You can use these tables/equations for Hawk. Just ran my simulator with only auto shot for a million second run.
It computes auto shot delay by checking for any haste effects when a shot fires, then computing when the next shot will go off. As far as I can tell that is exactly how it works in game.
No Haste Effects
Speed Hawk Uptime
1.8 0.5175
1.9 0.4984
2 0.48
2.1 0.4619
2.2 0.4463
2.3 0.4335
2.4 0.4205
2.5 0.4081
2.6 0.394
2.7 0.3816
2.8 0.3686
2.9 0.361
3 0.3489
3.1 0.3398
3.2 0.3364
3.3 0.3264
3.4 0.3144
15% Quiver
Speed Hawk Uptime
1.565 0.5604
1.652 0.54
1.739 0.5199
1.826 0.5046
1.913 0.4867
2 0.479
2.087 0.4626
2.174 0.4523
2.261 0.4312
2.348 0.4176
2.435 0.4055
2.522 0.4009
2.609 0.387
2.696 0.3828
2.783 0.3702
2.87 0.362
2.957 0.3509
15% Quiver and Serpent's Swiftness
1.304 0.6172
1.377 0.6179
1.449 0.5901
1.522 0.5628
1.594 0.5603
1.667 0.538
1.739 0.5158
1.812 0.5041
1.884 0.4975
1.957 0.4776
2.029 0.4653
2.102 0.4514
2.174 0.4494
2.247 0.432
2.319 0.4207
2.392 0.4173
2.464 0.4072
If you plug those into excel as separate data sets and plot them it looks like this:
If you plug all those into excel, plot them and add a power trend line it looks like this:
Edit: forgot a negative sign
I would feel confident using that formula for hawk uptime calculations: y = 0.777x^-0.7197
Where X is your weapon speed after permanent hastes and Y is your hawk uptime.