Average Error: 52.0 → 52.0
Time: 11.9s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}}\right)\]
\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({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}}\right)
double f(double x, double y) {
        double r88412 = 9.0;
        double r88413 = x;
        double r88414 = 4.0;
        double r88415 = pow(r88413, r88414);
        double r88416 = r88412 * r88415;
        double r88417 = y;
        double r88418 = pow(r88417, r88414);
        double r88419 = r88416 - r88418;
        double r88420 = 2.0;
        double r88421 = r88417 * r88417;
        double r88422 = r88420 * r88421;
        double r88423 = r88419 + r88422;
        return r88423;
}
↓
double f(double x, double y) {
        double r88424 = 2.0;
        double r88425 = y;
        double r88426 = r88424 * r88425;
        double r88427 = x;
        double r88428 = 4.0;
        double r88429 = pow(r88427, r88428);
        double r88430 = 9.0;
        double r88431 = pow(r88425, r88428);
        double r88432 = -r88431;
        double r88433 = fma(r88429, r88430, r88432);
        double r88434 = 3.0;
        double r88435 = pow(r88433, r88434);
        double r88436 = cbrt(r88435);
        double r88437 = fma(r88426, r88425, r88436);
        return r88437;
}

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

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

  6. Final simplification52.0

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

Reproduce

herbie shell --seed 2019303 +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))))