] XML2_jll v2.13.3+0
  [1317d2d5] oneTBB_jll v2021.12.0+0
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  [ade2ca70] Dates v1.11.0
  [8ba89e20] Distributed v1.11.0
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  [7b1f6079] FileWatching v1.11.0
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  [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
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  [44cfe95a] Pkg v1.11.0
  [de0858da] Printf v1.11.0
  [9a3f8284] Random v1.11.0
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  [1a1011a3] SharedArrays v1.11.0
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays 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
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  [3a97d323] MPFR_jll v4.2.1+0
  [c8ffd9c3] MbedTLS_jll v2.28.6+0
  [14a3606d] MozillaCACerts_jll v2023.12.12
  [4536629a] OpenBLAS_jll v0.3.27+1
  [05823500] OpenLibm_jll v0.8.1+2
  [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

• Output of versioninfo()

Julia Version 1.11.1
Commit 8f5b7ca12ad (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  CPU: 8 × Apple M2
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, apple-m2)
Threads: 16 default, 2 interactive, 4 GC (on 4 virtual cores)
Environment:
  JULIA_PKG_USE_CLI_GIT = true
  JULIA_PKG_SERVER = https://internal.juliahub.com

[avik-pal]

with inf-norm the residual norm is 1e-12. The default convergence is around 1e-14 IIRC

[ErikQQY]

Docs:

• abstol::Number: The absolute tolerance. Defaults to
  real(oneunit(T)) * (eps(real(one(T))))^(4 // 5).
• reltol::Number: The relative tolerance. Defaults to
  real(oneunit(T)) * (eps(real(one(T))))^(4 // 5).

julia> T = Float64
Float64

julia> real(oneunit(T)) * (eps(real(one(T))))^(4/5)
3.000213634488528e-13

[AayushSabharwal]

I see, thanks!