I suppose you can estimate the complexity of a particular approximate equation as the number of bit required to simulate it in a particular setup. I did something like that for the Schrodinger equation here a couple of years ago, frustrated by Eliezer's empty theorizing, but I cannot find my comment anymore. Anyway, it was basically the length of the computer code which simulates the equation, so not that large, maybe tens or hundreds of kilobytes. You have to keep adding other codes to describe the necessary math and physics, and pretty soon you have to count a large chunk of the scientific and engineering software required to simulate the physical phenomena and engineering machinery, with a multitude of special cases for special dragons. And we still cannot simulate everything we see.