Average Error: 0.3 → 0.0
Time: 11.5s
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 r3159517 = x;
        double r3159518 = log(r3159517);
        double r3159519 = log(r3159518);
        double r3159520 = r3159518 - r3159519;
        return r3159520;
}
↓
double f(double x) {
        double r3159521 = x;
        double r3159522 = log(r3159521);
        double r3159523 = r3159521 / r3159522;
        double r3159524 = log(r3159523);
        return r3159524;
}

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 2019169 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))