Average Error: 0.3 → 0.0
Time: 13.6s
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 r6837631 = x;
        double r6837632 = log(r6837631);
        double r6837633 = log(r6837632);
        double r6837634 = r6837632 - r6837633;
        return r6837634;
}
↓
double f(double x) {
        double r6837635 = x;
        double r6837636 = log(r6837635);
        double r6837637 = r6837635 / r6837636;
        double r6837638 = log(r6837637);
        return r6837638;
}

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 2019128 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))