Average Error: 52.0 → 52.0
Time: 11.2s
Precision: 64
\[x = 10864 \land y = 18817\]
\[\left(9 \cdot {x}^{4} - {y}^{4}\right) + 2 \cdot \left(y \cdot y\right)\]
↓
\[2 \cdot \left(y \cdot y\right) + \sqrt[3]{\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}\]
\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) \cdot \left(\left({x}^{4} \cdot 9 - {y}^{4}\right) \cdot \left({x}^{4} \cdot 9 - {y}^{4}\right)\right)}
double f(double x, double y) {
        double r3306632 = 9.0;
        double r3306633 = x;
        double r3306634 = 4.0;
        double r3306635 = pow(r3306633, r3306634);
        double r3306636 = r3306632 * r3306635;
        double r3306637 = y;
        double r3306638 = pow(r3306637, r3306634);
        double r3306639 = r3306636 - r3306638;
        double r3306640 = 2.0;
        double r3306641 = r3306637 * r3306637;
        double r3306642 = r3306640 * r3306641;
        double r3306643 = r3306639 + r3306642;
        return r3306643;
}
↓
double f(double x, double y) {
        double r3306644 = 2.0;
        double r3306645 = y;
        double r3306646 = r3306645 * r3306645;
        double r3306647 = r3306644 * r3306646;
        double r3306648 = x;
        double r3306649 = 4.0;
        double r3306650 = pow(r3306648, r3306649);
        double r3306651 = 9.0;
        double r3306652 = r3306650 * r3306651;
        double r3306653 = pow(r3306645, r3306649);
        double r3306654 = r3306652 - r3306653;
        double r3306655 = r3306654 * r3306654;
        double r3306656 = r3306654 * r3306655;
        double r3306657 = cbrt(r3306656);
        double r3306658 = r3306647 + r3306657;
        return r3306658;
}

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. Final simplification52.0

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

Reproduce

herbie shell --seed 2019179 
(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))))