Average Error: 0.0 → 0.0
Time: 8.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{1 + x} + \frac{1}{x - 1}\right)\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{x}{1 + x} + \frac{1}{x - 1}\right)\right)
double f(double x) {
        double r153573 = 1.0;
        double r153574 = x;
        double r153575 = r153574 - r153573;
        double r153576 = r153573 / r153575;
        double r153577 = r153574 + r153573;
        double r153578 = r153574 / r153577;
        double r153579 = r153576 + r153578;
        return r153579;
}
↓
double f(double x) {
        double r153580 = x;
        double r153581 = 1.0;
        double r153582 = r153581 + r153580;
        double r153583 = r153580 / r153582;
        double r153584 = r153580 - r153581;
        double r153585 = r153581 / r153584;
        double r153586 = r153583 + r153585;
        double r153587 = expm1(r153586);
        double r153588 = log1p(r153587);
        return r153588;
}

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 log1p-expm1-u0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

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