Unexpected `MaxIters` retcode

**Describe the bug 🐞**

The following `NonlinearProblem` (which is actually just a linear system) retcodes with `MaxIters` despite having an almost-zero residual:

```julia
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()`

```julia
  [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)`

```julia
  [47edcb42] ADTypes v1.9.0
⌅ [c3fe647b] AbstractAlgebra v0.41.11
  [398f06c4] AbstractLattices v0.3.1
  [1520ce14] AbstractTrees v0.4.5
  [7d9f7c33] Accessors v0.1.38
  [79e6a3ab] Adapt v4.1.0
  [66dad0bd] AliasTables v1.1.3
  [fb37089c] Arblib v1.2.1
  [ec485272] ArnoldiMethod v0.4.0
  [4fba245c] ArrayInterface v7.16.0
⌃ [4c555306] ArrayLayouts v1.10.3
  [a9b6321e] Atomix v0.1.0
  [e2ed5e7c] Bijections v0.1.9
  [62783981] BitTwiddlingConvenienceFunctions v0.1.6
  [8e7c35d0] BlockArrays v1.1.1
  [fa961155] CEnum v0.5.0
  [2a0fbf3d] CPUSummary v0.2.6
  [00ebfdb7] CSTParser v3.4.3
  [d360d2e6] ChainRulesCore v1.25.0
  [fb6a15b2] CloseOpenIntervals v0.1.13
  [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
  [b152e2b5] CompositeTypes v0.1.4
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.8
  [adafc99b] CpuId v0.3.1
  [a8cc5b0e] Crayons v4.1.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.20
  [e2d170a0] DataValueInterfaces v1.0.0
  [8bb1440f] DelimitedFiles v1.9.1
  [2b5f629d] DiffEqBase v6.158.3
  [459566f4] DiffEqCallbacks v4.0.0
  [77a26b50] DiffEqNoiseProcess v5.23.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
⌃ [a0c0ee7d] DifferentiationInterface v0.6.16
⌃ [8d63f2c5] DispatchDoctor v0.4.16
  [31c24e10] Distributions v0.25.112
  [ffbed154] DocStringExtensions v0.9.3
  [5b8099bc] DomainSets v0.7.14
  [7c1d4256] DynamicPolynomials v0.6.0
  [06fc5a27] DynamicQuantities v1.1.0
  [fdbdab4c] ElasticArrays v1.2.12
  [4e289a0a] EnumX v1.0.4
⌃ [7da242da] Enzyme v0.13.11
  [f151be2c] EnzymeCore v0.8.4
  [e2ba6199] ExprTools v0.1.10
⌅ [6b7a57c9] Expronicon v0.8.5
  [7034ab61] FastBroadcast v0.3.5
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.4
  [1a297f60] FillArrays v1.13.0
  [64ca27bc] FindFirstFunctions v1.4.1
  [6a86dc24] FiniteDiff v2.26.0
  [1fa38f19] Format v1.3.7
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.4.12
⌅ [46192b85] GPUArraysCore v0.1.6
⌃ [61eb1bfa] GPUCompiler v1.0.0
  [14197337] GenericLinearAlgebra v0.3.14
  [c27321d9] Glob v1.3.1
  [86223c79] Graphs v1.12.0
⌃ [0b43b601] Groebner v0.7.5
  [f213a82b] HomotopyContinuation v2.11.1
  [3e5b6fbb] HostCPUFeatures v0.1.17
  [34004b35] HypergeometricFunctions v0.3.24
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.5
  [18e54dd8] IntegerMathUtils v0.1.2
  [8197267c] IntervalSets v0.7.10
  [524e6230] IntervalTrees v1.1.0
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.2
  [c8e1da08] IterTools v1.10.0
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.6.1
  [98e50ef6] JuliaFormatter v1.0.62
  [ccbc3e58] JumpProcesses v9.14.0
  [ef3ab10e] KLU v0.6.0
⌃ [ba0b0d4f] Krylov v0.9.7
⌃ [929cbde3] LLVM v9.1.2
  [8ac3fa9e] LRUCache v1.6.1
  [b964fa9f] LaTeXStrings v1.4.0
  [23fbe1c1] Latexify v0.16.5
  [10f19ff3] LayoutPointers v0.1.17
  [5078a376] LazyArrays v2.2.1
  [9c8b4983] LightXML v0.9.1
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [9b3f67b0] LinearAlgebraX v0.2.10
  [7ed4a6bd] LinearSolve v2.36.1
  [2ab3a3ac] LogExpFunctions v0.3.28
  [bdcacae8] LoopVectorization v0.12.171
  [d8e11817] MLStyle v0.4.17
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [bb5d69b7] MaybeInplace v0.1.4
  [e1d29d7a] Missings v1.2.0
  [291d046c] MixedSubdivisions v1.1.5
⌃ [961ee093] ModelingToolkit v9.46.1
⌃ [7475f97c] Mods v2.2.5
  [46d2c3a1] MuladdMacro v0.2.4
  [bdf0d083] MultiFloats v2.3.0
  [3b2b4ff1] Multisets v0.4.5
  [102ac46a] MultivariatePolynomials v0.5.7
  [d8a4904e] MutableArithmetics v1.5.2
  [d41bc354] NLSolversBase v7.8.3
  [77ba4419] NaNMath v1.0.2
⌅ [2edaba10] Nemo v0.45.7
  [8913a72c] NonlinearSolve v3.15.1
  [d8793406] ObjectFile v0.4.2
  [6fe1bfb0] OffsetArrays v1.14.1
  [429524aa] Optim v1.9.4
  [bac558e1] OrderedCollections v1.6.3
  [90014a1f] PDMats v0.11.31
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [2ae35dd2] Permutations v0.4.22
  [e409e4f3] PoissonRandom v0.4.4
  [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
  [08abe8d2] PrettyTables v2.4.0
  [27ebfcd6] Primes v0.5.6
  [92933f4c] ProgressMeter v1.10.2
  [01f381cc] ProjectiveVectors v1.1.4
  [43287f4e] PtrArrays v1.2.1
  [1fd47b50] QuadGK v2.11.1
  [74087812] Random123 v1.7.0
  [fb686558] RandomExtensions v0.4.4
  [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
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.43
⌃ [0bca4576] SciMLBase v2.56.4
  [19f34311] SciMLJacobianOperators v0.1.0
  [c0aeaf25] SciMLOperators v0.3.11
  [53ae85a6] SciMLStructures v1.5.0
  [6c6a2e73] Scratch v1.2.1
  [8e049039] SemialgebraicSets v0.3.3
  [efcf1570] Setfield v1.1.1
  [55797a34] SimpleGraphs v0.8.6
  [727e6d20] SimpleNonlinearSolve v1.12.3
  [ec83eff0] SimplePartitions v0.3.3
  [cc47b68c] SimplePolynomials v0.2.18
  [a6525b86] SimpleRandom v0.3.2
  [699a6c99] SimpleTraits v0.9.4
  [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
  [2913bbd2] StatsBase v0.34.3
  [4c63d2b9] StatsFuns v1.3.2
  [7792a7ef] StrideArraysCore v0.5.7
  [892a3eda] StringManipulation v0.4.0
  [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
  [d5829a12] TriangularSolve v0.2.1
  [410a4b4d] Tricks v0.1.9
  [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
  [656ef2d0] OpenBLAS32_jll v0.3.28+3
  [efe28fd5] OpenSpecFun_jll v0.5.5+0
  [f50d1b31] Rmath_jll v0.5.1+0
⌅ [3428059b] SymEngine_jll v0.9.0+1
⌃ [02c8fc9c] XML2_jll v2.13.3+0
  [1317d2d5] oneTBB_jll v2021.12.0+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
  [9a3f8284] Random v1.11.0
  [ea8e919c] SHA v0.7.0
  [9e88b42a] Serialization v1.11.0
  [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
  [781609d7] GMP_jll v6.3.0+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [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
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
```


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Unexpected `MaxIters` retcode #492

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Unexpected `MaxIters` retcode #492