Average Error: 0.0 → 0.0
Time: 6.2s
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 r2183149 = 1.0;
        double r2183150 = x;
        double r2183151 = r2183150 - r2183149;
        double r2183152 = r2183149 / r2183151;
        double r2183153 = r2183150 + r2183149;
        double r2183154 = r2183150 / r2183153;
        double r2183155 = r2183152 + r2183154;
        return r2183155;
}
↓
double f(double x) {
        double r2183156 = 1.0;
        double r2183157 = x;
        double r2183158 = r2183157 - r2183156;
        double r2183159 = r2183156 / r2183158;
        double r2183160 = exp(r2183159);
        double r2183161 = log(r2183160);
        double r2183162 = r2183157 + r2183156;
        double r2183163 = r2183157 / r2183162;
        double r2183164 = r2183161 + r2183163;
        return r2183164;
}

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 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))