Average Error: 52.0 → 52.0
Time: 12.2s
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 r2558765 = 9.0;
        double r2558766 = x;
        double r2558767 = 4.0;
        double r2558768 = pow(r2558766, r2558767);
        double r2558769 = r2558765 * r2558768;
        double r2558770 = y;
        double r2558771 = pow(r2558770, r2558767);
        double r2558772 = r2558769 - r2558771;
        double r2558773 = 2.0;
        double r2558774 = r2558770 * r2558770;
        double r2558775 = r2558773 * r2558774;
        double r2558776 = r2558772 + r2558775;
        return r2558776;
}
↓
double f(double x, double y) {
        double r2558777 = 2.0;
        double r2558778 = y;
        double r2558779 = r2558777 * r2558778;
        double r2558780 = x;
        double r2558781 = 4.0;
        double r2558782 = pow(r2558780, r2558781);
        double r2558783 = 9.0;
        double r2558784 = r2558782 * r2558783;
        double r2558785 = pow(r2558778, r2558781);
        double r2558786 = r2558784 - r2558785;
        double r2558787 = r2558786 * r2558786;
        double r2558788 = r2558786 * r2558787;
        double r2558789 = cbrt(r2558788);
        double r2558790 = fma(r2558779, r2558778, r2558789);
        return r2558790;
}

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 2019179 +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))))