Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{\log \left(e^{\frac{x}{x + y} \cdot \frac{x}{x + y}}\right) - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}\]
\frac{x - y}{x + y}
↓
\frac{\log \left(e^{\frac{x}{x + y} \cdot \frac{x}{x + y}}\right) - \frac{y}{x + y} \cdot \frac{y}{x + y}}{\frac{x}{x + y} + \frac{y}{x + y}}
double code(double x, double y) {
	return ((x - y) / (x + y));
}
↓
double code(double x, double y) {
	return ((log(exp(((x / (x + y)) * (x / (x + y))))) - ((y / (x + y)) * (y / (x + y)))) / ((x / (x + y)) + (y / (x + y))));
}

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 flip--0.0

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

  7. Applied add-log-exp0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020075 
(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)))