Average Error: 52.0 → 52.0
Time: 13.5s
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 r2844760 = 9.0;
        double r2844761 = x;
        double r2844762 = 4.0;
        double r2844763 = pow(r2844761, r2844762);
        double r2844764 = r2844760 * r2844763;
        double r2844765 = y;
        double r2844766 = pow(r2844765, r2844762);
        double r2844767 = r2844764 - r2844766;
        double r2844768 = 2.0;
        double r2844769 = r2844765 * r2844765;
        double r2844770 = r2844768 * r2844769;
        double r2844771 = r2844767 + r2844770;
        return r2844771;
}
↓
double f(double x, double y) {
        double r2844772 = 2.0;
        double r2844773 = y;
        double r2844774 = r2844773 * r2844773;
        double r2844775 = r2844772 * r2844774;
        double r2844776 = x;
        double r2844777 = 4.0;
        double r2844778 = pow(r2844776, r2844777);
        double r2844779 = 9.0;
        double r2844780 = r2844778 * r2844779;
        double r2844781 = pow(r2844773, r2844777);
        double r2844782 = r2844780 - r2844781;
        double r2844783 = r2844782 * r2844782;
        double r2844784 = r2844782 * r2844783;
        double r2844785 = cbrt(r2844784);
        double r2844786 = r2844775 + r2844785;
        return r2844786;
}

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 2019171 +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))))