Average Error: 0.3 → 0.0
Time: 2.8s
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 r83997 = x;
        double r83998 = log(r83997);
        double r83999 = log(r83998);
        double r84000 = r83998 - r83999;
        return r84000;
}
↓
double f(double x) {
        double r84001 = x;
        double r84002 = log(r84001);
        double r84003 = r84001 / r84002;
        double r84004 = log(r84003);
        return r84004;
}

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 2020035 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))