Average Error: 0.3 → 0.0
Time: 9.5s
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 r631232 = x;
        double r631233 = log(r631232);
        double r631234 = log(r631233);
        double r631235 = r631233 - r631234;
        return r631235;
}
↓
double f(double x) {
        double r631236 = x;
        double r631237 = log(r631236);
        double r631238 = r631236 / r631237;
        double r631239 = log(r631238);
        return r631239;
}

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 2019139 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))