I've been thinking about Improved Aspect of The Hawk as well these days. I'll give it some thought during the weekend and see what I come up with, and if what I come up with matches what other people get :P

As for the waveforms thinking... Correct me if I'm wrong, but wouldn't the best time to shoot a special be immediately after Auto Shot, not when Auto Shot is in the middle of cooling down (i.e. -1 isn't the best time to fire)?
I'm not used to thinking in waveforms, so if I'm misunderstanding something here, please interpret or poke me with a link as to where I can read up on it =)

Also, I have no idea how you'd incorporate casting time of Steady Shot, as well as the delay of Auto Shot after a special with that kind of thinking...

Edit: Oh, forgot to answer this:
If shot x procs Quick Shots (Improved Aspect of the Hawk proc), shot x+1 is the first shot to be influenced by the haste effect.

Warning: wild speculation ahead
My feelings on the best way to model that would be to use an alternating series that accomodates for the delay from previous shots. My gut reaction is that because you're using sine/cosine to model shot time (which is continuous) but are really more interested in discrete events (shots) you would use a series that is essentially a time function that accounts for the time delay on the nth shot - for this case it would be a relatively (note: heavily stressing relatively) easy task to determine shot delay. As alluded to before, at this point I can only speculate on possible methods to account for delay, since I haven't worked out the math yet. Hopefully you kind of see where I'm headed with this line of thinking, though.

Despite all the mathematical masturbation, I maintain that discrete simulation is just going to be better than a generalized model. Likewise, empirical evidence from gameplay will surpass simulation in accuracy. It's just the order of things, really. Nonetheless, it would be valuable to have a reasonable model of shot rotations that does not rely on time averaging (which, unfortunately, appears to be a nontrivial task).

As for iAotH, here are my feelings: if you want to use average time of non-proc streaks, you're using time averaging. The 10% proc rate is only a valid number for extremely large sample sizes. Given that, as I understand it, your goal is to eliminate time-averaged accounting for haste effect and replace it with a more accurate model (which I can only gather would have to be discrete), you're on the wrong foot here. I can only echo the thoughts of others: I dislike modeling iAotH as a time-averaged percent increase in haste, but I don't have an alternative model that doesn't rely on simulation. I think Glau more or less did the best work possible in terms of describing it generally - if you want more accuracy, you have to independently simulate it for yourself.

Right, but the average is 10, correct?

I certainly understand the problem of scaling the modelling problem. The only limitation I see is the limit of only two trinkets available during combat (lets pretend feign/switch doesn't exist, because then you're correct - the problem has no practical upper bound). Perhaps I was overly general in stating the requirement to calculate for all permutations of gear. Rather, calculating based on what gear the player has more or less dictates that there will only be at most 2 on chance haste effects possible (are there non-trinkets that effects ranged haste or proc from ranged attacks? I'm not sure they exist). I do realize that's a tremendous amount of work - I don't honestly expect you to implement that kind of over-arching calculation to the spreadsheet (although it sounds like accomodating iAotH is a feasible option). From a purely theoretical standpoint, however, weighting rotations for time is probably more accurate than modeling iAotH as a flat haste increase.

Thanks for indulging me in the conversation of that - I realize I occasionally get long-winded.