Average Error: 0.3 → 0.0
Time: 17.7s
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 r2988184 = x;
        double r2988185 = log(r2988184);
        double r2988186 = log(r2988185);
        double r2988187 = r2988185 - r2988186;
        return r2988187;
}
↓
double f(double x) {
        double r2988188 = x;
        double r2988189 = log(r2988188);
        double r2988190 = r2988188 / r2988189;
        double r2988191 = log(r2988190);
        return r2988191;
}

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 2019141 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))