Average Error: 0.3 → 0.0
Time: 3.2s
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 r108662 = x;
        double r108663 = log(r108662);
        double r108664 = log(r108663);
        double r108665 = r108663 - r108664;
        return r108665;
}
↓
double f(double x) {
        double r108666 = x;
        double r108667 = log(r108666);
        double r108668 = r108666 / r108667;
        double r108669 = log(r108668);
        return r108669;
}

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 2020034 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))