Average Error: 0.0 → 0.0
Time: 8.0s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\left(\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right)\right) \cdot \left(\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right)\right) - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right) - \frac{x}{x + 1}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\left(\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right)\right) \cdot \left(\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right)\right) - \frac{x}{x + 1} \cdot \frac{x}{x + 1}}{\frac{1}{-1 + x \cdot x} \cdot \left(x + 1\right) - \frac{x}{x + 1}}
double f(double x) {
        double r4717870 = 1.0;
        double r4717871 = x;
        double r4717872 = r4717871 - r4717870;
        double r4717873 = r4717870 / r4717872;
        double r4717874 = r4717871 + r4717870;
        double r4717875 = r4717871 / r4717874;
        double r4717876 = r4717873 + r4717875;
        return r4717876;
}
↓
double f(double x) {
        double r4717877 = 1.0;
        double r4717878 = -1.0;
        double r4717879 = x;
        double r4717880 = r4717879 * r4717879;
        double r4717881 = r4717878 + r4717880;
        double r4717882 = r4717877 / r4717881;
        double r4717883 = r4717879 + r4717877;
        double r4717884 = r4717882 * r4717883;
        double r4717885 = r4717884 * r4717884;
        double r4717886 = r4717879 / r4717883;
        double r4717887 = r4717886 * r4717886;
        double r4717888 = r4717885 - r4717887;
        double r4717889 = r4717884 - r4717886;
        double r4717890 = r4717888 / r4717889;
        return r4717890;
}

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 flip--0.0

    \[\leadsto \frac{1}{\color{blue}{\frac{x \cdot x - 1 \cdot 1}{x + 1}}} + \frac{x}{x + 1}\]

  4. Applied associate-/r/0.0

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

  5. Simplified0.0

    \[\leadsto \color{blue}{\frac{1}{x \cdot x + -1}} \cdot \left(x + 1\right) + \frac{x}{x + 1}\]
  6. Using strategy rm

  7. Applied flip-+0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))