[Bug] Enzyme-based line search fails when storing dual variables in non-differentiable arrays

**Describe the bug”**
When using the :enzyme autodiff backend in LineSearch.jl, the solver throws an internal error if a differentiable (dual) variable is stored into a non-differentiable data structure during line search. This leads to a crash with the message “internal error: IR interpretation: encountered an unexpected or internal error."


**Expected behavior**
I expected the line search to run successfully using Enzyme’s autodiff without crashing, or at least produce a descriptive error about unsupported operations.

**Minimal Reproducible Example 👇**

I have wrote a test case below demonstrating this bug. Running the test suite also gives a similar bug.

```julia
using LineSearch
using LineSearches
using ADTypes
using Enzyme
using Test
using SciMLBase
using CommonSolve

# Define a simple in-place problem
function nlf(dx, x, p)
    dx .= x .^ 2 .- p
    return dx
end

# Create the problem
nlp = NonlinearProblem(nlf, [-1.0, 1.0], [3.0])

# Create the line search setup
ls = LineSearch.LineSearchesJL(
    method = LineSearches.BackTracking(order = 3),
    autodiff = AutoEnzyme()
)

@testset "Enzyme autodiff test" begin
    try
        # Initialize u and function evaluation
        u = copy(nlp.u0)
        fu = similar(u)
        nlp.f(fu, u, nlp.p)
        
        # Initialize the line search cache - using CommonSolve.init instead of LineSearch.init
        ls_cache = CommonSolve.init(nlp, ls, fu, u)
        
        # Define a descent direction
        du = -fu
        
        # Solve the line search step
        ls_sol = CommonSolve.solve!(ls_cache, u, du)
        
        # Check if the step was successful
        @test ls_sol.retcode == ReturnCode.Success
        
        println("Enzyme test passed!")
    catch e
        println("Enzyme test failed with error:")
        println(e)
        rethrow(e)
    end
end
```

**Error & Stacktrace ⚠️**

The error manifests in two stack traces, showing both the immediate broadcast operation failure and the full AD context:

#### First Stack Trace (Broadcast Operation)
```julia
Stacktrace:
    [1] size
      @ ./array.jl:194
    [2] axes
      @ ./abstractarray.jl:98
    [3] newindexer
      @ ./broadcast.jl:598
    [4] extrude
      @ ./broadcast.jl:645
    [5] preprocess
      @ ./broadcast.jl:953
    [6] preprocess_args
      @ ./broadcast.jl:956
    [7] preprocess_args
      @ ./broadcast.jl:955
    [8] preprocess
      @ ./broadcast.jl:952
    [9] override_bc_copyto!
      @ ~/.julia/packages/Enzyme/QsaeA/src/compiler/interpreter.jl:798
   [10] copyto!
      @ ./broadcast.jl:925
   [11] materialize!
      @ ./broadcast.jl:883
   [12] materialize!
      @ ./broadcast.jl:880
   [13] nlf
      @ /mnt/c/Users/sonth/OneDrive/Documents/Academia/Random CS Projects/GSOC2025/LineSearch.jl/test/enzyme_test.jl:11
```

#### Second Stack Trace (Full AD Context)
```julia
Stacktrace:
    [1] mightalias
      @ ./abstractarray.jl:1537 [inlined]
    [2] unalias
      @ ./abstractarray.jl:1500 [inlined]
    [3] broadcast_unalias
      @ ./broadcast.jl:946 [inlined]
    [4] preprocess
      @ ./broadcast.jl:953 [inlined]
    [5] preprocess_args
      @ ./broadcast.jl:956 [inlined]
    [6] preprocess_args
      @ ./broadcast.jl:955 [inlined]
    [7] preprocess
      @ ./broadcast.jl:952 [inlined]
    [8] override_bc_copyto!
      @ ~/.julia/packages/Enzyme/QsaeA/src/compiler/interpreter.jl:798 [inlined]
    [9] copyto!
      @ ./broadcast.jl:925 [inlined]
   [10] materialize!
      @ ./broadcast.jl:883 [inlined]
   [11] materialize!
      @ ./broadcast.jl:880 [inlined]
   [12] nlf
      @ /mnt/c/Users/sonth/OneDrive/Documents/Academia/Random CS Projects/GSOC2025/LineSearch.jl/test/enzyme_test.jl:11
   [13] NonlinearFunction
      @ ~/.julia/packages/SciMLBase/sYmAV/src/scimlfunctions.jl:2469 [inlined]
   [14] NonlinearFunction
      @ ~/.julia/packages/SciMLBase/sYmAV/src/scimlfunctions.jl:0 [inlined]
   [15] diffejulia_NonlinearFunction_18028_inner_3wrap
      @ ~/.julia/packages/SciMLBase/sYmAV/src/scimlfunctions.jl:0
   [21] value_and_pullback!
      @ DifferentiationInterfaceEnzymeExt ~/.julia/packages/DifferentiationInterface/0ZwTi/ext/DifferentiationInterfaceEnzymeExt/reverse_twoarg.jl:123
```

**Environment (please complete the following information):**

  - Output of `using Pkg; Pkg.status()`

```julia
Status `/mnt/c/Users/sonth/OneDrive/Documents/Academia/Random CS Projects/GSOC2025/LineSearch.jl/test/Project.toml`
  [47edcb42] ADTypes v1.14.0
  [38540f10] CommonSolve v0.2.4
  [7da242da] Enzyme v0.13.30
  [6a86dc24] FiniteDiff v2.27.0
  [f6369f11] ForwardDiff v0.10.38
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [37e2e3b7] ReverseDiff v1.15.3
  [0bca4576] SciMLBase v2.75.1
  [9f7883ad] Tracker v0.2.37
  [e88e6eb3] Zygote v0.7.4

```

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

```julia
Status `/mnt/c/Users/sonth/OneDrive/Documents/Academia/Random CS Projects/GSOC2025/LineSearch.jl/test/Manifest.toml`
  [47edcb42] ADTypes v1.14.0
  [621f4979] AbstractFFTs v1.5.0
  [7d9f7c33] Accessors v0.1.42
  [79e6a3ab] Adapt v4.3.0
  [4fba245c] ArrayInterface v7.18.0
  [a9b6321e] Atomix v1.1.1
  [fa961155] CEnum v0.5.0
  [082447d4] ChainRules v1.72.3
  [d360d2e6] ChainRulesCore v1.25.1
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.1
  [34da2185] Compat v4.16.0
  [a33af91c] CompositionsBase v0.1.2
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.8
  [9a962f9c] DataAPI v1.16.0
  [e2d170a0] DataValueInterfaces v1.0.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [a0c0ee7d] DifferentiationInterface v0.6.44
  [ffbed154] DocStringExtensions v0.9.3
  [4e289a0a] EnumX v1.0.4
  [7da242da] Enzyme v0.13.30
  [f151be2c] EnzymeCore v0.8.8
  [e2ba6199] ExprTools v0.1.10
  [55351af7] ExproniconLite v0.10.14
  [9aa1b823] FastClosures v0.3.2
  [1a297f60] FillArrays v1.13.0
  [6a86dc24] FiniteDiff v2.27.0
  [f6369f11] ForwardDiff v0.10.38
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [d9f16b24] Functors v0.5.2
  [0c68f7d7] GPUArrays v11.2.2
  [46192b85] GPUArraysCore v0.2.0
  [61eb1bfa] GPUCompiler v1.2.0
  [076d061b] HashArrayMappedTries v0.2.0
  [7869d1d1] IRTools v0.4.14
  [3587e190] InverseFunctions v0.1.17
  [92d709cd] IrrationalConstants v0.2.4
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.7.0
  [ae98c720] Jieko v0.2.1
  [63c18a36] KernelAbstractions v0.9.34
  [929cbde3] LLVM v9.2.0
  [87fe0de2] LineSearch v0.1.4
  [d3d80556] LineSearches v7.3.0
  [2ab3a3ac] LogExpFunctions v0.3.29
  [1914dd2f] MacroTools v0.5.15
  [bb5d69b7] MaybeInplace v0.1.4
  [2e0e35c7] Moshi v0.3.5
  [d41bc354] NLSolversBase v7.8.3
  [872c559c] NNlib v0.9.28
  [77ba4419] NaNMath v1.1.2
  [d8793406] ObjectFile v0.4.3
  [3bd65402] Optimisers v0.4.5
  [bac558e1] OrderedCollections v1.8.0
  [d96e819e] Parameters v0.12.3
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [c1ae055f] RealDot v0.1.0
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.31.1
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.1
  [37e2e3b7] ReverseDiff v1.15.3
  [7e49a35a] RuntimeGeneratedFunctions v0.5.13
  [0bca4576] SciMLBase v2.75.1
  [19f34311] SciMLJacobianOperators v0.1.1
  [c0aeaf25] SciMLOperators v0.3.12
  [53ae85a6] SciMLStructures v1.7.0
  [7e506255] ScopedValues v1.3.0
  [6c6a2e73] Scratch v1.2.1
  [efcf1570] Setfield v1.1.2
  [dc90abb0] SparseInverseSubset v0.1.2
  [276daf66] SpecialFunctions v2.5.0
  [90137ffa] StaticArrays v1.9.13
  [1e83bf80] StaticArraysCore v1.4.3
  [10745b16] Statistics v1.11.1
  [09ab397b] StructArrays v0.7.0
  [53d494c1] StructIO v0.3.1
  [2efcf032] SymbolicIndexingInterface v0.3.38
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.12.0
  [a759f4b9] TimerOutputs v0.5.28
  [9f7883ad] Tracker v0.2.37
  [3a884ed6] UnPack v1.0.2
  [013be700] UnsafeAtomics v0.3.0
  [e88e6eb3] Zygote v0.7.4
  [700de1a5] ZygoteRules v0.2.7
  [7cc45869] Enzyme_jll v0.0.172+0
  [dad2f222] LLVMExtra_jll v0.0.35+0
  [efe28fd5] OpenSpecFun_jll v0.5.6+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
  [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
  [6462fe0b] Sockets v1.11.0
  [2f01184e] SparseArrays v1.11.0
  [4607b0f0] SuiteSparse
  [fa267f1f] TOML v1.0.3
  [a4e569a6] Tar v1.10.0
  [cf7118a7] UUIDs v1.11.0
  [4ec0a83e] Unicode v1.11.0
  [e66e0078] CompilerSupportLibraries_jll v1.1.1+0
  [deac9b47] LibCURL_jll v8.6.0+0
  [e37daf67] LibGit2_jll v1.7.2+0
  [29816b5a] LibSSH2_jll v1.11.0+1
  [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+4
  [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 1.11.4
Commit 8561cc3d68d (2025-03-10 11:36 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 16 × 11th Gen Intel(R) Core(TM) i9-11900H @ 2.50GHz
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, tigerlake)
Threads: 1 default, 0 interactive, 1 GC (on 16 virtual cores)

```

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Uh oh!

[Bug] Enzyme-based line search fails when storing dual variables in non-differentiable arrays #19

First Stack Trace (Broadcast Operation)

Second Stack Trace (Full AD Context)

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Uh oh!

[Bug] Enzyme-based line search fails when storing dual variables in non-differentiable arrays #19

Description

First Stack Trace (Broadcast Operation)

Second Stack Trace (Full AD Context)

Metadata

Metadata

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