Error propagation in adaptive Simpson algorithm

[Albert Chan]

(07-30-2018 06:42 PM)Claudio L. Wrote:  For example (from another thread): Integral of exp(-x) between 0 and 500.
If I request 1e-8 tolerance, the result is:
1.00000000000704832....
This case has 2 more digits than requested.

Was the thread Casio fx-991EX vs Hp 50g speed differences ?

Tolerance setting is against successive iterations, not against true result.
If the algorithm knew the true result, why ask for tolerance ?

The extra precision may be just lucky (the integral is well-behaved)
Integral convergence rate may stall or (rare, but possible) even got worse on some iterations.

Worse, integral may converge very well, but converged to a wrong result
See above thread post#12, integral of sin(x), from 0 to 200.

So, if time permitted, double check the numbers with other methods.