Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
\[\frac{x - y}{x + y}\]
↓
\[\log \left(\frac{e^{\frac{x}{x + y}}}{e^{\frac{y}{x + y}}}\right)\]
\frac{x - y}{x + y}
↓
\log \left(\frac{e^{\frac{x}{x + y}}}{e^{\frac{y}{x + y}}}\right)
double code(double x, double y) {
	return ((double) (((double) (x - y)) / ((double) (x + y))));
}
↓
double code(double x, double y) {
	return ((double) log(((double) (((double) exp(((double) (x / ((double) (x + y)))))) / ((double) exp(((double) (y / ((double) (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 add-log-exp0.0

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

  5. Applied div-sub0.0

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

  6. Applied exp-diff0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020155 
(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)))