Average Error: 0.3 → 0.0
Time: 6.3s
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 r1419576 = x;
        double r1419577 = log(r1419576);
        double r1419578 = log(r1419577);
        double r1419579 = r1419577 - r1419578;
        return r1419579;
}
↓
double f(double x) {
        double r1419580 = x;
        double r1419581 = log(r1419580);
        double r1419582 = r1419580 / r1419581;
        double r1419583 = log(r1419582);
        return r1419583;
}

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 2019154 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))