Average Error: 0.0 → 0.2
Time: 10.1s
Precision: 64
\[\frac{x - y}{2 - \left(x + y\right)}\]
↓
\[{\left(\sqrt[3]{\frac{x}{2 - \left(x + y\right)}}\right)}^{3} - \frac{y}{\left(2 - x\right) - y}\]
\frac{x - y}{2 - \left(x + y\right)}
↓
{\left(\sqrt[3]{\frac{x}{2 - \left(x + y\right)}}\right)}^{3} - \frac{y}{\left(2 - x\right) - y}
double f(double x, double y) {
        double r1048585 = x;
        double r1048586 = y;
        double r1048587 = r1048585 - r1048586;
        double r1048588 = 2.0;
        double r1048589 = r1048585 + r1048586;
        double r1048590 = r1048588 - r1048589;
        double r1048591 = r1048587 / r1048590;
        return r1048591;
}
↓
double f(double x, double y) {
        double r1048592 = x;
        double r1048593 = 2.0;
        double r1048594 = y;
        double r1048595 = r1048592 + r1048594;
        double r1048596 = r1048593 - r1048595;
        double r1048597 = r1048592 / r1048596;
        double r1048598 = cbrt(r1048597);
        double r1048599 = 3.0;
        double r1048600 = pow(r1048598, r1048599);
        double r1048601 = r1048593 - r1048592;
        double r1048602 = r1048601 - r1048594;
        double r1048603 = r1048594 / r1048602;
        double r1048604 = r1048600 - r1048603;
        return r1048604;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.2
\[\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{2 - \left(x + y\right)}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{2 - \left(x + y\right)} - \frac{y}{2 - \left(x + y\right)}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt0.2

    \[\leadsto \frac{x}{2 - \left(x + y\right)} - \color{blue}{\left(\sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}\right) \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}}\]

  6. Applied add-cube-cbrt0.4

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{x}{2 - \left(x + y\right)}}\right) \cdot \sqrt[3]{\frac{x}{2 - \left(x + y\right)}}} - \left(\sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}\right) \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}\]

  7. Applied prod-diff0.4

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt[3]{\frac{x}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{x}{2 - \left(x + y\right)}}, \sqrt[3]{\frac{x}{2 - \left(x + y\right)}}, -\sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \left(\sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}\right)\right) + \mathsf{fma}\left(-\sqrt[3]{\frac{y}{2 - \left(x + y\right)}}, \sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}, \sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \left(\sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}\right)\right)}\]

  8. Simplified0.2

    \[\leadsto \color{blue}{\left({\left(\sqrt[3]{\frac{x}{2 - \left(x + y\right)}}\right)}^{3} - \frac{y}{\left(2 - x\right) - y}\right)} + \mathsf{fma}\left(-\sqrt[3]{\frac{y}{2 - \left(x + y\right)}}, \sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}, \sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \left(\sqrt[3]{\frac{y}{2 - \left(x + y\right)}} \cdot \sqrt[3]{\frac{y}{2 - \left(x + y\right)}}\right)\right)\]

  9. Simplified0.2

    \[\leadsto \left({\left(\sqrt[3]{\frac{x}{2 - \left(x + y\right)}}\right)}^{3} - \frac{y}{\left(2 - x\right) - y}\right) + \color{blue}{0}\]

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, C"
  :precision binary64

  :herbie-target
  (- (/ x (- 2 (+ x y))) (/ y (- 2 (+ x y))))

  (/ (- x y) (- 2 (+ x y))))