Average Error: 52.0 → 52.0
Time: 11.2s
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 r83005 = 9.0;
        double r83006 = x;
        double r83007 = 4.0;
        double r83008 = pow(r83006, r83007);
        double r83009 = r83005 * r83008;
        double r83010 = y;
        double r83011 = pow(r83010, r83007);
        double r83012 = r83009 - r83011;
        double r83013 = 2.0;
        double r83014 = r83010 * r83010;
        double r83015 = r83013 * r83014;
        double r83016 = r83012 + r83015;
        return r83016;
}
↓
double f(double x, double y) {
        double r83017 = x;
        double r83018 = 4.0;
        double r83019 = pow(r83017, r83018);
        double r83020 = 9.0;
        double r83021 = y;
        double r83022 = pow(r83021, r83018);
        double r83023 = -r83022;
        double r83024 = fma(r83019, r83020, r83023);
        double r83025 = 3.0;
        double r83026 = pow(r83024, r83025);
        double r83027 = cbrt(r83026);
        double r83028 = 2.0;
        double r83029 = r83021 * r83021;
        double r83030 = r83028 * r83029;
        double r83031 = r83027 + r83030;
        return r83031;
}

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 2019323 +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))))