Add precompile workload for Dual and SubArray broadcast operations

[ChrisRackauckas-Claude]

Summary

• Adds a PrecompileTools.@compile_workload block to DiffEqBaseForwardDiffExt.jl that exercises common scalar, array, and SubArray operations on Dual{Tag{OrdinaryDiffEqTag, Float64}, Float64, 1}
• The extension already defined this dualT type but had no precompilation, causing ~2.5s of broadcast compilation overhead at runtime for ODE functions using views

What's precompiled

Scalar Dual operations:

• Arithmetic: +, -, *, /, ^, negation, abs
• Math functions: exp, log, sin, cos, tan, sqrt, cbrt, asin, acos, atan, sinh, cosh, tanh
• Comparisons/predicates: <, >, min, max, isnan, isinf, isfinite
• Conversion: zero, one, float, ForwardDiff.value, ForwardDiff.partials

Vector{Dual} operations:

• Broadcast: .+, .-, .*, ./, .^
• In-place broadcast: out .= v1 .* s .+ v2, etc.
• Reductions: sum, sum(abs2, ...), maximum(abs, ...)
• LinearAlgebra: dot, norm (1, 2, Inf)
• copy, fill!

SubArray broadcast patterns (Float64 and Dual):

• dst .= -k .* src1 .+ k .* src2 .* src3 (linear combination of views)
• dst .= k .* src1 .- k .* src2 .^ 2 .- k .* src2 .* src3 (subtraction chain with power)
• dst .= k .* src .^ 2 (scaled power)
• Simple patterns: assignment, scaling, element-wise ops, negation

Benchmark

Testing with the ROBER problem from DifferentialEquations.jl#1125:

Scenario	First solve
Baseline (views, no pre-warming)	3.05s
With SubArray+Dual pre-warming	0.80s
Direct indexing (no views)	0.25s

73% reduction in first-solve overhead for view-based ODE functions.

Test plan

• All DiffEqBase tests pass locally
• Precompile workload code verified independently
• CI passes

🤖 Generated with Claude Code

[ChrisRackauckas-Claude]

Updated: Removed expression-specific fused broadcast patterns (e.g. dsv1 .= k .* sv1 .+ k .* sv2 .* sv3).

These create unique nested Broadcasted type trees per expression and can't be generically precompiled. The dominant TTFX cost for view-based ODE functions (~2.5s of 3.0s) comes from these fused trees, which is a Julia broadcast fusion design constraint.

The precompile workload now contains only generic building blocks:

• Scalar Dual arithmetic, math functions, comparisons
• Vector{Dual} broadcast, reductions, LinearAlgebra ops
• Primitive SubArray operations (copy, scale, multiply, add, subtract, power, negate)

These provide modest TTFX improvement (~13% for view-based functions) but are universally useful operations that benefit all ForwardDiff-based differentiation.