A rational function of the tangent of a linear argument with symbols in it is not simplified under the linear substitution

[Rafael-SOWNet]

Part of #718.

The substitution search reaches tan(g + h x) through u = g + h x, and simplified the integrand's quotient by h, written in u, before asking for its integral. With the nine symbols of Rubi's 4.3.4.2 in it that took about half a minute, for an expression that is the integrand with its argument renamed and holds nothing to simplify:

integrand	2.5.0	master ba8eb99b	this
(a + b tan(g + h x)) (A + B tan(g + h x) + K tan(g + h x)^2)/(c + d tan(g + h x))^2	declined after 26 s	28.7 s	4.5 s
(a + b tan(g + h x)) (A + B tan(g + h x))/(c + d tan(g + h x))^2	declined after 3.5 s	2.2 s	1.5 s
(A + B tan(g + h x) + K tan(g + h x)^2)/((a + b tan(g + h x)) (c + d tan(g + h x)))	declined after 4 s	2.9 s	0.8 s

Timed one integrand at a time, beside other work on the machine.

What changes. Under a linear candidate, whose quotient in u is free of x, the quotient is handed on as it is written, inner-simplified only, and not put through the simplifier's search. The partial-fraction rules after it read it as written.

Tests: LinearArgumentSubstitutionTest, three rows of 4.3.4.2's shapes, each answered and differentiated back with the symbols pinned; g + h x for the argument, since e is Euler's number here.

Measured first on 4.3.4.2 whole and every third problem of 4.3.3.1, 420 problems, at the corpus's 5-second budget, against master 8f3757cd, the branch's base:

	master	this
solved	263	281
wrong	0	0
past the budget	136	118

Measured then on the Rubi corpus against master 8f3757cd:

	master	this
family 0, independent suites (1814)	1766	1766
family 1, 40 a file (1381)	1296	1297
families 2 to 8, sampled (2410)	2215	2222

No answer is wrong in the sample on either build. Of the 29 problems the two builds disagreed on, run again one build at a time, 21 ran out of time on master and are answered here: 19 of 4.3.4.2's, (a + b tan(e + f x))^2 (A + B tan(e + f x) + C tan(e + f x)^2)/(c + d tan(e + f x))^3 among them, 4.3.3.1's sqrt(a + b tan(c + d x)) (A + B tan(c + d x))/tan(c + d x)^(9/2), and 1.2.1.9's (a + c x^2)^3 (A + B x + C x^2)/(d + e x)^3. 6.1.1's (c + d x)^3 (a + i a sinh(e + f x))^2 is answered on both, in a form the harness could check at no point on master and checks here. The other seven came out the same on both builds: four answered after about twenty seconds on either, past the corpus's budget, two past it on both, and one declined on both.

The suite passes on the commit measured, 490fc454, 14,594 tests with 13 skipped, and so does the allocation gate. Master ba8eb99b is merged in since, with one conflict, two entries at one anchor in BREAKING-CHANGES.md; the calculus tests pass on the merge, 4,031 of them, and every row above is as the table says on it.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura