[Rafael-SOWNet]

Part of #233.

• A hyperbolic quotient over a linear in its cosine, asked as the cosine's, before the tangent. Rubi's 6.2.5 sech(x)^3/(a + b cosh(x)) and 6.5.3 sech(x)^4/(a + b sech(x)) ran past the corpus's budget. SolveARationalFunctionOfTheHyperbolicTangent answered each under the tangent of the half argument, as a cube of 1 + t^2 beside a symbolic quadratic, in about 118,000 characters.
• The change. By Osborn's rule each is a rational function of a cosine alone, over a sum linear in it, and partial fractions in the cosine answer that. 1/(cos(s)^3 (a + b cos(s))) comes to 2,121 characters. A third mode of SolveAHyperbolicIntegrandAsATrigonometricOne asks that question beside Ask a hyperbolic quotient over a quadratic in its sine or cosine as the sine's, before the tangent #2042's, ahead of the tangent. It applies only where s stands in cos(s) alone and the sums below the bar are linear in it, to the first power. The answer in s goes back as the rule writes every one, and is checked by its derivative.
• The first chain flagged 6.7.1:971 (a + b cosh(x))/(b + a cosh(x))^2. Its denominator is a square written out, and asked in s it took 0.60 GB where the tangent takes 0.14, confirmed alone. Hence the sums must now be linear, and 971 is back at master's 0.136 GB.

Input	master ef4150e	this branch
6.2.5:89 sech(x)^3/(a + b cosh(x))	118,366 characters, 2.9 s, 0.65 GB	2,396 characters, 0.6 s, 0.04 GB
6.5.3:139 sech(x)^4/(a + b sech(x))	118,032 characters	2,412 characters
cosh(x)^3/(a + b cosh(x))	2,858 characters	1,108 characters
cosh(x)^2/(a + b sech(x))	2,820 characters	802 characters

The answers spell the tangent of the half argument through tan(-i x/2), as the Osborn rule's other answers do.

Chain against master ef4150e, re-run after the narrowing:

• The pocket of every family-6 row, 3,690 of them, went from 3,676 to 3,678 solved. The one "wrong" on each side is 6.1.5:94, the evaluator's at a large x.
• Every family's sample is unchanged.
• The two rows that moved are 6.2.5:89 and 6.5.3:139, run alone: timeouts on master, solved here.
• 9,281 rows were compared for allocation, and none grew past 1.3x and 300 MB.

The library builds for netstandard2.0, net8.0 and net10.0. The suite is left to CI. The BREAKING-CHANGES lengths were measured on the branch, and the 2.5.0 column on a v2.5.0 build. Rebased onto 79754e7.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura