Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}
double f(double x) {
        double r132911 = 1.0;
        double r132912 = x;
        double r132913 = r132912 - r132911;
        double r132914 = r132911 / r132913;
        double r132915 = r132912 + r132911;
        double r132916 = r132912 / r132915;
        double r132917 = r132914 + r132916;
        return r132917;
}
↓
double f(double x) {
        double r132918 = 1.0;
        double r132919 = x;
        double r132920 = r132919 * r132919;
        double r132921 = r132918 * r132918;
        double r132922 = r132920 - r132921;
        double r132923 = r132918 / r132922;
        double r132924 = r132919 + r132918;
        double r132925 = r132923 * r132924;
        double r132926 = r132919 / r132924;
        double r132927 = r132925 + r132926;
        return r132927;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))