Average Error: 52.0 → 52.0
Time: 6.9s
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 r38609 = 9.0;
        double r38610 = x;
        double r38611 = 4.0;
        double r38612 = pow(r38610, r38611);
        double r38613 = r38609 * r38612;
        double r38614 = y;
        double r38615 = pow(r38614, r38611);
        double r38616 = r38613 - r38615;
        double r38617 = 2.0;
        double r38618 = r38614 * r38614;
        double r38619 = r38617 * r38618;
        double r38620 = r38616 + r38619;
        return r38620;
}
↓
double f(double x, double y) {
        double r38621 = 2.0;
        double r38622 = y;
        double r38623 = r38622 * r38622;
        double r38624 = r38621 * r38623;
        double r38625 = x;
        double r38626 = 4.0;
        double r38627 = pow(r38625, r38626);
        double r38628 = 9.0;
        double r38629 = r38627 * r38628;
        double r38630 = pow(r38622, r38626);
        double r38631 = r38629 - r38630;
        double r38632 = 3.0;
        double r38633 = pow(r38631, r38632);
        double r38634 = cbrt(r38633);
        double r38635 = r38624 + r38634;
        return r38635;
}

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 2019196 
(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))))