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Oh, this is unfortunate, I've made a mistake defining dist[] as you've noticed. The sqrt should be in the denominator of the integrand. Thank you, I've corrected the definition of dist[] in the original post. Now the calculations take generally...
Thanks for the suggestions anyway! I have finally arrived at something promising! Basically I changed the method of handling the singularities, and the way I declare the exclusions. Any further suggestions that may speed things up are more than...