Average Error: 0.3 → 0.0
Time: 6.7s
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 r14181445 = x;
        double r14181446 = log(r14181445);
        double r14181447 = log(r14181446);
        double r14181448 = r14181446 - r14181447;
        return r14181448;
}
↓
double f(double x) {
        double r14181449 = x;
        double r14181450 = log(r14181449);
        double r14181451 = r14181449 / r14181450;
        double r14181452 = log(r14181451);
        return r14181452;
}

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 2019119 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))