Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\frac{1}{x - 1} + \log \left(e^{\frac{x}{x + 1}}\right)
double f(double x) {
        double r90944 = 1.0;
        double r90945 = x;
        double r90946 = r90945 - r90944;
        double r90947 = r90944 / r90946;
        double r90948 = r90945 + r90944;
        double r90949 = r90945 / r90948;
        double r90950 = r90947 + r90949;
        return r90950;
}
↓
double f(double x) {
        double r90951 = 1.0;
        double r90952 = x;
        double r90953 = r90952 - r90951;
        double r90954 = r90951 / r90953;
        double r90955 = r90952 + r90951;
        double r90956 = r90952 / r90955;
        double r90957 = exp(r90956);
        double r90958 = log(r90957);
        double r90959 = r90954 + r90958;
        return r90959;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))