I just wanted to chime in on the issue of delaying chimera shot until serpent sting is about to fall off.
It seems to me (based on napkin math) that this is a DPE tradeoff that should be based on incoming energy generation rate, and thus haste and haste effects.
This is all based on the information on shot damage contained in
Simulationcraft Results
If we normalize the damage per execute and damage per resource for aimed shot to the non-careful aim value (seems to be 35% based on simcraft numbers) we get...
DPE: 44827 (54240 including piercing shots)
DPR (assuming 48.25 average cost outside careful aim): 929 (1124)
And for steady shot:
DPE: 7668 (9278 including piercing shots)
Using the quoted values for chimera shot:
DPE: 34544 (41798 including piercing shots)
DPR: 786 (950)
And wild quiver:
DPE: 7395
If we assume as a starting case a hunter with no haste on gear, 10% haste from raid buffs, 3% from pathing and 15% from improved steady shot: 1.03 * 1.1 * 1.15 = 1.3
Thus aimed shot would have a cast time of 2.23 seconds, and steady shot would have a cast time of 1.54 seconds.
This gives aimed shot an effective DPET of 20102.
Given that there is an execution time difference between aimed shot and chimera shot, we should examine what we are using the excess time for. I believe in general this will be steady shot. By rolling a partial steady shot into the comparison, we can gain a little more insight into the true comparison.
If we include the damage from wild quiver (assuming about 20% chance to proc) and the ready, aim, fire proc, we end up with:
9278 + 0.2 * 7395 + 0.6 * 0.2 * 54240 = 17265 DPE, all things considered.
if we normalize this over the time delta between aimed shot and chimera shot, you end up with 13812 damage per partial execution.
Adding this to our chimera shot values gives an equivalent combined damage per execution of 55610 and a equivalent combined damage per energy of 1511.
So, in the 0 haste from gear case, we end up with the steady shot, chimera shot combo being roughly a 2.5% dps increase, with a much better damage per energy. As haste from gear increases, the damage per second increase will grow slowly, peak, then decline (with ridiculous levels of haste) while the damage per energy declines fairly rapidly until it is lower than that of aimed shot.
Of course this must be considered in terms of the rotation used as well. I would expect that the 4pcT11 would shift the curves to the right somewhat, supporting frequent chimera shots with slightly higher levels of haste. Termination would probably also encourage frequent chimera shot usage given the usefulness of a rapid focus dump. This leads me to believe that if termination is taken, chimera shot should be used on cooldown in termination range, and as a quick focus dump if needed or to refresh serpent sting at other times, depending on haste from gear. This is of course just a guess and further analysis will need to be done to flesh it out.