Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\log \left({\left(e^{\frac{x}{x - y} + \frac{y}{x - y}}\right)}^{1}\right)\]
\frac{x + y}{x - y}
↓
\log \left({\left(e^{\frac{x}{x - y} + \frac{y}{x - y}}\right)}^{1}\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) pow(((double) exp(((double) (((double) (x / ((double) (x - y)))) + ((double) (y / ((double) (x - y)))))))), 1.0))));
}

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
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

    \[\frac{x + y}{x - y}\]
  2. Using strategy rm

  3. Applied flip-+31.9

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

  4. Applied associate-/l/31.9

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

  6. Applied add-log-exp31.9

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

  7. Simplified0.0

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

  8. Final simplification0.0

    \[\leadsto \log \left({\left(e^{\frac{x}{x - y} + \frac{y}{x - y}}\right)}^{1}\right)\]

Reproduce

herbie shell --seed 2020120 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))