Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\log \left(e^{\frac{1}{x - 1} + \frac{x}{1 + x}}\right)\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\log \left(e^{\frac{1}{x - 1} + \frac{x}{1 + x}}\right)
double f(double x) {
        double r6072516 = 1.0;
        double r6072517 = x;
        double r6072518 = r6072517 - r6072516;
        double r6072519 = r6072516 / r6072518;
        double r6072520 = r6072517 + r6072516;
        double r6072521 = r6072517 / r6072520;
        double r6072522 = r6072519 + r6072521;
        return r6072522;
}
↓
double f(double x) {
        double r6072523 = 1.0;
        double r6072524 = x;
        double r6072525 = r6072524 - r6072523;
        double r6072526 = r6072523 / r6072525;
        double r6072527 = r6072523 + r6072524;
        double r6072528 = r6072524 / r6072527;
        double r6072529 = r6072526 + r6072528;
        double r6072530 = exp(r6072529);
        double r6072531 = log(r6072530);
        return r6072531;
}

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

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

  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

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1.0 (- x 1.0)) (/ x (+ x 1.0))))