Ask a hyperbolic integrand as a trigonometric one

[Rafael-SOWNet]

The parser writes the hyperbolic functions as exponentials, so the trigonometric rules never read them: (b cosh(x) + c sinh(x) + sqrt(b^2 - c^2))^(1/2) was declined where (b cos(x) + c sin(x) + sqrt(b^2 + c^2))^(1/2) is answered at once.

The rule uses Osborn's rule. With L = i s, cosh(L) = cos(s), sinh(L) = i sin(s) and dx = i ds/b, and the trigonometric rules answer the question in s. The answer is written back with s = -i L and checked against the integrand at sampled points. A branch that holds for a real s and differs on the imaginary axis is declined.

The rule fires only where:

• every exponential of x is a whole power of one e^L;
• x stands nowhere else;
• it is the question asked, not a sub-question;
• every rule in x has already declined.

A first version was asked early and allowed x beside the exponentials. It answered 46 problems and cost 11 that master answers, because the question in s is slow to decline and took the budget from rules that answer x/cosh(x)^(7/2) + 3/5 x sqrt(cosh(x)) and the like at once. This version is the one measured below.

Measured on 8a1ef454, branch against master:

Run	Problems	Master	Branch
Pocket: Rubi's 6.1–6.7	2,962	2,866 solved	2,897 solved
Family 1, 40 a file	1,381	1,362	1,362
Family 0, whole	1,814	1,789	1,789
Families 2 to 8, sampled	2,410	2,362	2,360

Re-run alone on both builds, 30 of the 38 problems that moved go from declined or timed out to answered: 27 in 6.7.1, two in 6.5.3 and one in 6.6.3. None goes the other way. The two-row drop in families 3 and 7 is the problems that time out on both builds when re-run alone. One problem reads wrong on both builds: 6.1.5:94, #1944, an evaluator defect.

AHyperbolicIntegrandAsATrigonometricOneIntegralTest differentiates the answers back. It also checks that the rules in x keep the problems the first version took from them. BREAKING-CHANGES.md has the entry, with the 2.5.0 column measured on v2.5.0.

Part of #233.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura