Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)
double f(double x) {
        double r83550 = 1.0;
        double r83551 = x;
        double r83552 = r83551 - r83550;
        double r83553 = r83550 / r83552;
        double r83554 = r83551 + r83550;
        double r83555 = r83551 / r83554;
        double r83556 = r83553 + r83555;
        return r83556;
}
↓
double f(double x) {
        double r83557 = 1.0;
        double r83558 = x;
        double r83559 = r83558 - r83557;
        double r83560 = r83557 / r83559;
        double r83561 = r83558 + r83557;
        double r83562 = r83558 / r83561;
        double r83563 = exp(r83562);
        double r83564 = log(r83563);
        double r83565 = r83560 + r83564;
        return r83565;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))