Average Error: 0.3 → 0.0
Time: 15.5s
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 r2877326 = x;
        double r2877327 = log(r2877326);
        double r2877328 = log(r2877327);
        double r2877329 = r2877327 - r2877328;
        return r2877329;
}
↓
double f(double x) {
        double r2877330 = x;
        double r2877331 = log(r2877330);
        double r2877332 = r2877330 / r2877331;
        double r2877333 = log(r2877332);
        return r2877333;
}

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 2019165 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))