Average Error: 14.3 → 0.1
Time: 11.6s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{x + 1}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{x + 1}}{x - 1}
double f(double x) {
        double r5528925 = 1.0;
        double r5528926 = x;
        double r5528927 = r5528926 + r5528925;
        double r5528928 = r5528925 / r5528927;
        double r5528929 = r5528926 - r5528925;
        double r5528930 = r5528925 / r5528929;
        double r5528931 = r5528928 - r5528930;
        return r5528931;
}
↓
double f(double x) {
        double r5528932 = -2.0;
        double r5528933 = x;
        double r5528934 = 1.0;
        double r5528935 = r5528933 + r5528934;
        double r5528936 = r5528932 / r5528935;
        double r5528937 = r5528933 - r5528934;
        double r5528938 = r5528936 / r5528937;
        return r5528938;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Simplified13.7

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

  5. Taylor expanded around 0 0.4

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

  7. Applied associate-/r*0.1

    \[\leadsto \color{blue}{\frac{\frac{-2}{x + 1}}{x - 1}}\]

  8. Final simplification0.1

    \[\leadsto \frac{\frac{-2}{x + 1}}{x - 1}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))