Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{x - 1} + \frac{x}{x + 1}}\right)
double f(double x) {
        double r116347 = 1.0;
        double r116348 = x;
        double r116349 = r116348 - r116347;
        double r116350 = r116347 / r116349;
        double r116351 = r116348 + r116347;
        double r116352 = r116348 / r116351;
        double r116353 = r116350 + r116352;
        return r116353;
}
↓
double f(double x) {
        double r116354 = 1.0;
        double r116355 = x;
        double r116356 = r116355 - r116354;
        double r116357 = r116354 / r116356;
        double r116358 = r116355 + r116354;
        double r116359 = r116355 / r116358;
        double r116360 = r116357 + r116359;
        double r116361 = exp(r116360);
        double r116362 = log(r116361);
        return r116362;
}

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. Applied add-log-exp0.0

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

  5. Applied sum-log0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))