Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\log \left(e^{\frac{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}}\right)\]
\frac{x - y}{x + y}
↓
\log \left(e^{\frac{\frac{x}{x + y} \cdot \frac{x}{x + y} - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}}\right)
double f(double x, double y) {
        double r720780 = x;
        double r720781 = y;
        double r720782 = r720780 - r720781;
        double r720783 = r720780 + r720781;
        double r720784 = r720782 / r720783;
        return r720784;
}
↓
double f(double x, double y) {
        double r720785 = x;
        double r720786 = y;
        double r720787 = r720785 + r720786;
        double r720788 = r720785 / r720787;
        double r720789 = r720788 * r720788;
        double r720790 = r720786 / r720787;
        double r720791 = r720790 * r720790;
        double r720792 = r720789 - r720791;
        double r720793 = r720788 + r720790;
        double r720794 = r720792 / r720793;
        double r720795 = exp(r720794);
        double r720796 = log(r720795);
        return r720796;
}

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. Applied add-log-exp0.0

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

  7. Applied diff-log0.0

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

  8. Simplified0.0

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

  10. Applied flip--0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2020034 +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)))