Average Error: 0.3 → 0.0
Time: 3.4s
Precision: binary64
\[\log x - \log \log x\]
↓
\[-\log \left(\frac{\log x}{x}\right)\]
\log x - \log \log x
↓
-\log \left(\frac{\log x}{x}\right)
(FPCore (x) :precision binary64 (- (log x) (log (log x))))
↓
(FPCore (x) :precision binary64 (- (log (/ (log x) x))))
double code(double x) {
	return log(x) - log(log(x));
}
↓
double code(double x) {
	return -log(log(x) / x);
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\log x - \log \log x\]
  2. Using strategy rm

  3. Applied diff-log_binary640.0

    \[\leadsto \color{blue}{\log \left(\frac{x}{\log x}\right)}\]
  4. Using strategy rm

  5. Applied clear-num_binary640.0

    \[\leadsto \log \color{blue}{\left(\frac{1}{\frac{\log x}{x}}\right)}\]
  6. Using strategy rm

  7. Applied log-rec_binary640.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2020273 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))