Average Error: 0.0 → 0.0
Time: 2.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\mathsf{fma}\left(\frac{x}{x + 1}, \frac{x}{x + 1} - \frac{1}{x - 1}, \frac{1}{x - 1} \cdot \frac{1}{x - 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\mathsf{fma}\left(\frac{x}{x + 1}, \frac{x}{x + 1} - \frac{1}{x - 1}, \frac{1}{x - 1} \cdot \frac{1}{x - 1}\right)}
double code(double x) {
	return ((1.0 / (x - 1.0)) + (x / (x + 1.0)));
}
↓
double code(double x) {
	return ((pow((1.0 / (x - 1.0)), 3.0) + pow((x / (x + 1.0)), 3.0)) / fma((x / (x + 1.0)), ((x / (x + 1.0)) - (1.0 / (x - 1.0))), ((1.0 / (x - 1.0)) * (1.0 / (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 flip3-+0.0

    \[\leadsto \color{blue}{\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right)}}\]

  4. Simplified0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{\mathsf{fma}\left(\frac{x}{x + 1}, \frac{x}{x + 1} - \frac{1}{x - 1}, \frac{1}{x - 1} \cdot \frac{1}{x - 1}\right)}}\]

  5. Final simplification0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\mathsf{fma}\left(\frac{x}{x + 1}, \frac{x}{x + 1} - \frac{1}{x - 1}, \frac{1}{x - 1} \cdot \frac{1}{x - 1}\right)}\]

Reproduce

herbie shell --seed 2020053 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))