Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}
double f(double x) {
        double r99613 = 1.0;
        double r99614 = x;
        double r99615 = r99614 - r99613;
        double r99616 = r99613 / r99615;
        double r99617 = r99614 + r99613;
        double r99618 = r99614 / r99617;
        double r99619 = r99616 + r99618;
        return r99619;
}
↓
double f(double x) {
        double r99620 = 1.0;
        double r99621 = x;
        double r99622 = r99621 - r99620;
        double r99623 = r99620 / r99622;
        double r99624 = 3.0;
        double r99625 = pow(r99623, r99624);
        double r99626 = r99621 + r99620;
        double r99627 = r99621 / r99626;
        double r99628 = pow(r99627, r99624);
        double r99629 = r99625 + r99628;
        double r99630 = r99623 * r99623;
        double r99631 = r99627 - r99623;
        double r99632 = r99627 * r99631;
        double r99633 = r99630 + r99632;
        double r99634 = r99629 / r99633;
        return r99634;
}

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 flip3-+0.0

    \[\leadsto \color{blue}{\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \left(\frac{x}{x + 1} \cdot \frac{x}{x + 1} - \frac{1}{x - 1} \cdot \frac{x}{x + 1}\right)}}\]

  4. Simplified0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}}\]

  5. Final simplification0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}\]

Reproduce

herbie shell --seed 2019235 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))