Average Error: 0.0 → 0.0
Time: 42.2s
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 r4442795 = 1.0;
        double r4442796 = x;
        double r4442797 = r4442796 - r4442795;
        double r4442798 = r4442795 / r4442797;
        double r4442799 = r4442796 + r4442795;
        double r4442800 = r4442796 / r4442799;
        double r4442801 = r4442798 + r4442800;
        return r4442801;
}
↓
double f(double x) {
        double r4442802 = x;
        double r4442803 = 1.0;
        double r4442804 = r4442802 - r4442803;
        double r4442805 = r4442802 + r4442803;
        double r4442806 = r4442805 / r4442802;
        double r4442807 = r4442804 + r4442806;
        double r4442808 = r4442804 * r4442806;
        double r4442809 = r4442807 / r4442808;
        return r4442809;
}

Error

Bits error versus x

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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. Using strategy rm

  5. Applied frac-add0.0

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

  6. 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 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))