Average Error: 0.0 → 0.1
Time: 2.5s
Precision: binary64
\[\frac{x - y}{x + y} \]
↓
\[\frac{x}{x + y} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right) \]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right)

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y)
 :precision binary64
 (- (/ x (+ x y)) (expm1 (log1p (/ y (+ x y))))))
double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
double code(double x, double y) {
	return (x / (x + y)) - expm1(log1p(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
Herbie0.1
\[\frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y} \]

  2. Applied div-sub_binary640.0

    \[\leadsto \color{blue}{\frac{x}{x + y} - \frac{y}{x + y}} \]

  3. Applied expm1-log1p-u_binary640.1

    \[\leadsto \frac{x}{x + y} - \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right)} \]

  4. Final simplification0.1

    \[\leadsto \frac{x}{x + y} - \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{x + y}\right)\right) \]

Reproduce

herbie shell --seed 2022067 
(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)))