Average Error: 52.0 → 52.0
Time: 7.5s
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 r44789 = 9.0;
        double r44790 = x;
        double r44791 = 4.0;
        double r44792 = pow(r44790, r44791);
        double r44793 = r44789 * r44792;
        double r44794 = y;
        double r44795 = pow(r44794, r44791);
        double r44796 = r44793 - r44795;
        double r44797 = 2.0;
        double r44798 = r44794 * r44794;
        double r44799 = r44797 * r44798;
        double r44800 = r44796 + r44799;
        return r44800;
}
↓
double f(double x, double y) {
        double r44801 = 9.0;
        double r44802 = x;
        double r44803 = 4.0;
        double r44804 = pow(r44802, r44803);
        double r44805 = r44801 * r44804;
        double r44806 = y;
        double r44807 = pow(r44806, r44803);
        double r44808 = r44805 - r44807;
        double r44809 = 3.0;
        double r44810 = pow(r44808, r44809);
        double r44811 = cbrt(r44810);
        double r44812 = 2.0;
        double r44813 = r44806 * r44806;
        double r44814 = r44812 * r44813;
        double r44815 = r44811 + r44814;
        return r44815;
}

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 2020047 
(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))))