[dpsanders]

Summary

• Adds derivative_ssa(ex, diff_var, vars) — builds an SSAFunction for the partial derivative ∂ex/∂diff_var using reverse-mode AD (gradient_code)
• Adds derivative_contractor(ex, diff_var, vars) — builds a compiled forward-backward contractor for the derivative
• Handles gradient code's non-elementary assignments by binarizing the SSA (decomposing n-ary and compound-argument operations into unary/binary ops via CSE)
• Filters non-reversible assignments (constant seeds, identity copies from gradient initialization) from the reverse pass

This builds on #80 (SSAFunction type). The gradient SSA is binarized and then fed through forward_backward_contractor via the SSAFunction interface.

Example

@variables x y
ex = x^2 + y^2

# Build contractor for ∂(x²+y²)/∂x = 2x
C = derivative_contractor(ex, x, [x, y])

# Contract: 2x ∈ [0,0] → x = 0
C(IntervalBox(-10..10, 2), interval(0, 0))
# → (([0,0], [-10,10]), [-20,20])

Test plan

• All 18 ReversePropagation tests pass (was 12, +6 new for derivative_contractor)
• All 16 IntervalConstraintProgramming tests pass (downstream consumer)
• Simple polynomial: d/dx(x²+y²) = 2x, equality and interval constraints
• Transcendental: d/dx(sin(xy)+x²) produces contracted result
• Derivative w.r.t. second variable works correctly

🤖 Generated with Claude Code

[dpsanders]

Closing in favour of a split: the actual derivative_contractor needs subgradient-aware interval reverses for abs/max/min (see #894 context and the ChainRules discussion on this PR), and that's cleaner as its own PR. The non-interval fixes (derivative hardening: trim the op registry, override scalar rules that produced non-reversible adjoints, expose binarize_ssa) will land in a separate smaller PR shortly.