Average Error: 0.0 → 0.0
Time: 2.3s
Precision: binary64
\[\frac{x - y}{x + y} \]
↓
\[\frac{x}{x + y} - \frac{y}{x + y} \]
\frac{x - y}{x + y}
↓
\frac{x}{x + y} - \frac{y}{x + y}

(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
↓
(FPCore (x y) :precision binary64 (- (/ x (+ x y)) (/ y (+ x y))))
double code(double x, double y) {
	return (x - y) / (x + y);
}
↓
double code(double x, double y) {
	return (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 flip-+_binary6431.0

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

  4. Applied associate-/r/_binary6431.1

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

  5. Simplified0.2

    \[\leadsto \color{blue}{\frac{1}{x + y}} \cdot \left(x - y\right) \]
  6. Using strategy rm

  7. Applied sub-neg_binary640.2

    \[\leadsto \frac{1}{x + y} \cdot \color{blue}{\left(x + \left(-y\right)\right)} \]

  8. Applied distribute-rgt-in_binary640.2

    \[\leadsto \color{blue}{x \cdot \frac{1}{x + y} + \left(-y\right) \cdot \frac{1}{x + y}} \]

  9. Simplified0.1

    \[\leadsto \color{blue}{\frac{x}{x + y}} + \left(-y\right) \cdot \frac{1}{x + y} \]

  10. Simplified0.0

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

  11. Final simplification0.0

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

Reproduce

herbie shell --seed 2021198 
(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)))