A logarithm of a nested quotient is written over one bar under the exponential substitution

[Rafael-SOWNet]

1/sqrt(atanh(tanh(a + b x))) was answered in 300 ms before the exponential substitution took a symbolic slope (#1377) and not after — the one known loss of that PR. atanh(tanh(a + b x)) reaches the chain as 1/2 ln((1 + (w - 1)/(w + 1))/(1 - (w - 1)/(w + 1))) in w = e^(2(a + b x)), and under u = w that logarithm is 1/2 ln(u); but SingleQuotient.Combine on the way in reaches the quotient the integrand is and not one inside a function, Simplify combines nothing (#1239 — (1 + (u - 1)/(u + 1))/(1 - (u - 1)/(u + 1)) simplifies to (8 - 8/(u + 1))(u + 1)/8), and the substitution search compared its candidates against the nested spelling and never saw the u.

Under the exponential substitution, every logarithm whose argument is a rational function of u with a quotient nested in it is now written over one bar in lowest terms (combine, polynomial gcd, and a Simplify of the small result), where that is smaller than what it replaces, before the question in u is asked. Nothing changes for Simplify itself.

row	2.5.0	master 84b0a9cf	this branch
1/sqrt(atanh(tanh(a + b x)))	unevaluated after 49 s	unevaluated, 1.4 s	2 sqrt(1/2 ln(e^(2bx + 2a)))/(1/2)/(2b), 0.3 s
atanh(tanh(a + b x))^(1/2)	unevaluated	unevaluated	answered, 50 ms

Measured, all detached and alone on the machine:

• suite green locally (11526 passed, 6 m 49 s); three rows in ExponentialSubstitutionIntegralTest, differentiated back with the parameters pinned.
• Independent Rubi suite: 1706/1774, 0 wrong, 0 timeouts — identical verdicts to master (0 changed).
• Family 7 (inverse hyperbolic, 270): 152/270 from 150, 0 wrong: 1/sqrt(atanh(tanh(a+b x))) and x/atanh(tanh(a+b x))^(5/2) Unsolved → Solved, nothing lost. The run reports four "errors": the sample was run under an 8 GB virtual-memory cap, and (c - c/(a^2 x^2))^(9/2)/e^(3 acoth(a x)) reaches 8.4 GB in 30 s on master as well (/usr/bin/time -v, both builds), not observing the 5 s budget; under the cap it throws OutOfMemoryException and the three asech rows after it inherit the exhausted process (2–12 ms each; all three are unevaluated solo, on both builds). A pre-existing runaway, next on my list, not this branch's.
• Family 6 (hyperbolic, 417): 316/417 from 315, 0 wrong: sech(c+d x)^3 (a + b tanh(c+d x)^2)^2 Timeout → Solved, nothing lost.

Part of #718.

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