Average Error: 0.0 → 0.0
Time: 2.1s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}
double code(double x) {
	return ((double) (((double) (1.0 / ((double) (x - 1.0)))) + ((double) (x / ((double) (x + 1.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) pow(((double) (1.0 / ((double) (x - 1.0)))), 3.0)) + ((double) pow(((double) (x / ((double) (x + 1.0)))), 3.0)))) / ((double) (((double) (((double) (x / ((double) (x + 1.0)))) * ((double) (((double) (x / ((double) (x + 1.0)))) - ((double) (1.0 / ((double) (x - 1.0)))))))) + ((double) (((double) (1.0 / ((double) (x - 1.0)))) * ((double) (1.0 / ((double) (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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020169 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))