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Read the gamma rule's integrand when it is written otherwise - #2096
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Rafael-SOWNet merged 1 commit intoOct 23, 2026
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The rule for x^m F^(a + b x^n) and (c + d x)^m F^(a + b x) read one exponential, one term in x in its exponent, and nothing else in x beside the power: - e^(a + c + b x^n + d x^n) had two terms of one degree, now read as (b + d) x^n; - f^(a + b x^n) g^(c + d x^n) had two exponentials, now read as one, e^(u ln f + v ln g), or F^(u + v) for one base; - (c + d x)^m (k + f x) F^(a + b x) has a polynomial beside the power of the linear, now written in powers of the linear, each term then the power alone. By parts leaves this of (c + d x)^m gamma(2, a + b x). Terms gathered so can cancel, and then it declines: e^x e^(-x)/x is 1/x, and read as a gamma function of order 0 at 0 it was NaN, where by parts leaves it beside Shi(a + b x)^2. And at a whole or half-whole order it declines, for the elementary, exponential-integral and error-function routes to answer. Where none of them does, it is now asked last at any order: (c + d x)^(-1 - 4 n) F^(a + b (c + d x)^n) is a gamma function of order -4, and by parts reaches -3. 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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Lets the gamma rule (#2083) read its integrand when it is written otherwise, and asks it last at a whole order. Part of #2075.
What it reads now. The rule for
x^m F^(a + b x^n)and(c + d x)^m F^(a + b x)read one exponential, one term inxin its exponent, and nothing else inxbeside the power.e^(a + c + b x^n + d x^n)has two terms of one degree, now read as(b + d) x^n.f^(a + b x^n) g^(c + d x^n)has two exponentials, now read as one:e^(u ln f + v ln g), orF^(u + v)for one base.(c + d x)^m (k + f x) F^(a + b x)has a polynomial beside the power of the linear. That polynomial is now written in powers of the linear, and each term is the power alone. By parts leaves this shape of(c + d x)^m gamma(2, a + b x).e^x e^(-x)/xis1/x, and read as a gamma function of order 0 at 0 it was NaN. By parts leaves exactly this besideShi(a + b x)^2, and the first run of this branch answeredShi(a + b x)^2andChi(a + b x)^2wrongly. Both are tests now.A whole order, last. At a whole or half-whole order the rule declines, for the elementary, exponential-integral and error-function routes to answer. Where none of them does, it is now asked again at the end of the dispatcher, at any order.
(c + d x)^(-1 - 4 n) F^(a + b (c + d x)^n)is a gamma function of order -4, and by parts reaches only -3.Measured on Rubi's suite, with the harness that reads
GAMMA, against68211405, the whole corpus each side. This branch was measured on2be40bad, which adds #2088 to that base, after the fix above. It is rebased onto master now.68211405The gains are
2.3:423,424,890and891,4.7.6:50, and8.6:222and223; #2091 has since solved the last two on master by another route. The other 5 are #2088's. Time per stream is 1.027, 1.011 and 0.906 of the base's, and allocation 1.0000, 1.0008 and 0.9939. One row's allocation grew in the run,6.1.7:196, which is the same alone on both builds, as before.Nine integrals differentiate back in the tests. The suite passes (16,961), and so do the MCP tests (329).
🤖 Generated with Claude Code
https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura