Most people think of math as "hard". By that, they really mean "incomprehensible". There's nothing hard about noting, or even proving, that the cardinality of the integers equals that of the rationals but is less than the cardinality of the reals, even if most people would prefer to simply call them all "infinite". Even most math-literate folks, like engineers and physicists are generally content to simply make the distinction between countably and uncountably infinite rather than trying to wrap their heads around the various degrees of uncountable sets. These things aren't "hard" if you trust your axioms and your methods but, intuitively, they are pretty far out there.
On the other hand, rigorous proof and its software analog, formal validation, are objectively hard tasks. They require discipline, patience, and, above all, attention to detail. Any attempt to do them quickly defeats the purpose. They necessarily require effort.
So, having completed the interesting part of comparing the sampling algorithms, I'm now left with the hard task of making sure that everything I did was correct. It's a long night of fairly unrewarding work. But, it is the hard work of math. It needs to be done.
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