Average Error: 0.2 → 0.0
Time: 1.0s
Precision: binary64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(x \cdot \frac{1}{\log x}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(x \cdot \frac{1}{\log x}\right)
double code(double x) {
	return ((double) (((double) log(x)) - ((double) log(((double) log(x))))));
}
↓
double code(double x) {
	return ((double) log(((double) (x * ((double) (1.0 / ((double) log(x))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\log x - \log \left(\log x\right)\]
  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 2020168 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))