Average Error: 0.0 → 0.0
Time: 12.1s
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 r6483453 = 1.0;
        double r6483454 = x;
        double r6483455 = r6483454 - r6483453;
        double r6483456 = r6483453 / r6483455;
        double r6483457 = r6483454 + r6483453;
        double r6483458 = r6483454 / r6483457;
        double r6483459 = r6483456 + r6483458;
        return r6483459;
}
↓
double f(double x) {
        double r6483460 = x;
        double r6483461 = 1.0;
        double r6483462 = r6483461 + r6483460;
        double r6483463 = r6483460 / r6483462;
        double r6483464 = r6483463 * r6483463;
        double r6483465 = r6483463 * r6483464;
        double r6483466 = r6483460 - r6483461;
        double r6483467 = r6483461 / r6483466;
        double r6483468 = r6483467 / r6483466;
        double r6483469 = r6483467 * r6483468;
        double r6483470 = r6483465 + r6483469;
        double r6483471 = r6483463 - r6483467;
        double r6483472 = r6483463 * r6483471;
        double r6483473 = r6483472 + r6483468;
        double r6483474 = r6483470 / r6483473;
        return r6483474;
}

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 2019162 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))