Average Error: 0.3 → 0.0
Time: 10.4s
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 r88100 = x;
        double r88101 = log(r88100);
        double r88102 = log(r88101);
        double r88103 = r88101 - r88102;
        return r88103;
}
↓
double f(double x) {
        double r88104 = x;
        double r88105 = log(r88104);
        double r88106 = r88104 / r88105;
        double r88107 = log(r88106);
        return r88107;
}

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 2019174 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))