[Rafael-SOWNet]

Part of #233.

Eleven shapes of Rubi's family 1, each answered where the rules declined or ran out of time. One test class per shape.

1. A rational function beside a half-odd power of P = a + b x^2 + c x^4, where it is a rational function of t = x/sqrt(P). Since dt/dx = (a - c x^4)/P^(3/2), (a - c x^4)/((a d + a e x^2 + c d x^4) sqrt(P)) is dt/(d + (a e - b d) t^2). Whether an integrand qualifies is read in y = x^2 modulo y^2 - w y + a/c; an elliptic integral does not pass.
2. (c x)^t, t not whole, written x^t beside (c x)^t x^(-t), which is constant wherever it is defined.
3. Two square roots whose radicands' quotient is a constant times an even power of x, as one root up to a factor whose square is constant.
4. A polynomial over high whole powers of two linears, under t = L1/L2.
5. An algebraic function of 1/x alone, under x = 1/u.
6. x^m (a + b x^n)^p for whole m and n and p <= -2, by the reduction that raises p to -1.
7. A power of a sum of powers of x beside a symbolic power of a binomial, multiplied out into binomial differentials.
8. A difference of radicands that is one power of x, written as one.
9. A rational function beside an odd root of a linear past the square, split first where a linear below meets the root at an irrational value.
10. An odd integrand beside a high power of a quadratic, left to u = x^2.
11. A quartic in one shifted linear, left to u = d + k x.

Chain against master f7f2a7a, with the harness at its current revision on both arms:

• pocket of 1,079 rows of family 1: 1,013 → 1,038 solved, 0 wrong;
• samples: unchanged, except family 1's every-40th sample, 1,375 → 1,379;
• the 25 rows that moved, alone: 0 → 25 solved, each in 18–772 ms. They span 1.1.1.3, 1.1.2.2, 1.1.3.2–4, 1.2.1.6, 1.2.2.7, 1.2.3.2 and 1.3.2;
• no row's allocation grew past 1.3×.

Re-measured with the probe on f7f2a7a and on this branch:

integrand	master	this
(a - c*x^4)/((a*d + a*k*x^2 + c*d*x^4)*sqrt(a + b*x^2 + c*x^4))	declined	1,949 characters
(g + h*x)*sqrt(a + b*x + c*x^2)/(a*d + b*d*x + c*d*x^2)^(3/2)	declined	4,376
x^2/((1 - a*x)^16*(1 + a*x)^11)	20.6 s, 8.5 GB, 16,292	0.12 s, 1,380
1/((a + b/x)^(5/2)*(c + d/x)^2)	6.2 s, 16,675	0.8 s, 4,667
(c*x)^(-1 - 2*n - n*p)*(a + b*x^n)^p	declined	255
1/(x^2*(a + b*x^3)^5)	declined	741
(d + k*x)^4/(a + b*(d + k*x)^2 + c*(d + k*x)^4)	past 30 s	452
1/(x*(1 - x^2)^(1/3)*(3 + x^2))	342	495

The probe calls master's answer to the third row wrong. It is exactly right: the difference is 0 at 50, 300 and 2,000 digits at two points. The probe's double evaluation of a 16,292-character expression is what fails. One answer gets longer, the last row.

One shape here, (c x)^t as x^t times a constant, is close to #2012's. The rows that moved are the ones #2012 leaves.

The BREAKING-CHANGES.md entry's "Now" column is re-measured on this build, and its comparison is against f7f2a7a.

🤖 Generated with Claude Code

https://claude.ai/code/session_012sonx8iAspMiwRwokT1Ura