Average Error: 14.6 → 0.1
Time: 17.2s
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 r2409288 = 1.0;
        double r2409289 = x;
        double r2409290 = r2409289 + r2409288;
        double r2409291 = r2409288 / r2409290;
        double r2409292 = r2409289 - r2409288;
        double r2409293 = r2409288 / r2409292;
        double r2409294 = r2409291 - r2409293;
        return r2409294;
}
↓
double f(double x) {
        double r2409295 = -2.0;
        double r2409296 = 1.0;
        double r2409297 = x;
        double r2409298 = r2409296 + r2409297;
        double r2409299 = r2409295 / r2409298;
        double r2409300 = r2409297 - r2409296;
        double r2409301 = r2409299 / r2409300;
        return r2409301;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.6

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

  3. Applied frac-sub14.0

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

  4. Simplified12.1

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

  5. Taylor expanded around inf 0.4

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

  7. Applied associate-/r*0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))