Average Error: 52.0 → 52.0
Time: 13.4s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \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)}
double f(double x, double y) {
        double r2667902 = 9.0;
        double r2667903 = x;
        double r2667904 = 4.0;
        double r2667905 = pow(r2667903, r2667904);
        double r2667906 = r2667902 * r2667905;
        double r2667907 = y;
        double r2667908 = pow(r2667907, r2667904);
        double r2667909 = r2667906 - r2667908;
        double r2667910 = 2.0;
        double r2667911 = r2667907 * r2667907;
        double r2667912 = r2667910 * r2667911;
        double r2667913 = r2667909 + r2667912;
        return r2667913;
}
↓
double f(double x, double y) {
        double r2667914 = 2.0;
        double r2667915 = y;
        double r2667916 = r2667915 * r2667915;
        double r2667917 = r2667914 * r2667916;
        double r2667918 = x;
        double r2667919 = 4.0;
        double r2667920 = pow(r2667918, r2667919);
        double r2667921 = 9.0;
        double r2667922 = r2667920 * r2667921;
        double r2667923 = pow(r2667915, r2667919);
        double r2667924 = r2667922 - r2667923;
        double r2667925 = r2667924 * r2667924;
        double r2667926 = r2667924 * r2667925;
        double r2667927 = cbrt(r2667926);
        double r2667928 = r2667917 + r2667927;
        return r2667928;
}

Error

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Your Program's Arguments

Results

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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. Final simplification52.0

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

Reproduce

herbie shell --seed 2019169 +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))))