Average Error: 0.3 → 0.0
Time: 8.5s
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 r4057951 = x;
        double r4057952 = log(r4057951);
        double r4057953 = log(r4057952);
        double r4057954 = r4057952 - r4057953;
        return r4057954;
}
↓
double f(double x) {
        double r4057955 = x;
        double r4057956 = log(r4057955);
        double r4057957 = r4057955 / r4057956;
        double r4057958 = log(r4057957);
        return r4057958;
}

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 2019158 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))