Average Error: 52.0 → 52.0
Time: 2.5s
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 r73057 = 9.0;
        double r73058 = x;
        double r73059 = 4.0;
        double r73060 = pow(r73058, r73059);
        double r73061 = r73057 * r73060;
        double r73062 = y;
        double r73063 = pow(r73062, r73059);
        double r73064 = r73061 - r73063;
        double r73065 = 2.0;
        double r73066 = r73062 * r73062;
        double r73067 = r73065 * r73066;
        double r73068 = r73064 + r73067;
        return r73068;
}
↓
double f(double x, double y) {
        double r73069 = 2.0;
        double r73070 = y;
        double r73071 = r73069 * r73070;
        double r73072 = 9.0;
        double r73073 = x;
        double r73074 = 4.0;
        double r73075 = pow(r73073, r73074);
        double r73076 = r73072 * r73075;
        double r73077 = pow(r73070, r73074);
        double r73078 = r73076 - r73077;
        double r73079 = 3.0;
        double r73080 = pow(r73078, r73079);
        double r73081 = cbrt(r73080);
        double r73082 = fma(r73071, r73070, r73081);
        return r73082;
}

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 2020024 +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))))