Average Error: 52.0 → 52.0
Time: 2.4s
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 r40847 = 9.0;
        double r40848 = x;
        double r40849 = 4.0;
        double r40850 = pow(r40848, r40849);
        double r40851 = r40847 * r40850;
        double r40852 = y;
        double r40853 = pow(r40852, r40849);
        double r40854 = r40851 - r40853;
        double r40855 = 2.0;
        double r40856 = r40852 * r40852;
        double r40857 = r40855 * r40856;
        double r40858 = r40854 + r40857;
        return r40858;
}
↓
double f(double x, double y) {
        double r40859 = 9.0;
        double r40860 = x;
        double r40861 = 4.0;
        double r40862 = pow(r40860, r40861);
        double r40863 = r40859 * r40862;
        double r40864 = y;
        double r40865 = pow(r40864, r40861);
        double r40866 = r40863 - r40865;
        double r40867 = 3.0;
        double r40868 = pow(r40866, r40867);
        double r40869 = cbrt(r40868);
        double r40870 = 2.0;
        double r40871 = r40864 * r40864;
        double r40872 = r40870 * r40871;
        double r40873 = r40869 + r40872;
        return r40873;
}

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 2020065 
(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))))