Average Error: 0.3 → 0.0
Time: 8.0s
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 r3119703 = x;
        double r3119704 = log(r3119703);
        double r3119705 = log(r3119704);
        double r3119706 = r3119704 - r3119705;
        return r3119706;
}
↓
double f(double x) {
        double r3119707 = x;
        double r3119708 = log(r3119707);
        double r3119709 = r3119707 / r3119708;
        double r3119710 = log(r3119709);
        return r3119710;
}

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 2019165 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))