Average Error: 0.2 → 0.0
Time: 9.7s
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 r21691 = x;
        double r21692 = log(r21691);
        double r21693 = log(r21692);
        double r21694 = r21692 - r21693;
        return r21694;
}
↓
double f(double x) {
        double r21695 = x;
        double r21696 = log(r21695);
        double r21697 = r21695 / r21696;
        double r21698 = log(r21697);
        return r21698;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\log x - \log \left(\log x\right)\]
  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 2019315 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))