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 r68875 = 9.0;
        double r68876 = x;
        double r68877 = 4.0;
        double r68878 = pow(r68876, r68877);
        double r68879 = r68875 * r68878;
        double r68880 = y;
        double r68881 = pow(r68880, r68877);
        double r68882 = r68879 - r68881;
        double r68883 = 2.0;
        double r68884 = r68880 * r68880;
        double r68885 = r68883 * r68884;
        double r68886 = r68882 + r68885;
        return r68886;
}
↓
double f(double x, double y) {
        double r68887 = 9.0;
        double r68888 = x;
        double r68889 = 4.0;
        double r68890 = pow(r68888, r68889);
        double r68891 = r68887 * r68890;
        double r68892 = y;
        double r68893 = pow(r68892, r68889);
        double r68894 = r68891 - r68893;
        double r68895 = 3.0;
        double r68896 = pow(r68894, r68895);
        double r68897 = cbrt(r68896);
        double r68898 = 2.0;
        double r68899 = r68892 * r68892;
        double r68900 = r68898 * r68899;
        double r68901 = r68897 + r68900;
        return r68901;
}

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 2020034 
(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))))