Average Error: 14.2 → 0.1
Time: 17.7s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{-2}{1 + x}}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{-2}{1 + x}}{x - 1}
double f(double x) {
        double r2131396 = 1.0;
        double r2131397 = x;
        double r2131398 = r2131397 + r2131396;
        double r2131399 = r2131396 / r2131398;
        double r2131400 = r2131397 - r2131396;
        double r2131401 = r2131396 / r2131400;
        double r2131402 = r2131399 - r2131401;
        return r2131402;
}
↓
double f(double x) {
        double r2131403 = -2.0;
        double r2131404 = 1.0;
        double r2131405 = x;
        double r2131406 = r2131404 + r2131405;
        double r2131407 = r2131403 / r2131406;
        double r2131408 = r2131405 - r2131404;
        double r2131409 = r2131407 / r2131408;
        return r2131409;
}

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-sub13.6

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

  4. Simplified13.6

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

  5. Simplified13.6

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

  6. Taylor expanded around 0 0.4

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

  8. Applied associate-/r*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))