Average Error: 52.0 → 52.0
Time: 3.0s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}\right)\]
\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(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}}\right)
double f(double x, double y) {
        double r81869 = 9.0;
        double r81870 = x;
        double r81871 = 4.0;
        double r81872 = pow(r81870, r81871);
        double r81873 = r81869 * r81872;
        double r81874 = y;
        double r81875 = pow(r81874, r81871);
        double r81876 = r81873 - r81875;
        double r81877 = 2.0;
        double r81878 = r81874 * r81874;
        double r81879 = r81877 * r81878;
        double r81880 = r81876 + r81879;
        return r81880;
}
↓
double f(double x, double y) {
        double r81881 = 2.0;
        double r81882 = y;
        double r81883 = r81881 * r81882;
        double r81884 = 9.0;
        double r81885 = x;
        double r81886 = 4.0;
        double r81887 = pow(r81885, r81886);
        double r81888 = r81884 * r81887;
        double r81889 = pow(r81882, r81886);
        double r81890 = r81888 - r81889;
        double r81891 = 3.0;
        double r81892 = pow(r81890, r81891);
        double r81893 = cbrt(r81892);
        double r81894 = fma(r81883, r81882, r81893);
        return r81894;
}

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

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

  6. Final simplification52.0

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

Reproduce

herbie shell --seed 2020033 +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))))