After reading the theories that coasting down a fast hill may be faster than pedaling, I've tried both on a couple of handy hills in my area. I've tried it with tailwinds and neutral wind, pedaling and coasting. Not a whole lot of difference.

My fastest times came from pedaling until I was nearly spun out, around 130 rpm (I can thrash around up to 160 rpm but do that only on the indoor trainer for HIIT sessions), then tucking in and coasting. It seemed to work best with crank arms parallel with the ground, knees tucked in, etc. It was very slightly faster than my best time pedaling all the way down on my other road bike with 52T big ring and 11T smallest cog.

But some pro racers like Froome seem to prefer pedaling, even in Froome's awkward position on the top tube, which looks like a pterodactyl swooped down and stole a bike. I don't know if it's possible to accurately measure wind resistance in that situation.

The main advantage I can think of for pedaling downhill, even if coasting is faster, is to keep the legs warmed up. After a hard climb my legs go dead quickly if I coast down the other side. So now I pedal downhill, even if with low effort, just to keep the blood circulating in my legs.