Average Error: 0.0 → 0.0
Time: 4.2s
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 r81672 = 1.0;
        double r81673 = x;
        double r81674 = r81673 - r81672;
        double r81675 = r81672 / r81674;
        double r81676 = r81673 + r81672;
        double r81677 = r81673 / r81676;
        double r81678 = r81675 + r81677;
        return r81678;
}
↓
double f(double x) {
        double r81679 = 1.0;
        double r81680 = x;
        double r81681 = r81680 - r81679;
        double r81682 = r81679 / r81681;
        double r81683 = 3.0;
        double r81684 = pow(r81682, r81683);
        double r81685 = r81680 + r81679;
        double r81686 = r81680 / r81685;
        double r81687 = pow(r81686, r81683);
        double r81688 = r81684 + r81687;
        double r81689 = r81682 * r81682;
        double r81690 = r81686 - r81682;
        double r81691 = r81686 * r81690;
        double r81692 = r81689 + r81691;
        double r81693 = r81688 / r81692;
        return r81693;
}

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 2020045 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))