Average Error: 0.0 → 0.0
Time: 3.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + 1}\right)\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \mathsf{expm1}\left(\mathsf{log1p}\left(\frac{x}{x + 1}\right)\right)
double code(double x) {
	return ((1.0 / (x - 1.0)) + (x / (x + 1.0)));
}
↓
double code(double x) {
	return ((1.0 / (x - 1.0)) + expm1(log1p((x / (x + 1.0)))));
}

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. Using strategy rm

  3. Applied expm1-log1p-u0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020092 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))