Average Error: 0.3 → 0.0
Time: 8.5s
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 r3451328 = x;
        double r3451329 = log(r3451328);
        double r3451330 = log(r3451329);
        double r3451331 = r3451329 - r3451330;
        return r3451331;
}
↓
double f(double x) {
        double r3451332 = x;
        double r3451333 = log(r3451332);
        double r3451334 = r3451332 / r3451333;
        double r3451335 = log(r3451334);
        return r3451335;
}

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 2019162 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))