Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}
double f(double x) {
        double r108212 = 1.0;
        double r108213 = x;
        double r108214 = r108213 - r108212;
        double r108215 = r108212 / r108214;
        double r108216 = r108213 + r108212;
        double r108217 = r108213 / r108216;
        double r108218 = r108215 + r108217;
        return r108218;
}
↓
double f(double x) {
        double r108219 = 1.0;
        double r108220 = x;
        double r108221 = r108220 - r108219;
        double r108222 = r108219 / r108221;
        double r108223 = 1.0;
        double r108224 = r108220 + r108219;
        double r108225 = r108224 / r108220;
        double r108226 = r108223 / r108225;
        double r108227 = r108222 + r108226;
        return r108227;
}

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 clear-num0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

    \[\leadsto \frac{1}{x - 1} + \frac{1}{\frac{x + 1}{x}}\]

Reproduce

herbie shell --seed 2019195 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))