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Read an exponential of an inverse below the bar as a negative multiple - #1935
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Rafael-SOWNet merged 3 commits intoOct 18, 2026
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Rafael-SOWNet merged 3 commits into
Rafael-SOWNet merged 3 commits into
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x^2/(e^(i arctan(a x)) (c + a^2 c x^2)^(3/2)) wrote the exponential as (1 + i a x)/sqrt(1 + a^2 x^2) below the bar, a linear with i in it the rational rules do not read there. Taken above the bar with its exponent negated, a negative whole multiple is written over the conjugate, (1 - i L)^(-n) (1 + L^2)^(n/2): x^2 (1 - i a x)/(c^(3/2) (1 + a^2 x^2)^2), which is answered (Rubi's 5.3.6:513). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
…le-of-the-arctangents-quadratic-splits
Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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x^2/(e^(i arctan(a x)) (c + a² c x²)^(3/2))was left unevaluated:SolveByWritingAnExponentialOfAnInverseAlgebraicallyread the exponential below the bar asn = 1. A pre-pass now takes an exponential of an inverse from below the bar to above it with its exponent negated. For a negative wholen,e^(n i arctan(L))is written over the conjugate,(1 - i L)^(-n) (1 + L²)^(n/2), so the linear withiin it is above the bar, where the rational rules read it.Part of #718 — Rubi's 5.3.6:513 and :515, and the
xand1siblings of :513. Master ran past the 5-second corpus budget on :515; it is answered in 110 ms.Measured against master b2ef509:
tanh(a + 2 ln x)^2/x^3and 3.5:37. They are Take a linear factor common to a sum below the bar out of it #1932's (the branch's base included it and the master arm did not), and they give the same result on Take a linear factor common to a sum below the bar out of it #1932's own build;After merging master 2bc0561 (which brings #1934's rule for the same exponentials): built for every target, suite 15,561 passed, and the pocket again, 317/325 with 0 wrong. The only change from the branch alone is #1934's two gains.
Recorded in BREAKING-CHANGES.md.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura