Average Error: 0.3 → 0.0
Time: 7.0s
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 r13854493 = x;
        double r13854494 = log(r13854493);
        double r13854495 = log(r13854494);
        double r13854496 = r13854494 - r13854495;
        return r13854496;
}
↓
double f(double x) {
        double r13854497 = x;
        double r13854498 = log(r13854497);
        double r13854499 = r13854497 / r13854498;
        double r13854500 = log(r13854499);
        return r13854500;
}

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 2019104 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))