Average Error: 52.0 → 52.0
Time: 9.6s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r82879 = 9.0;
        double r82880 = x;
        double r82881 = 4.0;
        double r82882 = pow(r82880, r82881);
        double r82883 = r82879 * r82882;
        double r82884 = y;
        double r82885 = pow(r82884, r82881);
        double r82886 = r82883 - r82885;
        double r82887 = 2.0;
        double r82888 = r82884 * r82884;
        double r82889 = r82887 * r82888;
        double r82890 = r82886 + r82889;
        return r82890;
}
↓
double f(double x, double y) {
        double r82891 = x;
        double r82892 = 4.0;
        double r82893 = pow(r82891, r82892);
        double r82894 = 9.0;
        double r82895 = y;
        double r82896 = pow(r82895, r82892);
        double r82897 = -r82896;
        double r82898 = fma(r82893, r82894, r82897);
        double r82899 = 3.0;
        double r82900 = pow(r82898, r82899);
        double r82901 = cbrt(r82900);
        double r82902 = 2.0;
        double r82903 = r82895 * r82895;
        double r82904 = r82902 * r82903;
        double r82905 = r82901 + r82904;
        return r82905;
}

Error

Derivation

  1. Initial program 52.0

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

  3. Applied add-cbrt-cube52.0

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

  4. Simplified52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019199 +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))))