Average Error: 52.0 → 52.0
Time: 2.5s
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 r66776 = 9.0;
        double r66777 = x;
        double r66778 = 4.0;
        double r66779 = pow(r66777, r66778);
        double r66780 = r66776 * r66779;
        double r66781 = y;
        double r66782 = pow(r66781, r66778);
        double r66783 = r66780 - r66782;
        double r66784 = 2.0;
        double r66785 = r66781 * r66781;
        double r66786 = r66784 * r66785;
        double r66787 = r66783 + r66786;
        return r66787;
}
↓
double f(double x, double y) {
        double r66788 = 9.0;
        double r66789 = x;
        double r66790 = 4.0;
        double r66791 = pow(r66789, r66790);
        double r66792 = r66788 * r66791;
        double r66793 = y;
        double r66794 = pow(r66793, r66790);
        double r66795 = r66792 - r66794;
        double r66796 = 3.0;
        double r66797 = pow(r66795, r66796);
        double r66798 = cbrt(r66797);
        double r66799 = 2.0;
        double r66800 = r66793 * r66793;
        double r66801 = r66799 * r66800;
        double r66802 = r66798 + r66801;
        return r66802;
}

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 2020024 
(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))))