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Read a linear exponent written as a negation in the gamma rule - #2084
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The rule for a power beside an exponential of a power read its exponent term by term, so e^(-a - b x) was answered and e^(-(a + b x)) was declined, though they are one function. The second is how gamma(2, a + b x) is elementary, e^(-(a + b x)) (1 + a + b x), and how a hyperbolic function of a + b x arrives as exponentials. A linear exponent written otherwise is now read as its offset and rate. Rubi's suite on the harness that reads GAMMA, against master 3dc5ac6: 48,634 -> 48,700 of 49,052, 0 wrong, no solved row lost. The gains are 23 in 6.2.1, 20 in 6.1.1, 9 in 6.7.1, 7 in 2.1, 7 in 8.6 (x^(p/3) gamma(2, a + b x) and (c + d x)^m gamma(1, a + b x)) and 1 in 2.3. Three rows of 6.1.1, (c + d x)^m (a + i a sinh(e + f x))^k, move from a quick decline to the harness's timeout: the library answers them in 0.4 s, correctly at x = 0.35, 0.9, 1.45, 18.1 and -12.7, and the harness's recheck at far points at 300 and 2,000 digits evaluates the gamma function there: 22 to 26 s for the derivative at one point at 300. 8.6:249, solved in 21 s in the base run, times out 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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…ny constant (#2086) 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. Claude-Session: https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura Co-authored-by: Claude Opus 5.5 (1M context) <noreply@anthropic.com>
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The rule from #2083 read its exponent term by term, so
e^(-a - b x)was answered ande^(-(a + b x))was declined, though they are one function. The second is howgamma(2, a + b x)is elementary,e^(-(a + b x)) (1 + a + b x), and how a hyperbolic function ofa + b xarrives as exponentials. A linear exponent written otherwise is now read as its offset and rate. Part of #2075.Measured on Rubi's suite, read with the harness that maps
GAMMA, against master3dc5ac6b, the whole corpus each side:The gains are 23 in 6.2.1, 20 in 6.1.1, 9 in 6.7.1, 7 in 2.1, 7 in 8.6 and 1 in 2.3. In 8.6 they are
x^(p/3) gamma(2, a + b x)and(c + d x)^m gamma(1, a + b x).Four rows move to the harness's timeout, and none is the library's.
(c + d x)^m (a + i a sinh(e + f x))^k, declined in 0.2–0.7 s before. The library answers them in 0.4 s. Its derivative matches the integrand exactly atx = 0.35, 0.9, 1.45and at the far points18.1and-12.7, at the default 100 digits. The harness rechecks far points at 300 and then 2,000 digits where there is an exponential of the variable, and the gamma function at 300 digits costs 22 to 26 s for the derivative at one point. That cost is the library's factorial at high precision, the same class as the 19 rows of 5.1.5 that recheck once timed out.(e x)^m GAMMA(p, d (a + b log(c x^n))), was solved in the base run in 21 s, past the 5 s budget. It times out alone on both builds.The suite passes (16,926) and so do the MCP tests (329). The new tests differentiate the three shapes above back.
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https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura