Average Error: 0.0 → 0.0
Time: 17.5s
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 r105943 = 1.0;
        double r105944 = x;
        double r105945 = r105944 - r105943;
        double r105946 = r105943 / r105945;
        double r105947 = r105944 + r105943;
        double r105948 = r105944 / r105947;
        double r105949 = r105946 + r105948;
        return r105949;
}
↓
double f(double x) {
        double r105950 = 1.0;
        double r105951 = x;
        double r105952 = r105951 - r105950;
        double r105953 = r105950 / r105952;
        double r105954 = exp(r105953);
        double r105955 = log(r105954);
        double r105956 = r105951 + r105950;
        double r105957 = r105951 / r105956;
        double r105958 = r105955 + r105957;
        return r105958;
}

Error

Bits error versus x

Try it out

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 2019235 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))