Average Error: 0.0 → 0.0
Time: 2.7s
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 r131085 = 1.0;
        double r131086 = x;
        double r131087 = r131086 - r131085;
        double r131088 = r131085 / r131087;
        double r131089 = r131086 + r131085;
        double r131090 = r131086 / r131089;
        double r131091 = r131088 + r131090;
        return r131091;
}
↓
double f(double x) {
        double r131092 = 1.0;
        double r131093 = x;
        double r131094 = r131093 - r131092;
        double r131095 = r131092 / r131094;
        double r131096 = r131095 * r131095;
        double r131097 = r131093 + r131092;
        double r131098 = r131093 / r131097;
        double r131099 = r131098 * r131098;
        double r131100 = r131096 - r131099;
        double r131101 = r131095 - r131098;
        double r131102 = r131100 / r131101;
        return r131102;
}

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 2020002 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))