Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1}{x - 1}}\right) + \frac{x}{x + 1}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{x - 1}}\right) + \frac{x}{x + 1}
double f(double x) {
        double r2733853 = 1.0;
        double r2733854 = x;
        double r2733855 = r2733854 - r2733853;
        double r2733856 = r2733853 / r2733855;
        double r2733857 = r2733854 + r2733853;
        double r2733858 = r2733854 / r2733857;
        double r2733859 = r2733856 + r2733858;
        return r2733859;
}
↓
double f(double x) {
        double r2733860 = 1.0;
        double r2733861 = x;
        double r2733862 = r2733861 - r2733860;
        double r2733863 = r2733860 / r2733862;
        double r2733864 = exp(r2733863);
        double r2733865 = log(r2733864);
        double r2733866 = r2733861 + r2733860;
        double r2733867 = r2733861 / r2733866;
        double r2733868 = r2733865 + r2733867;
        return r2733868;
}

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 add-log-exp0.0

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

  4. Final simplification0.0

    \[\leadsto \log \left(e^{\frac{1}{x - 1}}\right) + \frac{x}{x + 1}\]

Reproduce

herbie shell --seed 2019153 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))