Average Error: 0.3 → 0.0
Time: 12.8s
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 r10049444 = x;
        double r10049445 = log(r10049444);
        double r10049446 = log(r10049445);
        double r10049447 = r10049445 - r10049446;
        return r10049447;
}
↓
double f(double x) {
        double r10049448 = x;
        double r10049449 = log(r10049448);
        double r10049450 = r10049448 / r10049449;
        double r10049451 = log(r10049450);
        return r10049451;
}

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 2019173 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))