An interesting aspect is data dependencies. If your next statement reuses data you just computed, that can cause pipeline bubbles, as that result you want to use just isn't available yet. I dived into that topic for a video about relative performance of old PCs I just published today.
Yes, there is non-obvious structure in some algorithms solely for the purpose of turning a single logical stream of dependent instructions into multiple concurrent streams of dependent instructions running through the same pipeline. The caveat of doing this, of course, is that it typically increases register pressure.
