Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[\frac{x + y}{x - y} \]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\frac{x - y}{x + y}}\right)\right) \]
\frac{x + y}{x - y}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\frac{x - y}{x + y}}\right)\right)

(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))
↓
(FPCore (x y) :precision binary64 (log1p (expm1 (/ 1.0 (/ (- x y) (+ x y))))))
double code(double x, double y) {
	return (x + y) / (x - y);
}
↓
double code(double x, double y) {
	return log1p(expm1(1.0 / ((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. Applied log1p-expm1-u_binary640.0

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

  3. Applied clear-num_binary640.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{\frac{1}{\frac{x - y}{x + y}}}\right)\right) \]

  4. Final simplification0.0

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\frac{x - y}{x + y}}\right)\right) \]

Reproduce

herbie shell --seed 2021280 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

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