Average Error: 0.0 → 0.0
Time: 33.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\frac{x}{1 + x} \cdot \left(\frac{x}{1 + x} \cdot \frac{x}{1 + x}\right) + \frac{\frac{1}{x - 1}}{\left(x - 1\right) \cdot \left(x - 1\right)}}{\left(\frac{x}{1 + x} - \frac{1}{x - 1}\right) \cdot \frac{x}{1 + x} + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}\]
\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{\frac{1}{x - 1}}{\left(x - 1\right) \cdot \left(x - 1\right)}}{\left(\frac{x}{1 + x} - \frac{1}{x - 1}\right) \cdot \frac{x}{1 + x} + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}
double f(double x) {
        double r4573642 = 1.0;
        double r4573643 = x;
        double r4573644 = r4573643 - r4573642;
        double r4573645 = r4573642 / r4573644;
        double r4573646 = r4573643 + r4573642;
        double r4573647 = r4573643 / r4573646;
        double r4573648 = r4573645 + r4573647;
        return r4573648;
}
↓
double f(double x) {
        double r4573649 = x;
        double r4573650 = 1.0;
        double r4573651 = r4573650 + r4573649;
        double r4573652 = r4573649 / r4573651;
        double r4573653 = r4573652 * r4573652;
        double r4573654 = r4573652 * r4573653;
        double r4573655 = r4573649 - r4573650;
        double r4573656 = r4573650 / r4573655;
        double r4573657 = r4573655 * r4573655;
        double r4573658 = r4573656 / r4573657;
        double r4573659 = r4573654 + r4573658;
        double r4573660 = r4573652 - r4573656;
        double r4573661 = r4573660 * r4573652;
        double r4573662 = r4573656 * r4573656;
        double r4573663 = r4573661 + r4573662;
        double r4573664 = r4573659 / r4573663;
        return r4573664;
}

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

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))