Average Error: 52.0 → 52.0
Time: 13.2s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r2733794 = 9.0;
        double r2733795 = x;
        double r2733796 = 4.0;
        double r2733797 = pow(r2733795, r2733796);
        double r2733798 = r2733794 * r2733797;
        double r2733799 = y;
        double r2733800 = pow(r2733799, r2733796);
        double r2733801 = r2733798 - r2733800;
        double r2733802 = 2.0;
        double r2733803 = r2733799 * r2733799;
        double r2733804 = r2733802 * r2733803;
        double r2733805 = r2733801 + r2733804;
        return r2733805;
}
↓
double f(double x, double y) {
        double r2733806 = 2.0;
        double r2733807 = y;
        double r2733808 = r2733807 * r2733807;
        double r2733809 = r2733806 * r2733808;
        double r2733810 = x;
        double r2733811 = 4.0;
        double r2733812 = pow(r2733810, r2733811);
        double r2733813 = 9.0;
        double r2733814 = r2733812 * r2733813;
        double r2733815 = pow(r2733807, r2733811);
        double r2733816 = r2733814 - r2733815;
        double r2733817 = r2733816 * r2733816;
        double r2733818 = r2733816 * r2733817;
        double r2733819 = cbrt(r2733818);
        double r2733820 = r2733809 + r2733819;
        return r2733820;
}

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. Final simplification52.0

    \[\leadsto 2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(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))))