The solver tries the equation as written before asking for its alternatives: SolveHard -98.6% allocation

[Rafael-SOWNet]

Part of #746 — the standing condition on speed. Same method as #1205 and #1207: a temporary hook attributing allocated bytes to the stages of AnalyticalEquationSolver.Solve, per recursion depth, run on SolveHard.

What the attribution showed

stage	bytes
Entity.Alternate(4) before the replacement loop, top level	268 MB	a whole level-4 simplification of the equation; the loop solved the first spelling it produced and never looked past
the same, at depths 2 and 3	103 MB, 20 MB	the recursion asks again at every level
TrySplitOffRationalRoots + IsWorthFactoringToSolve	268 MB	each expands the whole equation — radical constants included — to learn that a sine is not a monomial; twice per equation visited, 18 visits at depth 2 alone
everything else	~200 MB	the solving

What changes

• The equation as written is tried first. SpellingsToSolveOver yields the equation, then the alternatives — and builds them only if the loop gets that far. A spelling that comes back as a condition rather than a finite set is kept as a fallback while the next spelling is tried; that is what keeps x^4 * x^y - 2 answered with a root (SolveOneEquation.ExpSimpl caught the first version).
• TryGetRationalCoefficients reads the tree before it expands. x only under sums, products, quotients by something free of it, and whole non-negative powers; no symbol or constant in a coefficient. A necessary condition only — what passes it is still expanded and checked — so it can lose nothing but time.

Measured

Gate on one machine, both columns in one session:

	baseline (e45413c2)	this change	allocation	time
SolveHard	859,268,416 B, 700 ms	11,818,936 B, 109 ms	−98.6%	0.16x
SolveMediumHard	94,415,256 B, 66.8 ms	1,435,934 B, 13.9 ms	−98.5%	0.21x
SolveMedium	662,923 B, 456 µs	452,901 B, 387 µs	−31.7%	0.85x
SolveEasyMedium	97,335 B, 29.7 µs	65,232 B, 19.2 µs	−33.0%	0.64x
SimplifyHard	733,188,536 B, 371 ms	680,457,400 B, 339 ms	−7.2%	0.92x
SimplifyEasy	116,291 B, 71.2 µs	110,051 B, 66.4 µs	−5.4%	0.93x

Every other entry within 0.1%. The gate's baseline is updated in the same change. Since the 1930th column this morning: SolveHard −99.2%, SolveMediumHard −99.1%, SimplifyHard −81%.

Answers

Every solve in the suite answers as before but one: (x - b)/(x + a) + c/(x + a) keeps its root, and the condition on it is spelled not -(-b + c) + a = 0 where it was not a + -(-b + c) = 0 — the terms in the order the equation had, since it is solved as written rather than resimplified first. Re-pinned with the reason; recorded in BREAKING-CHANGES.md. The SolveHard and SolveMediumHard answers are the same size as before (149,153 and 37,073 nodes) and the corpus gate holds.

Checks

Full suite in two chunks: 9,661 passed, 0 failed (Calculus 1,322, the rest 8,339).

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura