Average Error: 13.9 → 0.4
Time: 42.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\left(-2\right) \cdot \frac{1}{x \cdot x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\left(-2\right) \cdot \frac{1}{x \cdot x - 1}
double f(double x) {
        double r3381285 = 1.0;
        double r3381286 = x;
        double r3381287 = r3381286 + r3381285;
        double r3381288 = r3381285 / r3381287;
        double r3381289 = r3381286 - r3381285;
        double r3381290 = r3381285 / r3381289;
        double r3381291 = r3381288 - r3381290;
        return r3381291;
}
↓
double f(double x) {
        double r3381292 = -2.0;
        double r3381293 = /* ERROR: no posit support in C */;
        double r3381294 = /* ERROR: no posit support in C */;
        double r3381295 = 1.0;
        double r3381296 = x;
        double r3381297 = r3381296 * r3381296;
        double r3381298 = r3381297 - r3381295;
        double r3381299 = r3381295 / r3381298;
        double r3381300 = r3381294 * r3381299;
        return r3381300;
}

Error

Bits error versus x

Derivation

  1. Initial program 13.9

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

  3. Applied flip--28.9

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

  4. Applied associate-/r/28.9

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

  5. Applied flip-+13.9

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

  6. Applied associate-/r/13.9

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

  7. Applied distribute-lft-out--13.3

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

  9. Applied insert-posit1613.3

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

  10. Simplified0.4

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

  11. Final simplification0.4

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))