Average Error: 14.4 → 0.1
Time: 2.8s
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 r135406 = 1.0;
        double r135407 = x;
        double r135408 = r135407 + r135406;
        double r135409 = r135406 / r135408;
        double r135410 = r135407 - r135406;
        double r135411 = r135406 / r135410;
        double r135412 = r135409 - r135411;
        return r135412;
}
↓
double f(double x) {
        double r135413 = 1.0;
        double r135414 = 2.0;
        double r135415 = -r135414;
        double r135416 = r135413 * r135415;
        double r135417 = x;
        double r135418 = r135417 + r135413;
        double r135419 = r135416 / r135418;
        double r135420 = r135417 - r135413;
        double r135421 = r135419 / r135420;
        return r135421;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.4

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

  3. Applied frac-sub13.8

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

  4. Simplified13.8

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

  5. Simplified13.7

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

  6. Taylor expanded around 0 0.3

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

  8. Applied difference-of-squares0.3

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

  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 2020056 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))