Average Error: 52.0 → 52.0
Time: 7.9s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left(\mathsf{fma}\left(9, {x}^{4}, -{y}^{4}\right)\right)}^{3}}
double f(double x, double y) {
        double r39850 = 9.0;
        double r39851 = x;
        double r39852 = 4.0;
        double r39853 = pow(r39851, r39852);
        double r39854 = r39850 * r39853;
        double r39855 = y;
        double r39856 = pow(r39855, r39852);
        double r39857 = r39854 - r39856;
        double r39858 = 2.0;
        double r39859 = r39855 * r39855;
        double r39860 = r39858 * r39859;
        double r39861 = r39857 + r39860;
        return r39861;
}
↓
double f(double x, double y) {
        double r39862 = 2.0;
        double r39863 = y;
        double r39864 = r39863 * r39863;
        double r39865 = r39862 * r39864;
        double r39866 = 9.0;
        double r39867 = x;
        double r39868 = 4.0;
        double r39869 = pow(r39867, r39868);
        double r39870 = pow(r39863, r39868);
        double r39871 = -r39870;
        double r39872 = fma(r39866, r39869, r39871);
        double r39873 = 3.0;
        double r39874 = pow(r39872, r39873);
        double r39875 = cbrt(r39874);
        double r39876 = r39865 + r39875;
        return r39876;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019196 +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))))