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 r114678 = x;
        double r114679 = log(r114678);
        double r114680 = log(r114679);
        double r114681 = r114679 - r114680;
        return r114681;
}
↓
double f(double x) {
        double r114682 = x;
        double r114683 = log(r114682);
        double r114684 = r114682 / r114683;
        double r114685 = log(r114684);
        return r114685;
}

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 2020089 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))