Average Error: 0.0 → 0.0
Time: 4.7s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{x}{x + y} - \log \left(e^{\sqrt[3]{{\left(\frac{y}{x + y}\right)}^{3}}}\right)\]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \log \left(e^{\sqrt[3]{{\left(\frac{y}{x + y}\right)}^{3}}}\right)
double f(double x, double y) {
        double r858855 = x;
        double r858856 = y;
        double r858857 = r858855 - r858856;
        double r858858 = r858855 + r858856;
        double r858859 = r858857 / r858858;
        return r858859;
}
↓
double f(double x, double y) {
        double r858860 = x;
        double r858861 = y;
        double r858862 = r858860 + r858861;
        double r858863 = r858860 / r858862;
        double r858864 = r858861 / r858862;
        double r858865 = 3.0;
        double r858866 = pow(r858864, r858865);
        double r858867 = cbrt(r858866);
        double r858868 = exp(r858867);
        double r858869 = log(r858868);
        double r858870 = r858863 - r858869;
        return r858870;
}

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
Herbie0.0
\[\frac{x}{x + y} - \frac{y}{x + y}\]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.0

    \[\leadsto \frac{x}{x + y} - \color{blue}{\log \left(e^{\frac{y}{x + y}}\right)}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube24.5

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

  8. Applied add-cbrt-cube28.6

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

  9. Applied cbrt-undiv28.6

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

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020002 +o rules:numerics
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
  :precision binary64

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

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