Average Error: 62.0 → 52.0
Time: 15.1s
Precision: 64
\[x = 10864 \land y = 18817\]
\[9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)\]
↓
\[\sqrt[3]{\left(\left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right) \cdot \left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)\right) \cdot \left(9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y\right)\right)} - \left(y \cdot y\right) \cdot \left(-2\right)\]
9 \cdot {x}^{4} - \left(y \cdot y\right) \cdot \left(y \cdot y - 2\right)
↓
\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(y \cdot y\right) \cdot \left(-2\right)
double f(double x, double y) {
        double r4213698 = 9.0;
        double r4213699 = x;
        double r4213700 = 4.0;
        double r4213701 = pow(r4213699, r4213700);
        double r4213702 = r4213698 * r4213701;
        double r4213703 = y;
        double r4213704 = r4213703 * r4213703;
        double r4213705 = 2.0;
        double r4213706 = r4213704 - r4213705;
        double r4213707 = r4213704 * r4213706;
        double r4213708 = r4213702 - r4213707;
        return r4213708;
}
↓
double f(double x, double y) {
        double r4213709 = 9.0;
        double r4213710 = x;
        double r4213711 = 4.0;
        double r4213712 = pow(r4213710, r4213711);
        double r4213713 = r4213709 * r4213712;
        double r4213714 = y;
        double r4213715 = r4213714 * r4213714;
        double r4213716 = r4213715 * r4213715;
        double r4213717 = r4213713 - r4213716;
        double r4213718 = r4213717 * r4213717;
        double r4213719 = r4213718 * r4213717;
        double r4213720 = cbrt(r4213719);
        double r4213721 = 2.0;
        double r4213722 = -r4213721;
        double r4213723 = r4213715 * r4213722;
        double r4213724 = r4213720 - r4213723;
        return r4213724;
}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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-lft-in62.0

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

  5. Applied associate--r+52.0

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

  7. Applied add-cbrt-cube52.0

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

  8. Final simplification52.0

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

Reproduce

herbie shell --seed 2019174 
(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))))