Average Error: 0.3 → 0.0
Time: 9.1s
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 r2936089 = x;
        double r2936090 = log(r2936089);
        double r2936091 = log(r2936090);
        double r2936092 = r2936090 - r2936091;
        return r2936092;
}
↓
double f(double x) {
        double r2936093 = x;
        double r2936094 = log(r2936093);
        double r2936095 = r2936093 / r2936094;
        double r2936096 = log(r2936095);
        return r2936096;
}

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 2019164 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))