Average Error: 0.3 → 0.0
Time: 7.7s
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 r1068503 = x;
        double r1068504 = log(r1068503);
        double r1068505 = log(r1068504);
        double r1068506 = r1068504 - r1068505;
        return r1068506;
}
↓
double f(double x) {
        double r1068507 = x;
        double r1068508 = log(r1068507);
        double r1068509 = r1068507 / r1068508;
        double r1068510 = log(r1068509);
        return r1068510;
}

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 2019153 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))