Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{{\left(\frac{1}{x - 1}\right)}^{3} + {\left(\frac{x}{x + 1}\right)}^{3}}{\frac{x}{x + 1} \cdot \left(\frac{x}{x + 1} - \frac{1}{x - 1}\right) + \frac{1}{x - 1} \cdot \frac{1}{x - 1}}
double f(double x) {
        double r133927 = 1.0;
        double r133928 = x;
        double r133929 = r133928 - r133927;
        double r133930 = r133927 / r133929;
        double r133931 = r133928 + r133927;
        double r133932 = r133928 / r133931;
        double r133933 = r133930 + r133932;
        return r133933;
}
↓
double f(double x) {
        double r133934 = 1.0;
        double r133935 = x;
        double r133936 = r133935 - r133934;
        double r133937 = r133934 / r133936;
        double r133938 = 3.0;
        double r133939 = pow(r133937, r133938);
        double r133940 = r133935 + r133934;
        double r133941 = r133935 / r133940;
        double r133942 = pow(r133941, r133938);
        double r133943 = r133939 + r133942;
        double r133944 = r133941 - r133937;
        double r133945 = r133941 * r133944;
        double r133946 = r133937 * r133937;
        double r133947 = r133945 + r133946;
        double r133948 = r133943 / r133947;
        return r133948;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020020 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))