I have found a lot of people talking about how to compute the UV index, but have not found an example that shows the actual equations, so I could adapt them into an algorithm.
Probably the closest is this example here.
The most confusing part of the process is why there are so many cases that present hypothetical data rather than a real example. For instance, here is the EPA's explanation. They seem to compute a real number. But they say the weighing factors are fake.