Average Error: 0.3 → 0.0
Time: 37.8s
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 r3569504 = x;
        double r3569505 = log(r3569504);
        double r3569506 = log(r3569505);
        double r3569507 = r3569505 - r3569506;
        return r3569507;
}
↓
double f(double x) {
        double r3569508 = x;
        double r3569509 = log(r3569508);
        double r3569510 = r3569508 / r3569509;
        double r3569511 = log(r3569510);
        return r3569511;
}

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 2019200 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))