Average Error: 52.0 → 52.0
Time: 7.1s
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 r35016 = 9.0;
        double r35017 = x;
        double r35018 = 4.0;
        double r35019 = pow(r35017, r35018);
        double r35020 = r35016 * r35019;
        double r35021 = y;
        double r35022 = pow(r35021, r35018);
        double r35023 = r35020 - r35022;
        double r35024 = 2.0;
        double r35025 = r35021 * r35021;
        double r35026 = r35024 * r35025;
        double r35027 = r35023 + r35026;
        return r35027;
}
↓
double f(double x, double y) {
        double r35028 = x;
        double r35029 = 4.0;
        double r35030 = pow(r35028, r35029);
        double r35031 = 9.0;
        double r35032 = y;
        double r35033 = pow(r35032, r35029);
        double r35034 = -r35033;
        double r35035 = fma(r35030, r35031, r35034);
        double r35036 = 3.0;
        double r35037 = pow(r35035, r35036);
        double r35038 = cbrt(r35037);
        double r35039 = 2.0;
        double r35040 = r35032 * r35032;
        double r35041 = r35039 * r35040;
        double r35042 = r35038 + r35041;
        return r35042;
}

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 2019208 +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))))