Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{x}{x + 1} + \frac{1}{x - 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{x}{x + 1} + \frac{1}{x - 1}
double f(double x) {
        double r109530 = 1.0;
        double r109531 = x;
        double r109532 = r109531 - r109530;
        double r109533 = r109530 / r109532;
        double r109534 = r109531 + r109530;
        double r109535 = r109531 / r109534;
        double r109536 = r109533 + r109535;
        return r109536;
}
↓
double f(double x) {
        double r109537 = x;
        double r109538 = 1.0;
        double r109539 = r109537 + r109538;
        double r109540 = r109537 / r109539;
        double r109541 = r109537 - r109538;
        double r109542 = r109538 / r109541;
        double r109543 = r109540 + r109542;
        return r109543;
}

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

    \[\leadsto \frac{x}{x + 1} + \frac{1}{x - 1}\]

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))