Average Error: 52.0 → 52.0
Time: 27.9s
Precision: 64
\[x = 10864.0 \land y = 18817.0\]
\[\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) + 2.0 \cdot \left(y \cdot y\right)\]
↓
\[2.0 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left(\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right)\right)}\]
\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) + 2.0 \cdot \left(y \cdot y\right)
↓
2.0 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left(\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right)\right)}
double f(double x, double y) {
        double r2667788 = 9.0;
        double r2667789 = x;
        double r2667790 = 4.0;
        double r2667791 = pow(r2667789, r2667790);
        double r2667792 = r2667788 * r2667791;
        double r2667793 = y;
        double r2667794 = pow(r2667793, r2667790);
        double r2667795 = r2667792 - r2667794;
        double r2667796 = 2.0;
        double r2667797 = r2667793 * r2667793;
        double r2667798 = r2667796 * r2667797;
        double r2667799 = r2667795 + r2667798;
        return r2667799;
}
↓
double f(double x, double y) {
        double r2667800 = 2.0;
        double r2667801 = y;
        double r2667802 = r2667801 * r2667801;
        double r2667803 = r2667800 * r2667802;
        double r2667804 = x;
        double r2667805 = 4.0;
        double r2667806 = pow(r2667804, r2667805);
        double r2667807 = 9.0;
        double r2667808 = r2667806 * r2667807;
        double r2667809 = pow(r2667801, r2667805);
        double r2667810 = r2667808 - r2667809;
        double r2667811 = r2667810 * r2667810;
        double r2667812 = r2667810 * r2667811;
        double r2667813 = cbrt(r2667812);
        double r2667814 = r2667803 + r2667813;
        return r2667814;
}

Error

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Results

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Derivation

  1. Initial program 52.0

    \[\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) + 2.0 \cdot \left(y \cdot y\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube52.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right) \cdot \left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right)\right) \cdot \left(9.0 \cdot {x}^{4.0} - {y}^{4.0}\right)}} + 2.0 \cdot \left(y \cdot y\right)\]

  4. Final simplification52.0

    \[\leadsto 2.0 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left(\left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right) \cdot \left({x}^{4.0} \cdot 9.0 - {y}^{4.0}\right)\right)}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y)
  :name "From Rump in a 1983 paper"
  :pre (and (== x 10864.0) (== y 18817.0))
  (+ (- (* 9.0 (pow x 4.0)) (pow y 4.0)) (* 2.0 (* y y))))