Average Error: 0.3 → 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 r636590 = x;
        double r636591 = log(r636590);
        double r636592 = log(r636591);
        double r636593 = r636591 - r636592;
        return r636593;
}
↓
double f(double x) {
        double r636594 = x;
        double r636595 = log(r636594);
        double r636596 = r636594 / r636595;
        double r636597 = log(r636596);
        return r636597;
}

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 2019138 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))