Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\frac{x - y}{x + y}\]
↓
\[\frac{-\left(x - y\right)}{-\left(x + y\right)}\]
\frac{x - y}{x + y}
↓
\frac{-\left(x - y\right)}{-\left(x + y\right)}
double code(double x, double y) {
	return ((x - y) / (x + y));
}
↓
double code(double x, double y) {
	return (-(x - 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 frac-2neg0.0

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

  5. Applied *-un-lft-identity0.0

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

  6. Applied *-un-lft-identity0.0

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

  7. Applied times-frac0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020058 +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)))