Octane provides one thing: resistance to knock. Knock is caused by pre-ignition of the fuel due to high compression which is bad for performance and the health of your engine. If you're putting low octane in your M3's engine to save a few bucks you're in the wrong car and you are damaging your engine and you may find repairs costing you more than the money you've saved on gas over time.
These cars cost $70k+ because they are designed by the world's top engineers with years of R&D put into their design. The world's lightest V8 costs a lot to design and maintain and you pay for it when you buy one. Why would you ignore the manufacturer's warning on octane?
If you're eating ramen noodles to afford high octane gas for your M3 it's time to trade-in for a Civic or something more conducive to saving money on gas.