Average Error: 0.3 → 0.0
Time: 7.9s
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 r1311367 = x;
        double r1311368 = log(r1311367);
        double r1311369 = log(r1311368);
        double r1311370 = r1311368 - r1311369;
        return r1311370;
}
↓
double f(double x) {
        double r1311371 = x;
        double r1311372 = log(r1311371);
        double r1311373 = r1311371 / r1311372;
        double r1311374 = log(r1311373);
        return r1311374;
}

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 2019153 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))