Average Error: 0.3 → 0.0
Time: 6.0s
Precision: 64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(x \cdot \frac{1}{\log x}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(x \cdot \frac{1}{\log x}\right)
double f(double x) {
        double r107834 = x;
        double r107835 = log(r107834);
        double r107836 = log(r107835);
        double r107837 = r107835 - r107836;
        return r107837;
}
↓
double f(double x) {
        double r107838 = x;
        double r107839 = 1.0;
        double r107840 = log(r107838);
        double r107841 = r107839 / r107840;
        double r107842 = r107838 * r107841;
        double r107843 = log(r107842);
        return r107843;
}

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. Using strategy rm

  5. Applied div-inv0.0

    \[\leadsto \log \color{blue}{\left(x \cdot \frac{1}{\log x}\right)}\]

  6. Final simplification0.0

    \[\leadsto \log \left(x \cdot \frac{1}{\log x}\right)\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))