Average Error: 0.3 → 0.0
Time: 12.2s
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 r3713841 = x;
        double r3713842 = log(r3713841);
        double r3713843 = log(r3713842);
        double r3713844 = r3713842 - r3713843;
        return r3713844;
}
↓
double f(double x) {
        double r3713845 = x;
        double r3713846 = log(r3713845);
        double r3713847 = r3713845 / r3713846;
        double r3713848 = log(r3713847);
        return r3713848;
}

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 2019146 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))