Average Error: 0.0 → 0.0
Time: 12.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1}}{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} - \frac{1}{x - 1}\right) + \frac{\frac{1}{x - 1}}{x - 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{1}{x - 1} \cdot \frac{\frac{1}{x - 1}}{x - 1}}{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} - \frac{1}{x - 1}\right) + \frac{\frac{1}{x - 1}}{x - 1}}
double f(double x) {
        double r4344579 = 1.0;
        double r4344580 = x;
        double r4344581 = r4344580 - r4344579;
        double r4344582 = r4344579 / r4344581;
        double r4344583 = r4344580 + r4344579;
        double r4344584 = r4344580 / r4344583;
        double r4344585 = r4344582 + r4344584;
        return r4344585;
}
↓
double f(double x) {
        double r4344586 = x;
        double r4344587 = 1.0;
        double r4344588 = r4344587 + r4344586;
        double r4344589 = r4344586 / r4344588;
        double r4344590 = r4344589 * r4344589;
        double r4344591 = r4344589 * r4344590;
        double r4344592 = r4344586 - r4344587;
        double r4344593 = r4344587 / r4344592;
        double r4344594 = r4344593 / r4344592;
        double r4344595 = r4344593 * r4344594;
        double r4344596 = r4344591 + r4344595;
        double r4344597 = r4344589 - r4344593;
        double r4344598 = r4344589 * r4344597;
        double r4344599 = r4344598 + r4344594;
        double r4344600 = r4344596 / r4344599;
        return r4344600;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))