Average Error: 0.0 → 0.0
Time: 1.3s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1} \]
↓
\[\log \left(e^{\frac{1}{-1 + x} + \frac{x}{1 + x}}\right) \]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{-1 + x} + \frac{x}{1 + x}}\right)

(FPCore (x) :precision binary64 (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))
↓
(FPCore (x)
 :precision binary64
 (log (exp (+ (/ 1.0 (+ -1.0 x)) (/ x (+ 1.0 x))))))
double code(double x) {
	return (1.0 / (x - 1.0)) + (x / (x + 1.0));
}
↓
double code(double x) {
	return log(exp((1.0 / (-1.0 + x)) + (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 add-log-exp_binary640.0

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

  3. Applied add-log-exp_binary640.0

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

  4. Applied sum-log_binary640.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021280 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))