Guys, we did not expect to do this, but we just invented the theoretically optimal quadratic solver algorithm for all ethereum smart contracts. Because we need to approximate any Orderbook shape, we can't just use stuff like x*y=k. In order to fit to an Orderbook shape, we need a quadratic solver. For anyone who's run a regression, you know this is even doable from excel. But smart contracts have crazy numerical errors, and as a result, normal run-of-the-mill quadratic solvers yield un-bounded margin-of-errors especially when you can compose a chain of trades.