Average Error: 14.2 → 0.1
Time: 9.9s
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 r2029848 = 1.0;
        double r2029849 = x;
        double r2029850 = r2029849 + r2029848;
        double r2029851 = r2029848 / r2029850;
        double r2029852 = r2029849 - r2029848;
        double r2029853 = r2029848 / r2029852;
        double r2029854 = r2029851 - r2029853;
        return r2029854;
}
↓
double f(double x) {
        double r2029855 = -2.0;
        double r2029856 = x;
        double r2029857 = 1.0;
        double r2029858 = r2029856 - r2029857;
        double r2029859 = r2029855 / r2029858;
        double r2029860 = r2029856 + r2029857;
        double r2029861 = r2029859 / r2029860;
        return r2029861;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.2

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

  3. Applied frac-sub13.5

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

  4. Simplified13.5

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

  5. Simplified13.5

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

  6. Taylor expanded around 0 0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))