Average Error: 14.8 → 0.1
Time: 11.2s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1 \cdot \left(-2\right)}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1 \cdot \left(-2\right)}{x + 1}}{x - 1}
double f(double x) {
        double r93883 = 1.0;
        double r93884 = x;
        double r93885 = r93884 + r93883;
        double r93886 = r93883 / r93885;
        double r93887 = r93884 - r93883;
        double r93888 = r93883 / r93887;
        double r93889 = r93886 - r93888;
        return r93889;
}
↓
double f(double x) {
        double r93890 = 1.0;
        double r93891 = 2.0;
        double r93892 = -r93891;
        double r93893 = r93890 * r93892;
        double r93894 = x;
        double r93895 = r93894 + r93890;
        double r93896 = r93893 / r93895;
        double r93897 = r93894 - r93890;
        double r93898 = r93896 / r93897;
        return r93898;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.8

    \[\frac{1}{x + 1} - \frac{1}{x - 1}\]
  2. Using strategy rm

  3. Applied frac-sub14.1

    \[\leadsto \color{blue}{\frac{1 \cdot \left(x - 1\right) - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot \left(x - 1\right)}}\]

  4. Simplified14.1

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(x - 1\right) - \left(x + 1\right)\right)}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]

  5. Taylor expanded around 0 0.4

    \[\leadsto \frac{1 \cdot \color{blue}{\left(-2\right)}}{\left(x + 1\right) \cdot \left(x - 1\right)}\]
  6. Using strategy rm

  7. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{1 \cdot \left(-2\right)}{x + 1}}{x - 1}}\]

  8. Final simplification0.1

    \[\leadsto \frac{\frac{1 \cdot \left(-2\right)}{x + 1}}{x - 1}\]

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))