Average Error: 0.3 → 0.0
Time: 9.7s
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 r3624078 = x;
        double r3624079 = log(r3624078);
        double r3624080 = log(r3624079);
        double r3624081 = r3624079 - r3624080;
        return r3624081;
}
↓
double f(double x) {
        double r3624082 = x;
        double r3624083 = log(r3624082);
        double r3624084 = r3624082 / r3624083;
        double r3624085 = log(r3624084);
        return r3624085;
}

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 2019172 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))