Average Error: 52.0 → 52.0
Time: 12.0s
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 r47882 = 9.0;
        double r47883 = x;
        double r47884 = 4.0;
        double r47885 = pow(r47883, r47884);
        double r47886 = r47882 * r47885;
        double r47887 = y;
        double r47888 = pow(r47887, r47884);
        double r47889 = r47886 - r47888;
        double r47890 = 2.0;
        double r47891 = r47887 * r47887;
        double r47892 = r47890 * r47891;
        double r47893 = r47889 + r47892;
        return r47893;
}
↓
double f(double x, double y) {
        double r47894 = x;
        double r47895 = 4.0;
        double r47896 = pow(r47894, r47895);
        double r47897 = 9.0;
        double r47898 = y;
        double r47899 = pow(r47898, r47895);
        double r47900 = -r47899;
        double r47901 = fma(r47896, r47897, r47900);
        double r47902 = 3.0;
        double r47903 = pow(r47901, r47902);
        double r47904 = cbrt(r47903);
        double r47905 = 2.0;
        double r47906 = r47898 * r47898;
        double r47907 = r47905 * r47906;
        double r47908 = r47904 + r47907;
        return r47908;
}

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 2019326 +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))))