Average Error: 52.0 → 52.0
Time: 2.8s
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 r75904 = 9.0;
        double r75905 = x;
        double r75906 = 4.0;
        double r75907 = pow(r75905, r75906);
        double r75908 = r75904 * r75907;
        double r75909 = y;
        double r75910 = pow(r75909, r75906);
        double r75911 = r75908 - r75910;
        double r75912 = 2.0;
        double r75913 = r75909 * r75909;
        double r75914 = r75912 * r75913;
        double r75915 = r75911 + r75914;
        return r75915;
}
↓
double f(double x, double y) {
        double r75916 = 9.0;
        double r75917 = x;
        double r75918 = 4.0;
        double r75919 = pow(r75917, r75918);
        double r75920 = r75916 * r75919;
        double r75921 = y;
        double r75922 = pow(r75921, r75918);
        double r75923 = r75920 - r75922;
        double r75924 = 3.0;
        double r75925 = pow(r75923, r75924);
        double r75926 = cbrt(r75925);
        double r75927 = 2.0;
        double r75928 = r75921 * r75921;
        double r75929 = r75927 * r75928;
        double r75930 = r75926 + r75929;
        return r75930;
}

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 2020035 
(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))))