Average Error: 0.3 → 0.0
Time: 10.1s
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 r2517706 = x;
        double r2517707 = log(r2517706);
        double r2517708 = log(r2517707);
        double r2517709 = r2517707 - r2517708;
        return r2517709;
}
↓
double f(double x) {
        double r2517710 = x;
        double r2517711 = log(r2517710);
        double r2517712 = r2517710 / r2517711;
        double r2517713 = log(r2517712);
        return r2517713;
}

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 2019170 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))