Average Error: 0.0 → 0.0
Time: 3.0s
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 r114743 = 1.0;
        double r114744 = x;
        double r114745 = r114744 - r114743;
        double r114746 = r114743 / r114745;
        double r114747 = r114744 + r114743;
        double r114748 = r114744 / r114747;
        double r114749 = r114746 + r114748;
        return r114749;
}
↓
double f(double x) {
        double r114750 = 1.0;
        double r114751 = x;
        double r114752 = r114751 - r114750;
        double r114753 = r114750 / r114752;
        double r114754 = r114751 + r114750;
        double r114755 = r114751 / r114754;
        double r114756 = r114753 + r114755;
        double r114757 = exp(r114756);
        double r114758 = log(r114757);
        return r114758;
}

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 2020056 
(FPCore (x)
  :name "Asymptote B"
  :precision binary64
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))