91-93 octane is generally referred to as Premium or Super.
Many sport sedans and other sporty vehicles recommend or require premium to obtain the hp ratings they have, not to mention the compression ratios, etc. However, since they've been tuned/programmed that way, feeding them something other than higher octane fuels will lead to the computer dialing back the timing to adjust for the increase knock that the lower octanes will make on these type of motors. Certainly, the computer can adjust somewhat depending on what the knock sensor feeds back, but there is a limit. Some motors can adjust enough to run on lower octane, others just simply can't. That knock or ping is never good on the motor. It can lead to carbon buildup and hot spots on the motor. Plus, when the computer dials back the timing to adjust as much as it can/needs to, your hp goes down, which also could negatively affect MPG a tad. So, you have to ask is there a benefit with all of this risk?
You might be able to try midgrade or 89 octane and get by. But, you should try out a couple tanks to compare results. However, if you're buying a BMW, you should feed it premium.