Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1} \]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)\right) \]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{x - 1} + \frac{x}{1 + x}\right)\right)

(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (log1p (expm1 (+ (/ 1.0 (- x 1.0)) (/ x (+ 1.0 x))))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return log1p(expm1((1.0 / (x - 1.0)) + (x / (1.0 + x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Applied log1p-expm1-u_binary640.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022005 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))