Average Error: 0.3 → 0.0
Time: 11.7s
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 r6219730 = x;
        double r6219731 = log(r6219730);
        double r6219732 = log(r6219731);
        double r6219733 = r6219731 - r6219732;
        return r6219733;
}
↓
double f(double x) {
        double r6219734 = x;
        double r6219735 = log(r6219734);
        double r6219736 = r6219734 / r6219735;
        double r6219737 = log(r6219736);
        return r6219737;
}

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 diff-log0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019120 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))