Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)
double f(double x) {
        double r115448 = 1.0;
        double r115449 = x;
        double r115450 = r115449 - r115448;
        double r115451 = r115448 / r115450;
        double r115452 = r115449 + r115448;
        double r115453 = r115449 / r115452;
        double r115454 = r115451 + r115453;
        return r115454;
}
↓
double f(double x) {
        double r115455 = 1.0;
        double r115456 = x;
        double r115457 = r115456 - r115455;
        double r115458 = r115455 / r115457;
        double r115459 = r115456 + r115455;
        double r115460 = r115456 / r115459;
        double r115461 = r115458 + r115460;
        double r115462 = exp(r115461);
        double r115463 = log(r115462);
        return r115463;
}

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 add-log-exp0.0

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

  4. Applied add-log-exp0.0

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

  5. Applied sum-log0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))