Average Error: 0.0 → 0.0
Time: 7.8s
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 r79788 = 1.0;
        double r79789 = x;
        double r79790 = r79789 - r79788;
        double r79791 = r79788 / r79790;
        double r79792 = r79789 + r79788;
        double r79793 = r79789 / r79792;
        double r79794 = r79791 + r79793;
        return r79794;
}
↓
double f(double x) {
        double r79795 = 1.0;
        double r79796 = x;
        double r79797 = r79796 - r79795;
        double r79798 = r79795 / r79797;
        double r79799 = r79798 * r79798;
        double r79800 = r79796 + r79795;
        double r79801 = r79796 / r79800;
        double r79802 = r79801 * r79801;
        double r79803 = r79799 - r79802;
        double r79804 = r79798 - r79801;
        double r79805 = r79803 / r79804;
        return r79805;
}

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 2019199 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))