Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}
double f(double x) {
        double r113007 = 1.0;
        double r113008 = x;
        double r113009 = r113008 - r113007;
        double r113010 = r113007 / r113009;
        double r113011 = r113008 + r113007;
        double r113012 = r113008 / r113011;
        double r113013 = r113010 + r113012;
        return r113013;
}
↓
double f(double x) {
        double r113014 = 1.0;
        double r113015 = x;
        double r113016 = r113015 - r113014;
        double r113017 = r113014 / r113016;
        double r113018 = r113017 * r113017;
        double r113019 = r113015 + r113014;
        double r113020 = r113015 / r113019;
        double r113021 = r113020 * r113020;
        double r113022 = r113018 - r113021;
        double r113023 = r113017 - r113020;
        double r113024 = r113022 / r113023;
        return r113024;
}

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 flip-+0.0

    \[\leadsto \color{blue}{\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))