Average Error: 0.0 → 0.0
Time: 26.7s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{\left(x - 1\right) + \frac{x + 1}{x}}{\left(x - 1\right) \cdot \frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{\left(x - 1\right) + \frac{x + 1}{x}}{\left(x - 1\right) \cdot \frac{x + 1}{x}}
double f(double x) {
        double r4023230 = 1.0;
        double r4023231 = x;
        double r4023232 = r4023231 - r4023230;
        double r4023233 = r4023230 / r4023232;
        double r4023234 = r4023231 + r4023230;
        double r4023235 = r4023231 / r4023234;
        double r4023236 = r4023233 + r4023235;
        return r4023236;
}
↓
double f(double x) {
        double r4023237 = x;
        double r4023238 = 1.0;
        double r4023239 = r4023237 - r4023238;
        double r4023240 = r4023237 + r4023238;
        double r4023241 = r4023240 / r4023237;
        double r4023242 = r4023239 + r4023241;
        double r4023243 = r4023239 * r4023241;
        double r4023244 = r4023242 / r4023243;
        return r4023244;
}

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 *-un-lft-identity0.0

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

  4. Applied associate-/l*0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\frac{1}{\frac{x + 1}{x}}}\]
  5. Using strategy rm

  6. Applied frac-add0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019144 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))