There is a big misconception about how to warmup. The act of “warming up” means literally to warm up your body. Pulling a sweat. The problem is that you can go warmup in a sauna, but if you were going to jump on a bench or go all out on squats, you would probably still have better chances of getting injured. Why? Because you haven’t moved to get your muscles prepared for the coming lifting session.
So basically, unless it’s freakin’ cold in the gym (in that case I would probably go do a bit of prowler or bike beforehand), just grab the bar with very light weight on (50% of workout weight) for the given exercise you’re about to perform and crank out a few reps. This way you prepare you joints and muscles for the range of motion you need and then increase the weight load slowly. You just saved 15 minutes by skipping your 15 minutes treadmill or bike warmup while doing the “appropriate warmup”.