Average Error: 52.0 → 52.0
Time: 14.0s
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 r95793 = 9.0;
        double r95794 = x;
        double r95795 = 4.0;
        double r95796 = pow(r95794, r95795);
        double r95797 = r95793 * r95796;
        double r95798 = y;
        double r95799 = pow(r95798, r95795);
        double r95800 = r95797 - r95799;
        double r95801 = 2.0;
        double r95802 = r95798 * r95798;
        double r95803 = r95801 * r95802;
        double r95804 = r95800 + r95803;
        return r95804;
}
↓
double f(double x, double y) {
        double r95805 = 9.0;
        double r95806 = x;
        double r95807 = 4.0;
        double r95808 = pow(r95806, r95807);
        double r95809 = r95805 * r95808;
        double r95810 = y;
        double r95811 = pow(r95810, r95807);
        double r95812 = r95809 - r95811;
        double r95813 = 3.0;
        double r95814 = pow(r95812, r95813);
        double r95815 = cbrt(r95814);
        double r95816 = 2.0;
        double r95817 = r95810 * r95810;
        double r95818 = r95816 * r95817;
        double r95819 = r95815 + r95818;
        return r95819;
}

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))))