If you mean something like cos(3^^^3 * pi), then I think that one should be solveable. Maybe try induction.
EDIT: Whoops, I didn’t see the floor symbols. Nevermind me. With not-quite-so-large numbers it’s an interesting problem that might be solveable by finding digits of pi in linear time, but linear time is of limited help here.
If you mean something like cos(3^^^3 * pi), then I think that one should be solveable. Maybe try induction.EDIT: Whoops, I didn’t see the floor symbols. Nevermind me. With not-quite-so-large numbers it’s an interesting problem that might be solveable by finding digits of pi in linear time, but linear time is of limited help here.
↑ is not ^
https://en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation
I was too lazy to find the right character. Whoops, looks like I misread the comment though.