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A power of a logarithm is read as one of c x^r before its derivative is simplified - #1407
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…is simplified atanh(tanh(a + b x))^4 was answered in 300 ms and, since #1379, ran past three minutes: the reader for a power of A + B ln(c x^r) simplified the logarithmic derivative of any single logarithm's argument to see whether it was r/x, and the argument here is a quotient of exponentials whose derivative the simplifier turns over for minutes on the way to no. The argument is read first -- products, quotients and powers of x and of constants, however nested, c (d x^m)^n -- and anything else is not this shape without a derivative being taken. The reader of a linear in the quotient-of-linears rule gets the same guard: a leaf with a function of x in it is not a linear however it simplifies. Family 7's atanh(tanh) and acoth(coth) rows are answers again, in 300 ms and 41 ms; the 1774-problem suite is unchanged at 1706 with 0 wrong. 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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Found by re-sampling Rubi's family 7 on today's master:
atanh(tanh(a + b x))^4andacoth(coth(a + b x)), 300 ms and 41 ms answers on 2026-09-16, were timeouts. Bisected to #1379:IsAffineInALogarithmOfAPowerOfXsimplified the logarithmic derivative of any single logarithm's argument to see whether it wasr/x, and here the argument is a quotient of exponentials whose derivative the simplifier turns over for minutes (past 190 s on the probe) on the way to no.Change. The argument is read first — products, quotients and powers of
xand of constants, however nested (c (d x^m)^nincluded) — and anything else is not this shape without a derivative being taken. The linear reader inSolveByTheQuotientOfTheLogarithmsLinearsgets the same guard: a leaf with a function ofxin it is not a linear however it simplifies, so noSimplifyis spent on it. Both are declines made cheap; no answer changes.Measured.
atanh(tanh(a + b x))^4300 ms,acoth(coth(a + b x))41 ms, both differentiating back (two rows added toLogarithmOfARationalFunctionByPartsTest, bounded byIntegrationDecline.Guard); #1379's own rows still pass. The 1,774-problem suite: 1706/1774, 0 wrong, 0 timeouts, verdicts identical to master, 89.6 s → 83.5 s. All four suites green (11,513). Family 7 sample: 147 → 150 of 270, the threeatanh(tanh)/acoth(coth)timeouts answered (x^2 atanh(tanh(a + b x))at 18.6 s is past the budget and counted as a timeout still; three others go from a 5 s timeout to a 7–19 s decline, which the sample counts the same way).Also seen on the same re-sample and not fixed here:
1/sqrt(atanh(tanh(a + b x))), a 306 ms answer at 2aa0006 and unevaluated since #1377 (a846738), where the exponential substitution began taking a symbolic slope and the substitution search no longer reachesu =the logarithm. Noted for a separate look.Part of #718.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura