Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{1}{\frac{x + 1}{x}}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x \cdot x - 1 \cdot 1} \cdot \left(x + 1\right) + \frac{1}{\frac{x + 1}{x}}
double f(double x) {
        double r5091792 = 1.0;
        double r5091793 = x;
        double r5091794 = r5091793 - r5091792;
        double r5091795 = r5091792 / r5091794;
        double r5091796 = r5091793 + r5091792;
        double r5091797 = r5091793 / r5091796;
        double r5091798 = r5091795 + r5091797;
        return r5091798;
}
↓
double f(double x) {
        double r5091799 = 1.0;
        double r5091800 = x;
        double r5091801 = r5091800 * r5091800;
        double r5091802 = r5091799 * r5091799;
        double r5091803 = r5091801 - r5091802;
        double r5091804 = r5091799 / r5091803;
        double r5091805 = r5091800 + r5091799;
        double r5091806 = r5091804 * r5091805;
        double r5091807 = 1.0;
        double r5091808 = r5091805 / r5091800;
        double r5091809 = r5091807 / r5091808;
        double r5091810 = r5091806 + r5091809;
        return r5091810;
}

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. Using strategy rm

  5. Applied flip--0.0

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

  6. Applied associate-/r/0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))