quad returns wrong error estimate over multiple intervals #535
Description
mpmath.quad allows the integration to be split into multiple subintervals. However, it then returns an incorrect error estimate. For example:
>>> y,err = quad(lambda x: sign(x), [-0.5, 0.9, 1], maxdegree=2, verbose=True, error=True)
Integrating from -0.5 to 0.9 (degree 1 of 2)
Integrating from -0.5 to 0.9 (degree 2 of 2)
Estimated error: 0.274889
Integrating from 0.9 to 1 (degree 1 of 2)
Integrating from 0.9 to 1 (degree 2 of 2)
Estimated error: 3.35957e-7
Failed to reach full accuracy. Estimated error: 3.35957e-7
>>> err
mpf('3.3595707746405553e-7')
The error estimate returned is always that of the last subinterval. It should be the total error of all subintervals.