Average Error: 0.0 → 0.0
Time: 2.6s
Precision: 64
\[\frac{x + y}{x - y}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x + y}{x - y}\right)\right)\]
\frac{x + y}{x - y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x + y}{x - y}\right)\right)
double code(double x, double y) {
	return ((x + y) / (x - y));
}
↓
double code(double x, double y) {
	return log1p(expm1(((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
\[\frac{1}{\frac{x}{x + y} - \frac{y}{x + y}}\]

Derivation

  1. Initial program 0.0

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

  3. Applied log1p-expm1-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(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)))