Average Error: 52.0 → 52.0
Time: 11.8s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\mathsf{fma}\left(2 \cdot y, y, \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\right)\]
\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({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\right)
double f(double x, double y) {
        double r2436123 = 9.0;
        double r2436124 = x;
        double r2436125 = 4.0;
        double r2436126 = pow(r2436124, r2436125);
        double r2436127 = r2436123 * r2436126;
        double r2436128 = y;
        double r2436129 = pow(r2436128, r2436125);
        double r2436130 = r2436127 - r2436129;
        double r2436131 = 2.0;
        double r2436132 = r2436128 * r2436128;
        double r2436133 = r2436131 * r2436132;
        double r2436134 = r2436130 + r2436133;
        return r2436134;
}
↓
double f(double x, double y) {
        double r2436135 = 2.0;
        double r2436136 = y;
        double r2436137 = r2436135 * r2436136;
        double r2436138 = x;
        double r2436139 = 4.0;
        double r2436140 = pow(r2436138, r2436139);
        double r2436141 = 9.0;
        double r2436142 = r2436140 * r2436141;
        double r2436143 = pow(r2436136, r2436139);
        double r2436144 = r2436142 - r2436143;
        double r2436145 = r2436144 * r2436144;
        double r2436146 = r2436144 * r2436145;
        double r2436147 = cbrt(r2436146);
        double r2436148 = fma(r2436137, r2436136, r2436147);
        return r2436148;
}

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

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

  4. Applied add-cbrt-cube52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019171 +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))))