[Rafael-SOWNet]

About forty of Rubi's problems were answered only in 12–25 s, against the corpus harness's 5 s budget. They flip between solved and timed out with machine load, and they will time out for good once the budget binds (#1995). Four guards and reorderings get the answering route reached sooner, with no answer changed:

• The pair rule before the first sum split. SolvePairOfHyperbolicPowersTwoApart is asked for sums just before the SolveBySplittingSum that follows the linear-factor reduction. That split had spent 9–12 s declining each elliptic term before the pair rule answered at its later position; the rule's own remark says "before the split". It returns null unless the exponents are fractional, and then no term of the split is elementary alone.
• Exact pre-checks in five readers, read before the expensive numerator:
  • a whole power ≥ 2 of something in x below the bar, for SolveAPowerOfALinearBesideTheDerivativeOfAQuadraticOverItsPower, SolveAPowerOfALinearOverAPowerOfAQuadratic and SolveARationalFunctionOverAPowerOfASymbolicQuadratic;
  • the root below the bar, for SolveXOverACubicBinomialBesideTheRootOfAnother;
  • an arctangent, for SolveAnArctangentOverAPowerOfOnePlusICXUnderTheTangent.
    For 7.2.4:599, each had been expanding a numerator of thousands of terms.
• SolveByCombiningRadicals and an inverse hyperbolic function's logarithm. It counts the root inside such a logarithm as no root. It had rewritten ln(1/u + sqrt(1 + 1/u^2)) into a spelling nothing reads, then spent 18 s declining, before the inverse-hyperbolic substitution answered in 0.1 s (7.6.2:23).
• The substitution search's repeat test covers more candidates. It now covers any function of one trigonometric function of a linear, a quadratic mirrored across its vertex, and even powers of a quotient of linears. Its two values are compared in doubles, and nothing is refused where a double cannot hold them. It is skipped past a power of x of 64: an exact subtraction of two 1,900-digit rationals had hung x^24 (a x + b x^38)^12.

Measured on 8270086f, branch against master:

Run	Problems	Master	Branch
Pocket: the 2–12 s band, the borderline rows and 370 fast rows	710	691 solved	694 solved
Family 1, 40 a file	1,381	1,368	1,368
Family 0, whole	1,814	1,789	1,789
Families 2 to 8, sampled	2,410	2,380	2,381

On the pocket's problems answered on both builds, allocation falls from 1,361 GB to 1,071 GB. All eleven moves re-run alone are answered on the branch, against nine on master:

Row	Master alone	Branch alone
7.6.2:23	24.7 s, 41 GB	29 ms
3.2.1:292	23.4 s, 34 GB	6.2 s, 7 GB
4.7.7:117	22.3 s	4.6 s
1.2.3.4:111	22.1 s	4.9 s
7.2.4:599	timed out	3.9 s
1.2.1.4:1120	timed out	9.0 s

None allocates more. The four the pocket showed lost are 22–25 s rows that flipped under load; each is answered alone on both builds.

Answers are identical across 710 rows. A sweep of 5,018 rows of 1.1.1.x, 1.1.3.x and 1.1.4.x found no answer changes, allocation 12.7% lower, and nothing slower; it was made after the 1.1.4.2:487 fix. No run had a wrong answer.

Rebased over #2002, which adds a vertex test for quadratic candidates at the same call site; this branch's repeat test runs first. On the combined build both PRs' rows answer at their measured cost, and their 781 tests pass. SlowDeclinesAheadOfTheAnsweringRuleIntegralTest differentiates nine rows back, with no duration asserts. No answer changes, so BREAKING-CHANGES.md has no entry.

Part of #233.

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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura