Average Error: 52.0 → 52.0
Time: 8.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)\]
\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(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\right)
double f(double x, double y) {
        double r41363 = 9.0;
        double r41364 = x;
        double r41365 = 4.0;
        double r41366 = pow(r41364, r41365);
        double r41367 = r41363 * r41366;
        double r41368 = y;
        double r41369 = pow(r41368, r41365);
        double r41370 = r41367 - r41369;
        double r41371 = 2.0;
        double r41372 = r41368 * r41368;
        double r41373 = r41371 * r41372;
        double r41374 = r41370 + r41373;
        return r41374;
}
↓
double f(double x, double y) {
        double r41375 = 2.0;
        double r41376 = y;
        double r41377 = r41375 * r41376;
        double r41378 = 9.0;
        double r41379 = x;
        double r41380 = 4.0;
        double r41381 = pow(r41379, r41380);
        double r41382 = pow(r41376, r41380);
        double r41383 = -r41382;
        double r41384 = fma(r41378, r41381, r41383);
        double r41385 = 3.0;
        double r41386 = pow(r41384, r41385);
        double r41387 = cbrt(r41386);
        double r41388 = fma(r41377, r41376, r41387);
        return r41388;
}

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. Simplified52.0

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

  6. Final simplification52.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :precision binary64
  :pre (and (== x 10864) (== y 18817))
  (+ (- (* 9 (pow x 4)) (pow y 4)) (* 2 (* y y))))