One of my "computers are really fucking fast" experiments, almost a decade ago, was when I was trying to do a histogram plot of a function that I was 98% sure was terribly broken. It was expected to give a uniform distribution so I figured I'll just plot a bunch of values into a 2d space and then convert it to a greyscale image.
At first I tried to puzzle out a good sampling strategy to make sure I didn't bias the output, then on a whim I tried 2^32 samples and went to lunch. It took something like a half an hour to do 4 billion samples. Took me a couple times to figure out how to squeeze 4k megapixels into a graph so I ran it a few more times, but the results showed a very distinct banding pattern that confirmed that the problem was every bit as bad as I suspected, which was a blocking issue for our release. A couple of hours well spent, running through an 'intractable problem' that really wasn't.
At first I tried to puzzle out a good sampling strategy to make sure I didn't bias the output, then on a whim I tried 2^32 samples and went to lunch. It took something like a half an hour to do 4 billion samples. Took me a couple times to figure out how to squeeze 4k megapixels into a graph so I ran it a few more times, but the results showed a very distinct banding pattern that confirmed that the problem was every bit as bad as I suspected, which was a blocking issue for our release. A couple of hours well spent, running through an 'intractable problem' that really wasn't.