Average Error: 52.0 → 52.0
Time: 13.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
\sqrt[3]{{\left(9 \cdot {x}^{4} - {y}^{4}\right)}^{3}} + 2 \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r45920 = 9.0;
        double r45921 = x;
        double r45922 = 4.0;
        double r45923 = pow(r45921, r45922);
        double r45924 = r45920 * r45923;
        double r45925 = y;
        double r45926 = pow(r45925, r45922);
        double r45927 = r45924 - r45926;
        double r45928 = 2.0;
        double r45929 = r45925 * r45925;
        double r45930 = r45928 * r45929;
        double r45931 = r45927 + r45930;
        return r45931;
}
↓
double f(double x, double y) {
        double r45932 = 9.0;
        double r45933 = x;
        double r45934 = 4.0;
        double r45935 = pow(r45933, r45934);
        double r45936 = r45932 * r45935;
        double r45937 = y;
        double r45938 = pow(r45937, r45934);
        double r45939 = r45936 - r45938;
        double r45940 = 3.0;
        double r45941 = pow(r45939, r45940);
        double r45942 = cbrt(r45941);
        double r45943 = 2.0;
        double r45944 = r45937 * r45937;
        double r45945 = r45943 * r45944;
        double r45946 = r45942 + r45945;
        return r45946;
}

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

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

Reproduce

herbie shell --seed 2019326 
(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))))