Average Error: 14.3 → 0.1
Time: 9.2s
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 r77719 = 1.0;
        double r77720 = x;
        double r77721 = r77720 + r77719;
        double r77722 = r77719 / r77721;
        double r77723 = r77720 - r77719;
        double r77724 = r77719 / r77723;
        double r77725 = r77722 - r77724;
        return r77725;
}
↓
double f(double x) {
        double r77726 = 1.0;
        double r77727 = 2.0;
        double r77728 = -r77727;
        double r77729 = r77726 * r77728;
        double r77730 = x;
        double r77731 = r77730 + r77726;
        double r77732 = r77729 / r77731;
        double r77733 = r77730 - r77726;
        double r77734 = r77732 / r77733;
        return r77734;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 14.3

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

  3. Applied frac-sub13.7

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

  4. Simplified13.7

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

  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 2019303 
(FPCore (x)
  :name "Asymptote A"
  :precision binary64
  (- (/ 1 (+ x 1)) (/ 1 (- x 1))))