Average Error: 0.0 → 0.0
Time: 10.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{-1 + x \cdot x} \cdot \left(1 + x\right) + \frac{x}{1 + x}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{-1 + x \cdot x} \cdot \left(1 + x\right) + \frac{x}{1 + x}
double f(double x) {
        double r3854826 = 1.0;
        double r3854827 = x;
        double r3854828 = r3854827 - r3854826;
        double r3854829 = r3854826 / r3854828;
        double r3854830 = r3854827 + r3854826;
        double r3854831 = r3854827 / r3854830;
        double r3854832 = r3854829 + r3854831;
        return r3854832;
}
↓
double f(double x) {
        double r3854833 = 1.0;
        double r3854834 = -1.0;
        double r3854835 = x;
        double r3854836 = r3854835 * r3854835;
        double r3854837 = r3854834 + r3854836;
        double r3854838 = r3854833 / r3854837;
        double r3854839 = r3854833 + r3854835;
        double r3854840 = r3854838 * r3854839;
        double r3854841 = r3854835 / r3854839;
        double r3854842 = r3854840 + r3854841;
        return r3854842;
}

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

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019130 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))