Average Error: 0.3 → 0.0
Time: 10.7s
Precision: 64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{x}{\log x}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(\frac{x}{\log x}\right)
double f(double x) {
        double r4353806 = x;
        double r4353807 = log(r4353806);
        double r4353808 = log(r4353807);
        double r4353809 = r4353807 - r4353808;
        return r4353809;
}
↓
double f(double x) {
        double r4353810 = x;
        double r4353811 = log(r4353810);
        double r4353812 = r4353810 / r4353811;
        double r4353813 = log(r4353812);
        return r4353813;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\log x - \log \left(\log x\right)\]
  2. Using strategy rm

  3. Applied add-log-exp0.3

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

  4. Simplified0.0

    \[\leadsto \log \color{blue}{\left(\frac{x}{\log x}\right)}\]

  5. Final simplification0.0

    \[\leadsto \log \left(\frac{x}{\log x}\right)\]

Reproduce

herbie shell --seed 2019139 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))