You mean it would take the NSA 3 days given that they are able to test their solutions on my login system and my login system is able to take 1 trillion guesses per second?
If we did something simple like say SHA-256 the generated password. And compare this to the SHA-256 of a captured password.
It would take ~3 days, knowing the generation algorithm and dictionary to solve for a match.
:.:.:
Also nobody in their right mind would actually preform 1trillion HTTP post/get requests per second. They'd compare hashes locally within memory. Far faster.