Average Error: 0.3 → 0.0
Time: 8.2s
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 r1331560 = x;
        double r1331561 = log(r1331560);
        double r1331562 = log(r1331561);
        double r1331563 = r1331561 - r1331562;
        return r1331563;
}
↓
double f(double x) {
        double r1331564 = x;
        double r1331565 = log(r1331564);
        double r1331566 = r1331564 / r1331565;
        double r1331567 = log(r1331566);
        return r1331567;
}

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 2019153 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))