Example from the docs doesn't run

Describe the bug 🐞

The example from the README page/first page of the docs doesn't run.

Expected behavior

The solve call at the end should run with the retcode Success.

Minimal Reproducible Example 👇

using BoundaryValueDiffEq
tspan = (0.0, pi / 2)
function simplependulum!(du, u, p, t)
    θ = u[1]
    dθ = u[2]
    du[1] = dθ
    du[2] = -9.81 * sin(θ)
end
function bc!(residual, u, p, t)
    residual[1] = u[end ÷ 2][1] + pi / 2
    residual[2] = u[end][1] - pi / 2
end
prob = BVProblem(simplependulum!, bc!, [pi / 2, pi / 2], tspan)
@time sol = solve(prob, MIRK4(), dt = 0.05)

Error & Stacktrace ⚠️

There's no error, but this warning shows up 20+ times near the start of the run:

┌ Warning: The supplied DiffCache was too small and was enlarged. This incurs allocations
│     on the first call to `get_tmp`. If few calls to `get_tmp` occur and optimal performance is essential,
│     consider changing 'N'/chunk size of this DiffCache to 12.
└ @ PreallocationTools ~/.julia/packages/PreallocationTools/zJxgA/src/PreallocationTools.jl:191

I'm not sure

If I let the solve call run for a long time (I left it for several hours and I'm not sure when in there it finished), it returns with the retcode Failure:

retcode: Failure
Interpolation: MIRK Order 4 Interpolation
t: 2049-element Vector{Float64}:
 0.0
 0.0007669903939428206
 0.0015339807878856412
 0.0023009711818284618
 ⋮
 1.569262346007011
 1.5700293364009537
 1.5707963267948966
u: 2049-element Vector{Vector{Float64}}:
 [0.0, 0.0]
 [0.0, 0.0]
 [0.0, 0.0]
 [0.0, 0.0]
 ⋮
 [1.570784784853829, 0.015048351528957164]
 [1.5707934413096296, 0.007524175764572552]
 [1.5707963267948966, -2.196606842514e-312]

Environment (please complete the following information):

Output of using Pkg; Pkg.status()

Status `~/projects/bvptest/Project.toml`
  [764a87c0] BoundaryValueDiffEq v5.6.3

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

julia> using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)
Status `~/projects/bvptest/Manifest.toml`
  [47edcb42] ADTypes v0.2.7
  [79e6a3ab] Adapt v4.0.3
⌅ [ec485272] ArnoldiMethod v0.2.0
  [4fba245c] ArrayInterface v7.9.0
  [4c555306] ArrayLayouts v1.6.1
  [aae01518] BandedMatrices v1.6.0
  [62783981] BitTwiddlingConvenienceFunctions v0.1.5
  [764a87c0] BoundaryValueDiffEq v5.6.3
  [2a0fbf3d] CPUSummary v0.2.4
  [d360d2e6] ChainRulesCore v1.23.0
  [fb6a15b2] CloseOpenIntervals v0.1.12
  [38540f10] CommonSolve v0.2.4
  [bbf7d656] CommonSubexpressions v0.3.0
  [34da2185] Compat v4.14.0
  [2569d6c7] ConcreteStructs v0.2.3
  [187b0558] ConstructionBase v1.5.4
  [adafc99b] CpuId v0.3.1
  [9a962f9c] DataAPI v1.16.0
  [864edb3b] DataStructures v0.18.18
  [e2d170a0] DataValueInterfaces v1.0.0
  [2b5f629d] DiffEqBase v6.148.0
  [163ba53b] DiffResults v1.1.0
  [b552c78f] DiffRules v1.15.1
  [ffbed154] DocStringExtensions v0.9.3
  [4e289a0a] EnumX v1.0.4
⌃ [f151be2c] EnzymeCore v0.6.5
  [e2ba6199] ExprTools v0.1.10
  [9d29842c] FastAlmostBandedMatrices v0.1.0
  [7034ab61] FastBroadcast v0.2.8
  [9aa1b823] FastClosures v0.3.2
  [29a986be] FastLapackInterface v2.0.2
  [1a297f60] FillArrays v1.9.3
  [6a86dc24] FiniteDiff v2.23.0
  [f6369f11] ForwardDiff v0.10.36
  [069b7b12] FunctionWrappers v1.1.3
  [77dc65aa] FunctionWrappersWrappers v0.1.3
  [46192b85] GPUArraysCore v0.1.6
  [86223c79] Graphs v1.9.0
  [3e5b6fbb] HostCPUFeatures v0.1.16
  [615f187c] IfElse v0.1.1
  [d25df0c9] Inflate v0.1.4
  [92d709cd] IrrationalConstants v0.2.2
  [82899510] IteratorInterfaceExtensions v1.0.0
  [692b3bcd] JLLWrappers v1.5.0
  [ef3ab10e] KLU v0.6.0
  [ba0b0d4f] Krylov v0.9.5
  [10f19ff3] LayoutPointers v0.1.15
  [5078a376] LazyArrays v1.8.3
  [d3d80556] LineSearches v7.2.0
  [7ed4a6bd] LinearSolve v2.27.0
  [2ab3a3ac] LogExpFunctions v0.3.27
  [bdcacae8] LoopVectorization v0.12.166
  [1914dd2f] MacroTools v0.5.13
  [d125e4d3] ManualMemory v0.1.8
  [a3b82374] MatrixFactorizations v2.1.0
  [bb5d69b7] MaybeInplace v0.1.1
  [46d2c3a1] MuladdMacro v0.2.4
  [d41bc354] NLSolversBase v7.8.3
  [77ba4419] NaNMath v1.0.2
  [8913a72c] NonlinearSolve v3.8.0
  [6fe1bfb0] OffsetArrays v1.13.0
  [bac558e1] OrderedCollections v1.6.3
  [65ce6f38] PackageExtensionCompat v1.0.2
  [d96e819e] Parameters v0.12.3
  [f517fe37] Polyester v0.7.9
  [1d0040c9] PolyesterWeave v0.2.1
  [d236fae5] PreallocationTools v0.4.20
  [aea7be01] PrecompileTools v1.2.1
  [21216c6a] Preferences v1.4.3
  [3cdcf5f2] RecipesBase v1.3.4
  [731186ca] RecursiveArrayTools v3.12.0
  [f2c3362d] RecursiveFactorization v0.2.21
  [189a3867] Reexport v1.2.2
  [ae029012] Requires v1.3.0
  [7e49a35a] RuntimeGeneratedFunctions v0.5.12
  [94e857df] SIMDTypes v0.1.0
  [476501e8] SLEEFPirates v0.6.42
  [0bca4576] SciMLBase v2.29.0
  [c0aeaf25] SciMLOperators v0.3.8
  [efcf1570] Setfield v1.1.1
  [727e6d20] SimpleNonlinearSolve v1.6.0
  [699a6c99] SimpleTraits v0.9.4
  [47a9eef4] SparseDiffTools v2.17.0
  [e56a9233] Sparspak v0.3.9
  [276daf66] SpecialFunctions v2.3.1
  [aedffcd0] Static v0.8.10
  [0d7ed370] StaticArrayInterface v1.5.0
  [90137ffa] StaticArrays v1.9.3
  [1e83bf80] StaticArraysCore v1.4.2
  [7792a7ef] StrideArraysCore v0.5.2
  [2efcf032] SymbolicIndexingInterface v0.3.11
  [3783bdb8] TableTraits v1.0.1
  [bd369af6] Tables v1.11.1
  [8290d209] ThreadingUtilities v0.5.2
  [a759f4b9] TimerOutputs v0.5.23
  [d5829a12] TriangularSolve v0.1.20
  [410a4b4d] Tricks v0.1.8
  [781d530d] TruncatedStacktraces v1.4.0
  [3a884ed6] UnPack v1.0.2
  [3d5dd08c] VectorizationBase v0.21.65
  [19fa3120] VertexSafeGraphs v0.2.0
  [1d5cc7b8] IntelOpenMP_jll v2024.0.2+0
  [856f044c] MKL_jll v2024.0.0+0
  [efe28fd5] OpenSpecFun_jll v0.5.5+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
  [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 v1.1.0+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
  [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 ⌃ 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`

Output of versioninfo()

julia> versioninfo()
Julia Version 1.10.2
Commit bd47eca2c8a (2024-03-01 10:14 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: macOS (arm64-apple-darwin22.4.0)
  CPU: 10 × Apple M1 Pro
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-15.0.7 (ORCJIT, apple-m1)
Threads: 8 default, 0 interactive, 4 GC (on 8 virtual cores)
Environment:
  JULIA_NUM_THREADS = 8
  LD_LIBRARY_PATH = :/Users/adityasengupta/scetre/DAOROOT/lib:/Users/adityasengupta/scetre/DAOROOT/lib64:/opt/homebrew/lib
  JULIA_EDITOR = code

Additional context

I'd imagine this is because of the PreallocationTools issue, but I haven't been able to find anything over there about how to fix it.

SciML / BoundaryValueDiffEq.jl

Example from the docs doesn't run #170