Average Error: 0.3 → 0.0
Time: 7.2s
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 r4243511 = x;
        double r4243512 = log(r4243511);
        double r4243513 = log(r4243512);
        double r4243514 = r4243512 - r4243513;
        return r4243514;
}
↓
double f(double x) {
        double r4243515 = x;
        double r4243516 = log(r4243515);
        double r4243517 = r4243515 / r4243516;
        double r4243518 = log(r4243517);
        return r4243518;
}

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 add-log-exp0.3

    \[\leadsto \color{blue}{\log \left(e^{\log x - \log \left(\log x\right)}\right)}\]

  4. Simplified0.0

    \[\leadsto \log \color{blue}{\left(\frac{x}{\log x}\right)}\]

  5. Final simplification0.0

    \[\leadsto \log \left(\frac{x}{\log x}\right)\]

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))