Average Error: 0.3 → 0.0
Time: 12.2s
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 r12593150 = x;
        double r12593151 = log(r12593150);
        double r12593152 = log(r12593151);
        double r12593153 = r12593151 - r12593152;
        return r12593153;
}
↓
double f(double x) {
        double r12593154 = x;
        double r12593155 = log(r12593154);
        double r12593156 = r12593154 / r12593155;
        double r12593157 = log(r12593156);
        return r12593157;
}

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 2019173 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))