[Rafael-SOWNet]

#1956 integrates a function of the hyperbolic tangent alone under u = tanh. For a power of a + a coth(L) or a - a coth(L) alone, the 1 ± u of the Jacobian cancels into the base in u, which leaves a root over three linears. In W = e^(2L) the same integrand is a binomial differential written in a few terms. Under #1956, (1 + coth(x))^(7/2) became 14,533 characters and 1.3 GB, where the substitution writes 287 characters at 0.13 GB. The rule now declines when the only factor holding u is a power that is not whole of (p u + q)/(r u + s), with p = ±q and q, r not zero.

Each problem alone, before #1956 → master → this branch (allocation, answer length):

Problem	Before #1956	Master	Branch
6.4.2:99 (1+coth(x))^(7/2)	0.13 GB, 287	1.31 GB, 14,533	0.13 GB, 287
6.4.2:100	0.13, 235	0.48, 10,435	0.13, 235
6.4.2:101	0.13, 180	0.22, 3,785	0.13, 180
6.4.2:102–105	0.13, 140–341	0.05–0.06, 1,342–2,734	as before #1956

On 102–105 the branch allocates about 0.07 GB more than master, for answers 4 to 10 times shorter. Every answer in the branch column is character for character the one before #1956.

Measured on 8270086f, branch against master:

Run	Problems	Master	Branch
Pocket: all of Rubi's family 6	3,690	3,616 solved	3,616 solved
Family 1, 40 a file	1,381	1,368	1,368
Family 0, whole	1,814	1,789	1,789
Families 2 to 8, sampled	2,410	2,380	2,380

The three moves, 6.1.4:14, 6.7.1:653 and 6.7.1:737, come out the same on both builds when re-run alone; they are problems that take 12–20 s against a 5 s budget. #1956's 36 gained rows answer as on master, and the other 50 rows of 6.3 and 6.4 that #1956 reaches are unchanged. 6.4.2:185 looked more expensive in the pocket, but alone it allocates 0.417 GB on both builds and gives the same answer. v2.5.0 declined all of these rows, so BREAKING-CHANGES.md has no entry: the branch restores the unreleased spelling from before #1956.

AFunctionOfTheHyperbolicTangentIntegralTest differentiates the answers back and requires them to be under 1,000 characters; master's are 1,342–14,533.

Part of #233.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura