Average Error: 0.3 → 0.0
Time: 2.7s
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. Applied egg0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2022125 
(FPCore (x)
  :name "Jmat.Real.lambertw, estimator"
  :precision binary64
  (- (log x) (log (log x))))