Multiples of one linear argument are written in it with x beside them in a linear

[Rafael-SOWNet]

Part of #718.

csc(a + b x) sin(3a + 3b x)/(c + d x) and its powers of c + d x below the bar were left unevaluated. The rule that writes multiples of one linear argument in u = a + b x declined whenever x also stood outside the functions. Now, where x appears there only in sums, products and powers, it is written in u as well, as (u - a)/b. The linears in the answer are then put back in lowest terms. These are Rubi's 4.7.3:469–472.

Input	master c267991	2.5.0	this branch
csc(a+b*x)*sin(3*a+3*b*x)/(c+d*x)	unevaluated	unevaluated	190 chars
…/(c+d*x)^2	unevaluated	unevaluated	447 chars
…/(c+d*x)^3	unevaluated	unevaluated	592 chars
…/(c+d*x)^4	unevaluated	unevaluated	736 chars
csc(2+3*x)*sin(6+9*x)/(c+d*x)	unevaluated	unevaluated	194 chars

Controls ((1+2*cos(2*a+2*b*x))/(c+d*x), cos(2*a+2*b*x)/(c+d*x), sin(3*x)/sin(x), …): unchanged.

Measured

• Pocket over all of 4.7.1 and 4.7.3: master 310/314, branch 314/314. The only moves are 4.7.3:469–472. 0 wrong.
• Corpus, branch against master c267991:
  • the 1.1.3.4 pocket: 14589 vs 14585 of 14707;
  • family 1 and family 0: equal;
  • families 2–8, sampled: equal;
  • 0 wrong on every arm.
• Moves rerun alone: the four 4.7.3 rows were gained. The other three rows (1.1.3.4:857, 1.2.3.4:111, 1.3.1:568) come out the same on both arms.
• Allocation gate passed; unit suite 15287 passed, 0 failed.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura