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Read the gamma rule's exponent expanded, and its constant factor as any constant - #2086
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…ny constant A hyperbolic function of a power of x arrives as (e^u - e^(-u))/2, and the gamma rule read -(c + d x^3) as one term, which is not a power of x: sinh(c + d x^3) was declined. The exponent is now read expanded where it does not read as written. And where the answer's constant factor x^(m + 1) z^(-s) is the same on both half-lines it is written as that constant, so that the answer has a value at 0; it had to be a number, and x^(1/3) e^(-1 - 3 x^2), with 3^(-2/3) on both sides, left its integral from 0 to 1 as written. It is now 0.11693893956963..., which quadrature agrees with. Rubi's suite on the harness that reads GAMMA, against master 6a7b656: 48,850 -> 48,875 of 49,052, 0 wrong, no solved row lost. The gains are 19 in 6.1.3, 5 in 6.2.3, and 8.6:249, solved in 21 s as in earlier runs. Two rows of 6.1.3, (e x)^m sinh(a + b/x^2)^k, move from a decline to the harness's timeout: the library answers them in 0.4 and 0.1 s, and they differentiate back; the time is the harness's verification, as for #2084's three. Two rows' allocation grew in the run and is identical alone on both builds. Part of #2075. Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura
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Two small extensions of the gamma rule from #2083. Part of #2075.
xarrives as(e^u - e^(-u))/2, and the rule read-(c + d x^3)as one term, which is not a power ofx. Sosinh(c + d x^3)was declined, and so was every 6.1.3 integrand beside it. The exponent is now read expanded where it does not read as written.x^(m + 1) z^(-s)is the same constant on both half-lines it is written as that constant, so that the answer has a value at 0. It had to be a number.x^(1/3) e^(-1 - 3 x^2)has3^(-2/3)on both sides and left its integral from 0 to 1 as written. That integral is now0.11693893956963…, and quadrature agrees.Measured on Rubi's suite, read with the harness that maps
GAMMA, against master6a7b656a, the whole corpus each side:The gains are 19 in 6.1.3 and 5 in 6.2.3. 8.6:249 is solved too, in 21 s, as it was in an earlier run: it is slow either way.
Two rows of 6.1.3,
(e x)^m sinh(a + b/x^2)^k, move from a decline to the harness's timeout. In a fresh process the library answers them in 0.4 s and 0.1 s, and the answers differentiate back. The time is the harness's verification of a gamma function at far points, as for #2084's three. Two rows' allocation grew in the run,6.3.7:86and8.4:174, and alone it is identical on both builds.The suite passes (16,939) and so do the MCP tests (329).
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura