Average Error: 0.3 → 0.0
Time: 14.1s
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 r5379422 = x;
        double r5379423 = log(r5379422);
        double r5379424 = log(r5379423);
        double r5379425 = r5379423 - r5379424;
        return r5379425;
}
↓
double f(double x) {
        double r5379426 = x;
        double r5379427 = log(r5379426);
        double r5379428 = r5379426 / r5379427;
        double r5379429 = log(r5379428);
        return r5379429;
}

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 2019168 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  (- (log x) (log (log x))))