Average Error: 0.3 → 0.0
Time: 2.7s
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 r118846 = x;
        double r118847 = log(r118846);
        double r118848 = log(r118847);
        double r118849 = r118847 - r118848;
        return r118849;
}
↓
double f(double x) {
        double r118850 = x;
        double r118851 = log(r118850);
        double r118852 = r118850 / r118851;
        double r118853 = log(r118852);
        return r118853;
}

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 2020100 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))