Error propagation in adaptive Simpson algorithm

[Albert Chan]

Now I see why you set a fixed tolerance down the chain.
A slightly off answer is better than no answer.

But, are you better off keep the algorithm as-is, and raise tolerance ?
(To take advantage of the "wasted" accuracy)

To get 6 digits accuracy, say, set tolerance to 1e-4 ?

I do that for my Guassian Quadrature routine, expecting 2 extra good digits.
So, if difference between 2 iteration is +/- 1e-4, last result is about 6 digits accurate.

Edit:
another trick is to limit recursion depth, say, 10 levels deep.
This forced the calculator to give a reasonable answer in seconds.