Average Error: 52.0 → 52.0
Time: 9.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)\]
\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)
↓
2 \cdot \left(y \cdot y\right) + \left(9 \cdot {x}^{4} - {y}^{4}\right)
double f(double x, double y) {
        double r58593 = 9.0;
        double r58594 = x;
        double r58595 = 4.0;
        double r58596 = pow(r58594, r58595);
        double r58597 = r58593 * r58596;
        double r58598 = y;
        double r58599 = pow(r58598, r58595);
        double r58600 = r58597 - r58599;
        double r58601 = 2.0;
        double r58602 = r58598 * r58598;
        double r58603 = r58601 * r58602;
        double r58604 = r58600 + r58603;
        return r58604;
}
↓
double f(double x, double y) {
        double r58605 = 2.0;
        double r58606 = y;
        double r58607 = r58606 * r58606;
        double r58608 = r58605 * r58607;
        double r58609 = 9.0;
        double r58610 = x;
        double r58611 = 4.0;
        double r58612 = pow(r58610, r58611);
        double r58613 = r58609 * r58612;
        double r58614 = pow(r58606, r58611);
        double r58615 = r58613 - r58614;
        double r58616 = r58608 + r58615;
        return r58616;
}

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

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

Reproduce

herbie shell --seed 2019303 
(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))))