New version broke DI tests

[gdalle]

Hi there,
As discovered in JuliaDiff/DifferentiationInterface.jl#966, one of the latest versions of Symbolics broke DI's test suite. More specifically:

• The bug either started with 7.15.3 (probably due to ) or 7.15.2, because the last CI run with 7.15.1 worked fine. I haven't bisected by testing 7.15.2 yet, but looking at the release notes, I'd say fix: properly handle differentiating operator applications #1805 is the most likely culprit (my test functions don't involve transposition so fix: fix transpose(::Arr) * Arr #1807 seems innocent).
• It is common to Julia 1.10, 1.11 and 1.12.
• It only affects DI's Cache mechanism.
• More surprisingly, it only affects the jacobian function: all the other operators work fine with Cache

Minimum working example (maybe we can unleash Claude?):

using DifferentiationInterface, DifferentiationInterfaceTest, Symbolics

test_differentiation(
    AutoSymbolics(),
    DifferentiationInterfaceTest.default_scenarios(; include_normal = false, include_cachified = true, use_tuples = false);
    logging = LOGGING,
    excluded=[:hessian, :hvp, :second_derivative, :derivative, :pushforward, :gradient, :pullback]
);

It wasn't caught in the downstream tests here because we put a minimal setup without contexts, but that can be changed if necessary.

[ChrisRackauckas-Claude]

Root Cause Analysis

The regression is actually in SymbolicUtils.jl v4.18.4 (not Symbolics.jl), specifically in PR JuliaSymbolics/SymbolicUtils.jl#862 which refactored toexpr for performance.

The bug: In v4.18.4, toexpr(O::BasicSymbolic{T}, st) checks st.rewrites for all BasicSymbolic types, including Const. The old code had a guard (issym(O) || iscall(O)) in substitute_name that prevented constants from being rewritten.

When DI's build_function is called with erased cache variables (arrays of Const(0)), those zeros get added to st.rewrites as argument references (e.g., Const(0) → ˍ₋arg2[12]). Due to hash consing, all Const(0) values are the same object. So when toexpr encounters a literal 0 in the Jacobian expression (off-diagonal entries), it finds the rewrite and replaces it with ˍ₋arg2[12]. At runtime, arg2 contains actual cache data (non-zero), producing the incorrect results.

Version bisection:

• SymbolicUtils 4.18.3: ✅ all 620 DI cachified Jacobian tests pass
• SymbolicUtils 4.18.4: ❌ 184 failures (same as 4.18.5)
• The Symbolics.jl version (7.15.1 vs 7.15.3) does not matter; both fail with SymbolicUtils ≥4.18.4

Fix: JuliaSymbolics/SymbolicUtils.jl#870 — skip st.rewrites lookup for Const values in toexpr.