Average Error: 14.1 → 0.1
Time: 13.0s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1}{x + 1}}{x - 1} \cdot \left(-2\right)\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1}{x + 1}}{x - 1} \cdot \left(-2\right)
double f(double x) {
        double r85618 = 1.0;
        double r85619 = x;
        double r85620 = r85619 + r85618;
        double r85621 = r85618 / r85620;
        double r85622 = r85619 - r85618;
        double r85623 = r85618 / r85622;
        double r85624 = r85621 - r85623;
        return r85624;
}
↓
double f(double x) {
        double r85625 = 1.0;
        double r85626 = x;
        double r85627 = r85626 + r85625;
        double r85628 = r85625 / r85627;
        double r85629 = r85626 - r85625;
        double r85630 = r85628 / r85629;
        double r85631 = 2.0;
        double r85632 = -r85631;
        double r85633 = r85630 * r85632;
        return r85633;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.1

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

  3. Applied flip--29.2

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

  4. Applied associate-/r/29.2

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

  5. Applied flip-+14.2

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

  6. Applied associate-/r/14.1

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

  7. Applied distribute-lft-out--13.6

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

  8. Taylor expanded around 0 0.3

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

  10. Applied difference-of-squares0.3

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

  11. Applied associate-/r*0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))