Maxima scripts do not produce exakt quadrature coefficients

While working on the redesign of the quadraturerules I found out that the automatically generated 1d rules are not as exact as assumed, i.e. although the points and weights are printed with 100 digits the actual precision is only about 16-17 digits. This might be fine for double precision calculations, but when changing the ctype to long double or Float128 or even GMP it is not applicable.

I'm not an expert in Maxima, so I don't see the error in the script. It seems that the actual calculation is performed in double precision only and just the output is in high precision. @christi I think, you have uploaded the maxima scripts. Any ideas?

The error can be seen by simply summing up the weights. It should be 1 but the difference is about 1.e-16 for rules with order >= 8 at least.

To be mode precise: the quadrature weights are of low precision.