I'd like to profile the performance of tmux. In particular how fast starting up a session is (and maybe also attaching to a session). I'm especially interested in how the content of my .tmux.conf file affects startup times (I use plugins). 
How could I measure that in an objective way?
As an example of what I'm interested in, I run this to profile the startup times of my zsh setup.
repeat 5 {/usr/bin/time zsh -i -c exit}
I've tried automating things with commands like the one below, but I can't figure out how to get timings. Also, this seems to execute asynchonously, the command finishes before the session is killed.
tmux new-session -d -s test && tmux send-keys "exit" Enter