Average Error: 0.3 → 0.0
Time: 6.4s
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 r1047623 = x;
        double r1047624 = log(r1047623);
        double r1047625 = log(r1047624);
        double r1047626 = r1047624 - r1047625;
        return r1047626;
}
↓
double f(double x) {
        double r1047627 = x;
        double r1047628 = log(r1047627);
        double r1047629 = r1047627 / r1047628;
        double r1047630 = log(r1047629);
        return r1047630;
}

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 2019156 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))