Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1}{x - 1}}\right) + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{x - 1}}\right) + \frac{1}{\frac{x + 1}{x}}
double code(double x) {
	return ((1.0 / (x - 1.0)) + (x / (x + 1.0)));
}
↓
double code(double x) {
	return (log(exp((1.0 / (x - 1.0)))) + (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. Using strategy rm

  3. Applied clear-num0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\frac{1}{\frac{x + 1}{x}}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))