Average Error: 52.0 → 52.0
Time: 11.8s
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 r82907 = 9.0;
        double r82908 = x;
        double r82909 = 4.0;
        double r82910 = pow(r82908, r82909);
        double r82911 = r82907 * r82910;
        double r82912 = y;
        double r82913 = pow(r82912, r82909);
        double r82914 = r82911 - r82913;
        double r82915 = 2.0;
        double r82916 = r82912 * r82912;
        double r82917 = r82915 * r82916;
        double r82918 = r82914 + r82917;
        return r82918;
}
↓
double f(double x, double y) {
        double r82919 = 2.0;
        double r82920 = y;
        double r82921 = r82919 * r82920;
        double r82922 = x;
        double r82923 = 4.0;
        double r82924 = pow(r82922, r82923);
        double r82925 = 9.0;
        double r82926 = pow(r82920, r82923);
        double r82927 = -r82926;
        double r82928 = fma(r82924, r82925, r82927);
        double r82929 = 3.0;
        double r82930 = pow(r82928, r82929);
        double r82931 = cbrt(r82930);
        double r82932 = fma(r82921, r82920, r82931);
        return r82932;
}

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 2019323 +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))))