Average Error: 52.0 → 52.0
Time: 9.8s
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 r37446 = 9.0;
        double r37447 = x;
        double r37448 = 4.0;
        double r37449 = pow(r37447, r37448);
        double r37450 = r37446 * r37449;
        double r37451 = y;
        double r37452 = pow(r37451, r37448);
        double r37453 = r37450 - r37452;
        double r37454 = 2.0;
        double r37455 = r37451 * r37451;
        double r37456 = r37454 * r37455;
        double r37457 = r37453 + r37456;
        return r37457;
}
↓
double f(double x, double y) {
        double r37458 = 2.0;
        double r37459 = y;
        double r37460 = r37459 * r37459;
        double r37461 = r37458 * r37460;
        double r37462 = 9.0;
        double r37463 = x;
        double r37464 = 4.0;
        double r37465 = pow(r37463, r37464);
        double r37466 = r37462 * r37465;
        double r37467 = pow(r37459, r37464);
        double r37468 = r37466 - r37467;
        double r37469 = r37461 + r37468;
        return r37469;
}

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 2019297 
(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))))