gem: simplifications supporting Jacobian product cancellation#255
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- Fold Indexed(Identity, (i, j)) into Delta(i, j), so that Kronecker deltas introduced by UFL participate in delta elimination. Lower Delta via a Literal identity table in replace_delta, as Indexed(Identity, ...) now folds back into Delta. - COFFEE: iterate argument factorisation to a fixpoint, so that factorised subexpressions are grouped as common factors in subsequent rounds, and group monomials that share the same rest coefficient, so that c*a1 + c*a2 becomes c*(a1 + a2). Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
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Description
GEM-side companion of firedrakeproject/ufl#68, improving the code generated for PhysicallyMapped (zany) elements:
gem.py: foldIndexed(Identity, (i, j))intoDelta(i, j), so the Kronecker deltas introduced by the UFL Jacobian-product cancellation participate in delta elimination and unroll to 0/1 constants.optimise.py: lowerDeltavia aLiteralidentity table inreplace_delta, sinceIndexed(Identity, ...)now folds back intoDelta(this previously madereplace_deltaa no-op, leaking deltas into code generation).coffee.py: iterate argument factorisation to a fixpoint, so subexpressions factorised in one round are grouped as common factors in the next (resolving the long-standing TODO infactorise_atomics), and group monomials sharing the same rest coefficient, soc*a1 + c*a2 + c*a3becomesc*(a1 + a2 + a3). For the Johnson-Mercier div-div term this turns the element tensor accumulation into optimal rank-1 updates.Benchmark (JM mass + div-div, spectral mode, with the companion PRs): 3D flops 763527 -> 444574 (-42%), compile time 3.62s -> 1.81s (-51%), generated code 323kB -> 143kB (-56%).
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