A symbolic constant factor no longer stops the rounds of parts - #1473
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`F^(c (a + b x)) sin(d + pe x)^3` was left as written. The exponent's constant part becomes a factor -- `F^(a c)` -- and the by-parts loop for a polynomial times an exponential times a trigonometric stops when the factor it carries differentiates to nothing. `F^(a c)` differentiates to a *conditional* zero, `0 provided not F = 0 or a c > 0`, and the loop compared against the number: it carried on, the degree never fell, and after the step bound it declined. The derivative is read bare now. The conditions are the constant's own and travel with it in the answer -- the factor is there whatever they say -- and what the loop asks is whether the degree has fallen to nothing, which is a question about the variable. Family 4 of the Rubi suite: 286 -> 287 of 422, 0 wrong, with two rows that produced nothing now producing answers; family 6 377/417 and the 1774-problem suite 1707 unchanged. Suite 12644 passed; allocation gate passed on all 19 gated benchmarks. Part of #718. Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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F^(c (a + b x)) sin(d + pe x)^3was left as written, whileF^(c x) sin(pe x)^3andF^(2 x) sin(3 x + 1)^3both came out — the difference being the exponent's constant part.That part becomes a factor: the reader turns
F^(c(a + b x))intoF^(a c)times an exponential at rateb c ln F. The by-parts loop then stops when the factor it carries differentiates to nothing — andF^(a c)differentiates to a conditional zero,0 provided not F = 0 or a c > 0, which is not the number0. So the comparison failed, the loop carried on with the same carried factor, the degree never fell, and after the step bound the rule declined.The derivative is read bare now (
PartialFractions.Bare). The conditions are the constant's own and travel with it in the answer — the factor is in the integrand whatever they say — and what the loop asks is whether the degree has fallen to nothing, which is a question about the variable, not aboutF.Measured (final build):
familycap.sh 4 6): 286 → 287/422, 0 wrong, unevaluated 85 → 83.bench.sh: PASSED on all 19 gated benchmarks.sin^3,cos^2andsin·cosforms verified by differentiating the answer back with every symbol pinned — worst relative deviation 0 at five points each.Part of #718.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura