Average Error: 0.0 → 0.0
Time: 7.5s
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 r2936498 = 1.0;
        double r2936499 = x;
        double r2936500 = r2936499 - r2936498;
        double r2936501 = r2936498 / r2936500;
        double r2936502 = r2936499 + r2936498;
        double r2936503 = r2936499 / r2936502;
        double r2936504 = r2936501 + r2936503;
        return r2936504;
}
↓
double f(double x) {
        double r2936505 = 1.0;
        double r2936506 = x;
        double r2936507 = r2936506 - r2936505;
        double r2936508 = r2936505 / r2936507;
        double r2936509 = exp(r2936508);
        double r2936510 = log(r2936509);
        double r2936511 = r2936506 + r2936505;
        double r2936512 = r2936506 / r2936511;
        double r2936513 = r2936510 + r2936512;
        return r2936513;
}

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))))