Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1}{x - 1} + \frac{x}{1 + x}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{x - 1} + \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 (- x 1.0)) (/ x (+ 1.0 x))))))
double code(double x) {
	return ((double) ((1.0 / ((double) (x - 1.0))) + (x / ((double) (x + 1.0)))));
}
↓
double code(double x) {
	return ((double) log(((double) exp(((double) ((1.0 / ((double) (x - 1.0))) + (x / ((double) (1.0 + x)))))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 0.0 bits

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-log-expError: 0.0 bits

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

  4. Applied add-log-expError: 0.0 bits

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

  5. Applied sum-logError: 0.0 bits

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

  6. SimplifiedError: 0.0 bits

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

  7. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))