Average Error: 52.0 → 52.0
Time: 11.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\right)\]
\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({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\right)
double f(double x, double y) {
        double r2015751 = 9.0;
        double r2015752 = x;
        double r2015753 = 4.0;
        double r2015754 = pow(r2015752, r2015753);
        double r2015755 = r2015751 * r2015754;
        double r2015756 = y;
        double r2015757 = pow(r2015756, r2015753);
        double r2015758 = r2015755 - r2015757;
        double r2015759 = 2.0;
        double r2015760 = r2015756 * r2015756;
        double r2015761 = r2015759 * r2015760;
        double r2015762 = r2015758 + r2015761;
        return r2015762;
}
↓
double f(double x, double y) {
        double r2015763 = 2.0;
        double r2015764 = y;
        double r2015765 = r2015763 * r2015764;
        double r2015766 = x;
        double r2015767 = 4.0;
        double r2015768 = pow(r2015766, r2015767);
        double r2015769 = 9.0;
        double r2015770 = r2015768 * r2015769;
        double r2015771 = pow(r2015764, r2015767);
        double r2015772 = r2015770 - r2015771;
        double r2015773 = r2015772 * r2015772;
        double r2015774 = r2015772 * r2015773;
        double r2015775 = cbrt(r2015774);
        double r2015776 = fma(r2015765, r2015764, r2015775);
        return r2015776;
}

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

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

  4. Applied add-cbrt-cube52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019172 +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))))