I'm a software engineer who really didn't know much about recursion or algorithmic analysis- I was a bio major/computer hacker. I did terrible on my first set of google interviews, at least on the algorithmic questions.

None of that was a reasonable predictor of my future performance at Google. You would have filtered out a perfectly good candidate (and this is, IMHO, the biggest issue is that Google rejects a number of people who would be great employees with its early filters). I can't say I have a better system.

The only interviews that made any sense for the time I got hired were the ones with the specific team members I was going to join. Once we got to chatting it was pretty clear I was a good technical fit for the team.

I still want to emphasize I don't have a solution to the high false negative rate in the pre-screening procecss.