Average Error: 0.0 → 0.0
Time: 20.4s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \mathsf{expm1}\left(\left(\mathsf{log1p}\left(\left(\frac{x}{x + 1}\right)\right)\right)\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \mathsf{expm1}\left(\left(\mathsf{log1p}\left(\left(\frac{x}{x + 1}\right)\right)\right)\right)
double f(double x) {
        double r13780827 = 1.0;
        double r13780828 = x;
        double r13780829 = r13780828 - r13780827;
        double r13780830 = r13780827 / r13780829;
        double r13780831 = r13780828 + r13780827;
        double r13780832 = r13780828 / r13780831;
        double r13780833 = r13780830 + r13780832;
        return r13780833;
}
↓
double f(double x) {
        double r13780834 = 1.0;
        double r13780835 = x;
        double r13780836 = r13780835 - r13780834;
        double r13780837 = r13780834 / r13780836;
        double r13780838 = r13780835 + r13780834;
        double r13780839 = r13780835 / r13780838;
        double r13780840 = log1p(r13780839);
        double r13780841 = expm1(r13780840);
        double r13780842 = r13780837 + r13780841;
        return r13780842;
}

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 expm1-log1p-u0.0

    \[\leadsto \frac{1}{x - 1} + \color{blue}{\mathsf{expm1}\left(\left(\mathsf{log1p}\left(\left(\frac{x}{x + 1}\right)\right)\right)\right)}\]

  4. Final simplification0.0

    \[\leadsto \frac{1}{x - 1} + \mathsf{expm1}\left(\left(\mathsf{log1p}\left(\left(\frac{x}{x + 1}\right)\right)\right)\right)\]

Reproduce

herbie shell --seed 2019120 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))