Average Error: 62.0 → 52.0
Time: 15.7s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{\left(\left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\sqrt[3]{\left(\left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left({x}^{4} \cdot 9 - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(-2\right) \cdot \left(y \cdot y\right)
double f(double x, double y) {
        double r3221677 = 9.0;
        double r3221678 = x;
        double r3221679 = 4.0;
        double r3221680 = pow(r3221678, r3221679);
        double r3221681 = r3221677 * r3221680;
        double r3221682 = y;
        double r3221683 = r3221682 * r3221682;
        double r3221684 = 2.0;
        double r3221685 = r3221683 - r3221684;
        double r3221686 = r3221683 * r3221685;
        double r3221687 = r3221681 - r3221686;
        return r3221687;
}
↓
double f(double x, double y) {
        double r3221688 = x;
        double r3221689 = 4.0;
        double r3221690 = pow(r3221688, r3221689);
        double r3221691 = 9.0;
        double r3221692 = r3221690 * r3221691;
        double r3221693 = y;
        double r3221694 = r3221693 * r3221693;
        double r3221695 = r3221694 * r3221694;
        double r3221696 = r3221692 - r3221695;
        double r3221697 = r3221696 * r3221696;
        double r3221698 = r3221697 * r3221696;
        double r3221699 = cbrt(r3221698);
        double r3221700 = 2.0;
        double r3221701 = -r3221700;
        double r3221702 = r3221701 * r3221694;
        double r3221703 = r3221699 - r3221702;
        return r3221703;
}

Error

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Your Program's Arguments

Results

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Derivation

  1. Initial program 62.0

    \[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg62.0

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

  4. Applied distribute-rgt-in62.0

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

  5. Applied associate--r+52.0

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) - \left(-2\right) \cdot \left(y \cdot y\right)}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube52.0

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

  8. Final simplification52.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x y)
  :name "From Rump in a 1983 paper, rewritten"
  :pre (and (== x 10864.0) (== y 18817.0))
  (- (* 9.0 (pow x 4.0)) (* (* y y) (- (* y y) 2.0))))