Average Error: 52.0 → 52.0
Time: 13.0s
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 r77598 = 9.0;
        double r77599 = x;
        double r77600 = 4.0;
        double r77601 = pow(r77599, r77600);
        double r77602 = r77598 * r77601;
        double r77603 = y;
        double r77604 = pow(r77603, r77600);
        double r77605 = r77602 - r77604;
        double r77606 = 2.0;
        double r77607 = r77603 * r77603;
        double r77608 = r77606 * r77607;
        double r77609 = r77605 + r77608;
        return r77609;
}
↓
double f(double x, double y) {
        double r77610 = 9.0;
        double r77611 = x;
        double r77612 = 4.0;
        double r77613 = pow(r77611, r77612);
        double r77614 = r77610 * r77613;
        double r77615 = y;
        double r77616 = pow(r77615, r77612);
        double r77617 = r77614 - r77616;
        double r77618 = 3.0;
        double r77619 = pow(r77617, r77618);
        double r77620 = cbrt(r77619);
        double r77621 = 2.0;
        double r77622 = r77615 * r77615;
        double r77623 = r77621 * r77622;
        double r77624 = r77620 + r77623;
        return r77624;
}

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 2019326 
(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))))