Average Error: 52.0 → 52.0
Time: 7.3s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{{\left({x}^{4} \cdot 9 - {y}^{4}\right)}^{3}}\]
\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)}^{3}}
double f(double x, double y) {
        double r40720 = 9.0;
        double r40721 = x;
        double r40722 = 4.0;
        double r40723 = pow(r40721, r40722);
        double r40724 = r40720 * r40723;
        double r40725 = y;
        double r40726 = pow(r40725, r40722);
        double r40727 = r40724 - r40726;
        double r40728 = 2.0;
        double r40729 = r40725 * r40725;
        double r40730 = r40728 * r40729;
        double r40731 = r40727 + r40730;
        return r40731;
}
↓
double f(double x, double y) {
        double r40732 = 2.0;
        double r40733 = y;
        double r40734 = r40733 * r40733;
        double r40735 = r40732 * r40734;
        double r40736 = x;
        double r40737 = 4.0;
        double r40738 = pow(r40736, r40737);
        double r40739 = 9.0;
        double r40740 = r40738 * r40739;
        double r40741 = pow(r40733, r40737);
        double r40742 = r40740 - r40741;
        double r40743 = 3.0;
        double r40744 = pow(r40742, r40743);
        double r40745 = cbrt(r40744);
        double r40746 = r40735 + r40745;
        return r40746;
}

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

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

  5. Final simplification52.0

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

Reproduce

herbie shell --seed 2019195 
(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))))