Average Error: 0.0 → 0.0
Time: 40.4s
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 r3428156 = 1.0;
        double r3428157 = x;
        double r3428158 = r3428157 - r3428156;
        double r3428159 = r3428156 / r3428158;
        double r3428160 = r3428157 + r3428156;
        double r3428161 = r3428157 / r3428160;
        double r3428162 = r3428159 + r3428161;
        return r3428162;
}
↓
double f(double x) {
        double r3428163 = 1.0;
        double r3428164 = x;
        double r3428165 = r3428164 - r3428163;
        double r3428166 = r3428163 / r3428165;
        double r3428167 = exp(r3428166);
        double r3428168 = log(r3428167);
        double r3428169 = r3428164 + r3428163;
        double r3428170 = r3428164 / r3428169;
        double r3428171 = r3428168 + r3428170;
        return r3428171;
}

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 2019146 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))