Average Error: 0.3 → 0.0
Time: 12.7s
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 r2454913 = x;
        double r2454914 = log(r2454913);
        double r2454915 = log(r2454914);
        double r2454916 = r2454914 - r2454915;
        return r2454916;
}
↓
double f(double x) {
        double r2454917 = x;
        double r2454918 = log(r2454917);
        double r2454919 = r2454917 / r2454918;
        double r2454920 = log(r2454919);
        return r2454920;
}

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 2019142 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))