Average Error: 52.0 → 52.0
Time: 7.2s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(\mathsf{fma}\left({x}^{4}, 9, -{y}^{4}\right)\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r47789 = 9.0;
        double r47790 = x;
        double r47791 = 4.0;
        double r47792 = pow(r47790, r47791);
        double r47793 = r47789 * r47792;
        double r47794 = y;
        double r47795 = pow(r47794, r47791);
        double r47796 = r47793 - r47795;
        double r47797 = 2.0;
        double r47798 = r47794 * r47794;
        double r47799 = r47797 * r47798;
        double r47800 = r47796 + r47799;
        return r47800;
}
↓
double f(double x, double y) {
        double r47801 = x;
        double r47802 = 4.0;
        double r47803 = pow(r47801, r47802);
        double r47804 = 9.0;
        double r47805 = y;
        double r47806 = pow(r47805, r47802);
        double r47807 = -r47806;
        double r47808 = fma(r47803, r47804, r47807);
        double r47809 = 3.0;
        double r47810 = pow(r47808, r47809);
        double r47811 = cbrt(r47810);
        double r47812 = 2.0;
        double r47813 = r47805 * r47805;
        double r47814 = r47812 * r47813;
        double r47815 = r47811 + r47814;
        return r47815;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019350 +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))))