Average Error: 14.0 → 0.1
Time: 3.6s
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 r126255 = 1.0;
        double r126256 = x;
        double r126257 = r126256 + r126255;
        double r126258 = r126255 / r126257;
        double r126259 = r126256 - r126255;
        double r126260 = r126255 / r126259;
        double r126261 = r126258 - r126260;
        return r126261;
}
↓
double f(double x) {
        double r126262 = 1.0;
        double r126263 = 2.0;
        double r126264 = -r126263;
        double r126265 = r126262 * r126264;
        double r126266 = x;
        double r126267 = r126266 + r126262;
        double r126268 = r126265 / r126267;
        double r126269 = r126266 - r126262;
        double r126270 = r126268 / r126269;
        return r126270;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.0

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

  3. Applied frac-sub13.4

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

  4. Simplified13.4

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

  5. Simplified13.4

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

  6. Taylor expanded around 0 0.4

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

  8. Applied difference-of-squares0.4

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

  9. Applied associate-/r*0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))