TTFX: Upstream invalidation fixes to reduce compilation time by ~40k invalidations

[ChrisRackauckas-Claude]

Problem

Profiling the TTFX of a standard MTK DAE case (Cartesian pendulum) on Julia 1.12 reveals ~127s total time-to-first-solve, with the dominant cost being recompilation from method invalidations:

• @mtkbuild (structural simplification): 66.5s (85% recompilation)
• ODEProblem construction: 31.5s (58% recompilation)
• First solve: 15.7s
• Package loading: 13.2s

Using SnoopCompile.@snoop_invalidations, we identified 70,261 total invalidations across 621 trees when loading the MTK + OrdinaryDiffEq stack. The top 3 sources account for 57% of all invalidations:

#	Package	Method	Invalidations	% of Total
1	SparseMatrixColorings.jl	eltype(::SparsityPatternCSC{T})	24,906	35.4%
2	BlockArrays.jl	getindex(::AbstractArray{T,N}, ::BlockIndices{N})	12,082	17.2%
3	StaticArrays.jl	any(f::Function, a::StaticArray; dims)	3,081	4.4%

Upstream PRs

Fixes have been submitted to all three packages:

1. SparseMatrixColorings.jl — gdalle/SparseMatrixColorings.jl#304

   • Base.eltype(::SparsityPatternCSC{Ti}) was returning Ti (the index type) instead of Bool, invalidating all eltype(::AbstractArray) backedges
   • Fix: Changed to SparseArrays.indtype since Ti is the index type, not element type

2. BlockArrays.jl — JuliaArrays/BlockArrays.jl#499

   • getindex(::AbstractArray{T,N}, ::BlockIndices{N}) invalidated all compiled getindex instances because BlockIndices <: AbstractArray
   • Fix: Removed the AbstractArray fallback and added specialized unblock methods that decompose BlockIndices into block-level + sub-indexing for non-blocked axes

3. StaticArrays.jl — JuliaArrays/StaticArrays.jl#1334

   • any(f::Function, a::StaticArray; dims) invalidated Base.any(::Function, ::AbstractArray)
   • Fix: Override Base._any/Base._all (internal dispatch targets) instead of the entry-point methods

All three fixes pass their respective full test suites locally.

Expected impact

Eliminating ~40,069 invalidations (57% of total) should significantly reduce the recompilation overhead in @mtkbuild and ODEProblem construction, which together account for ~98s of the ~127s TTFX.

Full profiling details

TTFX breakdown (Julia 1.12.4, MTK v11.12.0)

Phase                          Time      Compile%  Recompile%
─────────────────────────────  ────────  ────────  ──────────
Package loading (MTK)          ~11.0s    -         -
Package loading (ODE solvers)  ~0.7s     -         -
Model definition               ~1.3s    99.72%    -
@mtkbuild (structural simpl.) ~66.5s    99.93%    85%
ODEProblem construction       ~31.5s    99.82%    58%
First solve                   ~15.7s    99.96%    -
Second solve                   ~0.001s  -         -
───────────────────────────────────────────────────────────────
TOTAL TTFX                    ~127s

Top 10 import times (@time_imports)

Package                        Time (ms)  % of total
──────────────────────────     ─────────  ──────────
SymbolicUtils                     870      12.1%
BlockArrays                       716       9.9%
ArrayLayouts                      680       9.4%
NonlinearSolveFirstOrder          583       8.1%
Pkg→REPLExt                       577       8.0%
MutableArithmetics                528       7.3%
SciMLBase                         474       6.6%
ModelingToolkit                   330       4.6%
OrdinaryDiffEqNonlinearSolve     325       4.5%
FillArrays                        308       4.3%

Remaining invalidation sources (after top 3 fixed)

The remaining ~30k invalidations come from many smaller sources. The next largest contributors should be profiled once the top 3 fixes are merged to see the updated landscape.

[ChrisRackauckas]

The last one was tracked down to be a Base Julia thing: JuliaLang/julia#61185. At least, that's the better fix than trying to do every any dispatch.