Average Error: 0.3 → 0.0
Time: 1.2s
Precision: binary64
\[\log x - \log \left(\log x\right)\]
↓
\[\log \left(\frac{x}{\log x}\right)\]
\log x - \log \left(\log x\right)
↓
\log \left(\frac{x}{\log x}\right)
(FPCore (x) :precision binary64 (- (log x) (log (log x))))
↓
(FPCore (x) :precision binary64 (log (/ x (log x))))
double code(double x) {
	return ((double) (((double) log(x)) - ((double) log(((double) log(x))))));
}
↓
double code(double x) {
	return ((double) log((x / ((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 Error: 0.3 bits

    \[\log x - \log \left(\log x\right)\]
  2. Using strategy rm

  3. Applied diff-logError: 0.0 bits

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

  4. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020204 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))