Average Error: 0.3 → 0.0
Time: 8.6s
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 r3178380 = x;
        double r3178381 = log(r3178380);
        double r3178382 = log(r3178381);
        double r3178383 = r3178381 - r3178382;
        return r3178383;
}
↓
double f(double x) {
        double r3178384 = x;
        double r3178385 = log(r3178384);
        double r3178386 = r3178384 / r3178385;
        double r3178387 = log(r3178386);
        return r3178387;
}

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 2019164 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))