Average Error: 0.0 → 0.0
Time: 7.7s
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 r92519 = 1.0;
        double r92520 = x;
        double r92521 = r92520 - r92519;
        double r92522 = r92519 / r92521;
        double r92523 = r92520 + r92519;
        double r92524 = r92520 / r92523;
        double r92525 = r92522 + r92524;
        return r92525;
}
↓
double f(double x) {
        double r92526 = 1.0;
        double r92527 = x;
        double r92528 = r92527 - r92526;
        double r92529 = r92526 / r92528;
        double r92530 = 3.0;
        double r92531 = pow(r92529, r92530);
        double r92532 = r92527 + r92526;
        double r92533 = r92527 / r92532;
        double r92534 = pow(r92533, r92530);
        double r92535 = r92531 + r92534;
        double r92536 = r92529 * r92529;
        double r92537 = r92533 - r92529;
        double r92538 = r92533 * r92537;
        double r92539 = r92536 + r92538;
        double r92540 = r92535 / r92539;
        return r92540;
}

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 2019347 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))