Average Error: 52.0 → 52.0
Time: 9.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)
double f(double x, double y) {
        double r53878 = 9.0;
        double r53879 = x;
        double r53880 = 4.0;
        double r53881 = pow(r53879, r53880);
        double r53882 = r53878 * r53881;
        double r53883 = y;
        double r53884 = pow(r53883, r53880);
        double r53885 = r53882 - r53884;
        double r53886 = 2.0;
        double r53887 = r53883 * r53883;
        double r53888 = r53886 * r53887;
        double r53889 = r53885 + r53888;
        return r53889;
}
↓
double f(double x, double y) {
        double r53890 = 2.0;
        double r53891 = y;
        double r53892 = r53891 * r53891;
        double r53893 = r53890 * r53892;
        double r53894 = 9.0;
        double r53895 = x;
        double r53896 = 4.0;
        double r53897 = pow(r53895, r53896);
        double r53898 = r53894 * r53897;
        double r53899 = pow(r53891, r53896);
        double r53900 = r53898 - r53899;
        double r53901 = r53893 + r53900;
        return r53901;
}

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. Simplified52.0

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019294 
(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))))