Average Error: 0.3 → 0.0
Time: 11.2s
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 r9294117 = x;
        double r9294118 = log(r9294117);
        double r9294119 = log(r9294118);
        double r9294120 = r9294118 - r9294119;
        return r9294120;
}
↓
double f(double x) {
        double r9294121 = x;
        double r9294122 = log(r9294121);
        double r9294123 = r9294121 / r9294122;
        double r9294124 = log(r9294123);
        return r9294124;
}

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 2019107 +o rules:numerics
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))