Average Error: 0.0 → 0.0
Time: 4.7s
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 r93060 = 1.0;
        double r93061 = x;
        double r93062 = r93061 - r93060;
        double r93063 = r93060 / r93062;
        double r93064 = r93061 + r93060;
        double r93065 = r93061 / r93064;
        double r93066 = r93063 + r93065;
        return r93066;
}
↓
double f(double x) {
        double r93067 = 1.0;
        double r93068 = x;
        double r93069 = r93068 - r93067;
        double r93070 = r93067 / r93069;
        double r93071 = r93070 * r93070;
        double r93072 = r93068 + r93067;
        double r93073 = r93068 / r93072;
        double r93074 = r93073 * r93073;
        double r93075 = r93071 - r93074;
        double r93076 = r93070 - r93073;
        double r93077 = r93075 / r93076;
        return r93077;
}

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