Average Error: 0.0 → 0.0
Time: 25.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{{\left(\frac{1}{x - 1}\right)}^{2} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{{\left(\frac{1}{x - 1}\right)}^{2} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}
double f(double x) {
        double r83736 = 1.0;
        double r83737 = x;
        double r83738 = r83737 - r83736;
        double r83739 = r83736 / r83738;
        double r83740 = r83737 + r83736;
        double r83741 = r83737 / r83740;
        double r83742 = r83739 + r83741;
        return r83742;
}
↓
double f(double x) {
        double r83743 = 1.0;
        double r83744 = x;
        double r83745 = r83744 - r83743;
        double r83746 = r83743 / r83745;
        double r83747 = 3.0;
        double r83748 = pow(r83746, r83747);
        double r83749 = r83744 + r83743;
        double r83750 = r83744 / r83749;
        double r83751 = pow(r83750, r83747);
        double r83752 = r83748 + r83751;
        double r83753 = 2.0;
        double r83754 = pow(r83746, r83753);
        double r83755 = r83750 - r83746;
        double r83756 = r83750 * r83755;
        double r83757 = r83754 + r83756;
        double r83758 = r83752 / r83757;
        return r83758;
}

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

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{\mathsf{fma}\left(\frac{1}{x - 1}, \frac{1}{x - 1}, \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)\right)}}\]
  5. Using strategy rm

  6. Applied fma-udef0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{\frac{1}{x - 1} \cdot \frac{1}{x - 1} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}}\]

  7. Simplified0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\color{blue}{{\left(\frac{1}{x - 1}\right)}^{\left(1 + 1\right)}} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}\]

  8. Final simplification0.0

    \[\leadsto \frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{{\left(\frac{1}{x - 1}\right)}^{2} + \frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right)}\]

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))