Average Error: 52.0 → 52.0
Time: 12.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)}\right)
double f(double x, double y) {
        double r4231356 = 9.0;
        double r4231357 = x;
        double r4231358 = 4.0;
        double r4231359 = pow(r4231357, r4231358);
        double r4231360 = r4231356 * r4231359;
        double r4231361 = y;
        double r4231362 = pow(r4231361, r4231358);
        double r4231363 = r4231360 - r4231362;
        double r4231364 = 2.0;
        double r4231365 = r4231361 * r4231361;
        double r4231366 = r4231364 * r4231365;
        double r4231367 = r4231363 + r4231366;
        return r4231367;
}
↓
double f(double x, double y) {
        double r4231368 = 2.0;
        double r4231369 = y;
        double r4231370 = r4231368 * r4231369;
        double r4231371 = 9.0;
        double r4231372 = x;
        double r4231373 = 4.0;
        double r4231374 = pow(r4231372, r4231373);
        double r4231375 = r4231371 * r4231374;
        double r4231376 = pow(r4231369, r4231373);
        double r4231377 = r4231375 - r4231376;
        double r4231378 = r4231377 * r4231377;
        double r4231379 = r4231378 * r4231377;
        double r4231380 = cbrt(r4231379);
        double r4231381 = fma(r4231370, r4231369, r4231380);
        return r4231381;
}

Error

Derivation

  1. Initial program 52.0

    \[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]

  2. Simplified52.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(2 \cdot y, y, 9 \cdot {x}^{4} - {y}^{4}\right)}\]
  3. Using strategy rm

  4. Applied add-cbrt-cube52.0

    \[\leadsto \mathsf{fma}\left(2 \cdot y, y, \color{blue}{\sqrt[3]{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)}}\right)\]

  5. Final simplification52.0

    \[\leadsto \mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{\left(\left(9 \cdot {x}^{4} - {y}^{4}\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)\right) \cdot \left(9 \cdot {x}^{4} - {y}^{4}\right)}\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))