Average Error: 0.0 → 0.0
Time: 15.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}\]
double f(double x) {
        double r13738058 = 1.0;
        double r13738059 = x;
        double r13738060 = r13738059 - r13738058;
        double r13738061 = r13738058 / r13738060;
        double r13738062 = r13738059 + r13738058;
        double r13738063 = r13738059 / r13738062;
        double r13738064 = r13738061 + r13738063;
        return r13738064;
}
↓
double f(double x) {
        double r13738065 = 1.0;
        double r13738066 = x;
        double r13738067 = r13738066 * r13738066;
        double r13738068 = r13738067 - r13738065;
        double r13738069 = r13738065 / r13738068;
        double r13738070 = r13738066 + r13738065;
        double r13738071 = r13738069 * r13738070;
        double r13738072 = r13738066 / r13738070;
        double r13738073 = r13738071 + r13738072;
        return r13738073;
}


\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x \cdot x - 1} \cdot \left(x + 1\right) + \frac{x}{x + 1}

Error

Bits error versus x

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

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

Reproduce

herbie shell --seed 2019101 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))