Average Error: 52.0 → 52.0
Time: 10.9s
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 r2975868 = 9.0;
        double r2975869 = x;
        double r2975870 = 4.0;
        double r2975871 = pow(r2975869, r2975870);
        double r2975872 = r2975868 * r2975871;
        double r2975873 = y;
        double r2975874 = pow(r2975873, r2975870);
        double r2975875 = r2975872 - r2975874;
        double r2975876 = 2.0;
        double r2975877 = r2975873 * r2975873;
        double r2975878 = r2975876 * r2975877;
        double r2975879 = r2975875 + r2975878;
        return r2975879;
}
↓
double f(double x, double y) {
        double r2975880 = 2.0;
        double r2975881 = y;
        double r2975882 = r2975881 * r2975881;
        double r2975883 = r2975880 * r2975882;
        double r2975884 = x;
        double r2975885 = 4.0;
        double r2975886 = pow(r2975884, r2975885);
        double r2975887 = 9.0;
        double r2975888 = r2975886 * r2975887;
        double r2975889 = pow(r2975881, r2975885);
        double r2975890 = r2975888 - r2975889;
        double r2975891 = r2975890 * r2975890;
        double r2975892 = r2975890 * r2975891;
        double r2975893 = cbrt(r2975892);
        double r2975894 = r2975883 + r2975893;
        return r2975894;
}

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 2019171 
(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))))