Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(\left(x + 1\right) \cdot \frac{1}{x - 1}\right) - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(\left(x + 1\right) \cdot \frac{1}{x - 1}\right) - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}
double f(double x) {
        double r125611 = 1.0;
        double r125612 = x;
        double r125613 = r125612 - r125611;
        double r125614 = r125611 / r125613;
        double r125615 = r125612 + r125611;
        double r125616 = r125612 / r125615;
        double r125617 = r125614 + r125616;
        return r125617;
}
↓
double f(double x) {
        double r125618 = 1.0;
        double r125619 = x;
        double r125620 = r125619 * r125619;
        double r125621 = r125618 * r125618;
        double r125622 = r125620 - r125621;
        double r125623 = r125618 / r125622;
        double r125624 = r125619 + r125618;
        double r125625 = r125619 - r125618;
        double r125626 = r125618 / r125625;
        double r125627 = r125624 * r125626;
        double r125628 = r125623 * r125627;
        double r125629 = r125619 / r125624;
        double r125630 = r125629 * r125629;
        double r125631 = r125628 - r125630;
        double r125632 = r125626 - r125629;
        double r125633 = r125631 / r125632;
        return r125633;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied flip-+0.0

    \[\leadsto \color{blue}{\frac{\frac{1}{x - 1} \cdot \frac{1}{x - 1} - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{x - 1} - \frac{x}{x + 1}}}\]
  4. Using strategy rm

  5. Applied flip--0.0

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

  6. Applied associate-/r/0.0

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

  7. Applied associate-*l*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))