in reply to Empirically solving complex problems

As I've said elsewhere, I don't think this does quite what you think it does. What measure is it you want again? I assumed from your description that you want the area under both the curves, but that's not really what you're computing - it looks like you're computing the area underneath distribution 1 but above distribution 2.

At the moment, among other things, your solution gives different answers if I switch distribution 1 and distribution 2. That doesn't seem right, given what you've said about the particular problem.

Also, I should note that multiplying by 10000 doesn't help you any - you'd get the same results if $area were "1", since the computer is using floating point variables in these computations. 

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