Average Error: 0.2 → 0.0
Time: 9.7s
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 r3095834 = x;
        double r3095835 = log(r3095834);
        double r3095836 = log(r3095835);
        double r3095837 = r3095835 - r3095836;
        return r3095837;
}
↓
double f(double x) {
        double r3095838 = x;
        double r3095839 = log(r3095838);
        double r3095840 = r3095838 / r3095839;
        double r3095841 = log(r3095840);
        return r3095841;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\log x - \log \left(\log x\right)\]
  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 2019171 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))