Average Error: 52.0 → 52.0
Time: 8.2s
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 r41702 = 9.0;
        double r41703 = x;
        double r41704 = 4.0;
        double r41705 = pow(r41703, r41704);
        double r41706 = r41702 * r41705;
        double r41707 = y;
        double r41708 = pow(r41707, r41704);
        double r41709 = r41706 - r41708;
        double r41710 = 2.0;
        double r41711 = r41707 * r41707;
        double r41712 = r41710 * r41711;
        double r41713 = r41709 + r41712;
        return r41713;
}
↓
double f(double x, double y) {
        double r41714 = 2.0;
        double r41715 = y;
        double r41716 = r41715 * r41715;
        double r41717 = r41714 * r41716;
        double r41718 = 9.0;
        double r41719 = x;
        double r41720 = 4.0;
        double r41721 = pow(r41719, r41720);
        double r41722 = pow(r41715, r41720);
        double r41723 = -r41722;
        double r41724 = fma(r41718, r41721, r41723);
        double r41725 = 3.0;
        double r41726 = pow(r41724, r41725);
        double r41727 = cbrt(r41726);
        double r41728 = r41717 + r41727;
        return r41728;
}

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 2019194 +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))))