Average Error: 0.2 → 0.0
Time: 9.0s
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 r3333896 = x;
        double r3333897 = log(r3333896);
        double r3333898 = log(r3333897);
        double r3333899 = r3333897 - r3333898;
        return r3333899;
}
↓
double f(double x) {
        double r3333900 = x;
        double r3333901 = log(r3333900);
        double r3333902 = r3333900 / r3333901;
        double r3333903 = log(r3333902);
        return r3333903;
}

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 2019163 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))