A hyperbolic function of a logarithm is integrated, the exponent folded structurally

[Rafael-SOWNet]

tanh(ln(x)) was left as written. The library spells tanh(y) with e^(2y), so a hyperbolic function of a logarithm is an exponential whose exponent is a sum holding one logarithm — e^(a + b ln(q)) — and SolveByFoldingAnExponentialOfALogarithm read only a product, e^(k ln q).

It reads the exponent structurally now: e^(u + v) is e^u e^v, e^(u - v) is e^u/e^v, e^(k u) and e^(u/d) are powers of e^u for an x-free k and d, and e^(ln q) is q. So a + b ln(c x^n) folds to e^a (c x^n)^b, and its negation — which the same function writes below the bar — to the reciprocal.

Two conditions, both from measurements rather than taste:

• Composed exponents are flattened as they fold. n (ln(q)/2) is q^(n/2), not (sqrt(q))^n. The nested spelling is the same value and a different question to every rule below: with it, e^(n acoth(a x))/(c - a^2 c x^2)^4 (family 7, 7.4.2:854) went from a 3 s decline to a 50 s search.
• One logarithm in the exponent. A difference of two — how an inverse hyperbolic cotangent of a reciprocal arrives — folds to a power of a quotient of quotients that nothing below reads, and costs the same way.

Measured (final build, rebased onto 48d447c8):

• Family 6 (familycap.sh 6 20): 375 → 377/417, 0 wrong, timeouts 17 → 16 — 6.3.2:214 x tanh(a + 2 ln x)^2 and 6.5.3:253 sech(a + 2 ln(c/sqrt x))^3; nothing lost.
• Family 7: 215/270, 0 wrong, unchanged (one row flips Unsolved → Timeout on the 5 s cap and times out identically on master solo).
• 1774-problem suite: 1707, 0 wrong, 0 timeout, unchanged. Unit suite: 12,632 tests, 0 failed. bench.sh: PASSED on all 19 gated benchmarks.

Still declined, and deliberately: sinh(a + b ln(c x^n)) with a symbolic n and b, which needs int (c x^n)^b dx — that is c^b x^(n b + 1)/(n b + 1) only under c > 0 and x > 0, a restriction on the variable rather than on a parameter, which deserves its own decision.

BREAKING-CHANGES.md carries the entry with the 2.5.0 column measured on a 2.5.0 build.

Part of #718.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura