Average Error: 0.0 → 0.0
Time: 26.5s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{1 \cdot \frac{1}{x - 1}}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right)}{\left(\frac{x}{1 + x} \cdot \frac{x}{1 + x} - \frac{x}{1 + x} \cdot \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\frac{1 \cdot \frac{1}{x - 1}}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right)}{\left(\frac{x}{1 + x} \cdot \frac{x}{1 + x} - \frac{x}{1 + x} \cdot \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}
double f(double x) {
        double r5828432 = 1.0;
        double r5828433 = x;
        double r5828434 = r5828433 - r5828432;
        double r5828435 = r5828432 / r5828434;
        double r5828436 = r5828433 + r5828432;
        double r5828437 = r5828433 / r5828436;
        double r5828438 = r5828435 + r5828437;
        return r5828438;
}
↓
double f(double x) {
        double r5828439 = 1.0;
        double r5828440 = x;
        double r5828441 = r5828440 - r5828439;
        double r5828442 = r5828439 / r5828441;
        double r5828443 = r5828439 * r5828442;
        double r5828444 = r5828443 / r5828441;
        double r5828445 = r5828444 * r5828442;
        double r5828446 = r5828439 + r5828440;
        double r5828447 = r5828440 / r5828446;
        double r5828448 = r5828447 * r5828447;
        double r5828449 = r5828447 * r5828448;
        double r5828450 = r5828445 + r5828449;
        double r5828451 = r5828447 * r5828442;
        double r5828452 = r5828448 - r5828451;
        double r5828453 = r5828442 * r5828442;
        double r5828454 = r5828452 + r5828453;
        double r5828455 = r5828450 / r5828454;
        return r5828455;
}

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

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))