Average Error: 15.0 → 0.1
Time: 7.8s
Precision: 64
\[\frac{1}{x + 1} - \frac{1}{x - 1}\]
↓
\[\frac{\frac{1}{x + 1} \cdot \left(-2\right)}{x - 1}\]
\frac{1}{x + 1} - \frac{1}{x - 1}
↓
\frac{\frac{1}{x + 1} \cdot \left(-2\right)}{x - 1}
double f(double x) {
        double r184353 = 1.0;
        double r184354 = x;
        double r184355 = r184354 + r184353;
        double r184356 = r184353 / r184355;
        double r184357 = r184354 - r184353;
        double r184358 = r184353 / r184357;
        double r184359 = r184356 - r184358;
        return r184359;
}
↓
double f(double x) {
        double r184360 = 1.0;
        double r184361 = x;
        double r184362 = r184361 + r184360;
        double r184363 = r184360 / r184362;
        double r184364 = 2.0;
        double r184365 = -r184364;
        double r184366 = r184363 * r184365;
        double r184367 = r184361 - r184360;
        double r184368 = r184366 / r184367;
        return r184368;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

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

  3. Applied flip--29.0

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

  4. Applied associate-/r/29.0

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

  5. Applied flip-+15.1

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

  6. Applied associate-/r/15.0

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

  7. Applied distribute-lft-out--14.3

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

  8. Taylor expanded around 0 0.4

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

  10. Applied difference-of-squares0.4

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

  11. Applied associate-/r*0.1

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

  13. Applied associate-*l/0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))