Right, first off:
Think of Auto Shot as an ability with a cooldown. When Auto Shot fires, it checks weapon speeds and hastes, then issues a cooldown based on these factors. Any change inbetween Auto Shots are not factored in; the only time the cooldown is calculated is at moment of firing.
Basically, the cooldown for [Auto Shot x+1] is set when [Auto Shot x] fires.
This can be tested with Rapid Fire, using it right after an Auto Shot does not decrease the time until the next, but every shot after that.
Note also that this means if a haste effect fades 0.1 seconds after the Auto Shot, the haste effect is still effectively still there.
15% quiver for everything, 0 points in Improved Aspect of the Hawk vs 5 points in Improved Aspect of the Hawk.
Single proc only, no overlapping considered.
Every proc occurs at time 0. Times after just show when the next shots fire.
1.5 weapon (1.3 after quiver)
0 0
1.30 1.30
2.61 2.44
3.91 3.57
5.22 4.71
6.52 5.84
7.83 6.98
9.13 8.11
10.43 9.24
11.74 10.38
13.04 11.51
14.35 12.65
In this example, after one proc you fire 11 shots with Quick Shots in 12.65 seconds. After this time, the effect of the proc is gone, and you're back to WeaponSpeed/1.15 for both scenarios.
With this weapon, a 5/5 Quick Shots proc allows for 11 shots in 12.65 seconds. 11 shots would usually take 14.35 seconds. Average damage per shot does not change based on Quick Shots, so what we have here is a pure
(14.35-12.65)/14.35 * 100 = 11.86% Auto Shot DPS increase.
I won't bore you with listing every timestamp combination for every weapon, so I'll just do Auto Shot DPS increase per weapon. If needed, I can list them though :P
Assuming equal weapon DPS, an equal percentage increase will yield the same Auto Shot DPS increase.
1.5 weapon: 11.86%
1.6 weapon --> 1.8 weapon: 11.74%
1.9 weapon --> 2.0 weapon: 11.59%
2.1 weapon --> 2.2 weapon: 11.41%
2.3 weapon --> 2.5 weapon: 11.18%
2.6 weapon --> 3.0 weapon: 10.87%
3.1 weapon --> 3.4 weapon: 10.43%
I found this at least slightly interesting. Of course, the faster weapons will proc Quick Shots more often, but on a per proc basis, it's pretty equal, regardless of weapon speed.