Average Error: 52.0 → 52.0
Time: 6.9s
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 r48150 = 9.0;
        double r48151 = x;
        double r48152 = 4.0;
        double r48153 = pow(r48151, r48152);
        double r48154 = r48150 * r48153;
        double r48155 = y;
        double r48156 = pow(r48155, r48152);
        double r48157 = r48154 - r48156;
        double r48158 = 2.0;
        double r48159 = r48155 * r48155;
        double r48160 = r48158 * r48159;
        double r48161 = r48157 + r48160;
        return r48161;
}
↓
double f(double x, double y) {
        double r48162 = x;
        double r48163 = 4.0;
        double r48164 = pow(r48162, r48163);
        double r48165 = 9.0;
        double r48166 = y;
        double r48167 = pow(r48166, r48163);
        double r48168 = -r48167;
        double r48169 = fma(r48164, r48165, r48168);
        double r48170 = 3.0;
        double r48171 = pow(r48169, r48170);
        double r48172 = cbrt(r48171);
        double r48173 = 2.0;
        double r48174 = r48166 * r48166;
        double r48175 = r48173 * r48174;
        double r48176 = r48172 + r48175;
        return r48176;
}

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 2019305 +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))))