Should you attempt to rescue your dog if they fall through ice into deep water?

Where I live, the winters are not typically cold enough to freeze lakes and canals, but this winter it's been a bit colder than usual so some large bodies of water have completely frozen over. However, the air hasn't stayed cold long enough for the ice to become sufficiently thick to allow people to safely walk or skate on it. Under these circumstances, it's not advised for people or dogs to walk on the ice, due to serious risk of drowning if the ice breaks.

I was on a walk recently and my dog walked on a frozen canal for a few seconds (I quickly put a stop to it). Luckily the ice didn't crack at all, so no harm done. But it got me thinking. What if the ice did break and my dog got trapped in a deep canal or lake? Should I attempt to rescue her, risking my own life, or helplessly watch as they potentially drown right in front of me?

My heart says attempt a rescue, but my brain says don't risk it.

I've talked to a couple people about this and opinion is mixed. Of course dogs shouldn't be allowed to get themselves into such dangerous situations in the first place, but suppose it happened and your dog fell through the ice, and there was no life ring or any other rescue equipment. What would you do?