A sine of a double argument beside the argument is written as a product

[Rafael-SOWNet]

Part of #718.

csc(a + b x)^3 sin(2a + 2b x)^7 was declined, with five more of Rubi's 4.7.1. SolveByUnifyingTrigonometricArguments writes the functions of several multiples of one argument in it, but it reads a numeric slope, and with x for the argument it bounds the degree it writes, so sin(2x)^7 was past it too. A sine of the double is one product whatever its power,

sin(2A) = 2 sin(A) cos(A)

so SolveByWritingASineOfADoubleArgumentAsAProduct, ahead of it, writes it so where the argument itself stands beside it and nothing else of the double does, for any slope, and asks the same question.

integrand	2.5.0	master b8b252b6	this
csc(a + b x)^3 sin(2a + 2b x)^7	declined	declined	127 characters, 0.4 s
csc(a + b x) sin(2a + 2b x)^8	declined	declined	134 characters, 0.1 s

Tests: ASineOfADoubleArgumentIntegralTest, the two rows above, each differentiated back and compared at six points.

Measured on every corpus problem with a sine of a double in it and every one of 4.7, 1,760 of them, at the corpus's 5-second budget, against master b8b252b6:

	master	this
solved	1655	1661
unevaluated	85	79
wrong	0	0
past the budget	10	10

Six problems are answered here and not on master, the six of 4.7.1, and none the other way; on the 1,655 both answer the time is 192 seconds and 191.

	master	this
family 0, independent suites (1814)	1782	1782
family 1, 40 a file (1381)	1341	1341
families 2 to 8, sampled (2410)	2330	2330

The harness counts no answer wrong in either. The six problems the builds disagreed on, run again one build at a time: master answers none, this all six.

The suite passes: 15,167 passed, 13 skipped, none failed, on the change before its test was added; with it, the related tests pass, 495. The allocation gate passes: every gated benchmark allocates what the baseline says. The library builds for every target.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura