Average Error: 0.3 → 0.0
Time: 12.7s
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 r2903733 = x;
        double r2903734 = log(r2903733);
        double r2903735 = log(r2903734);
        double r2903736 = r2903734 - r2903735;
        return r2903736;
}
↓
double f(double x) {
        double r2903737 = x;
        double r2903738 = log(r2903737);
        double r2903739 = r2903737 / r2903738;
        double r2903740 = log(r2903739);
        return r2903740;
}

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 2019151 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))