Average Error: 52.0 → 52.0
Time: 13.4s
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 r95787 = 9.0;
        double r95788 = x;
        double r95789 = 4.0;
        double r95790 = pow(r95788, r95789);
        double r95791 = r95787 * r95790;
        double r95792 = y;
        double r95793 = pow(r95792, r95789);
        double r95794 = r95791 - r95793;
        double r95795 = 2.0;
        double r95796 = r95792 * r95792;
        double r95797 = r95795 * r95796;
        double r95798 = r95794 + r95797;
        return r95798;
}
↓
double f(double x, double y) {
        double r95799 = 9.0;
        double r95800 = x;
        double r95801 = 4.0;
        double r95802 = pow(r95800, r95801);
        double r95803 = r95799 * r95802;
        double r95804 = y;
        double r95805 = pow(r95804, r95801);
        double r95806 = r95803 - r95805;
        double r95807 = 3.0;
        double r95808 = pow(r95806, r95807);
        double r95809 = cbrt(r95808);
        double r95810 = 2.0;
        double r95811 = r95804 * r95804;
        double r95812 = r95810 * r95811;
        double r95813 = r95809 + r95812;
        return r95813;
}

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 2019303 
(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))))