Sometimes it’s simpler to compute things exactly than to use an approximation. When you work on problems that cannot be computed exactly long enough, you start to assume everything falls in that category. I posted a tech report a few days ago about a problem in studying clinical trials that could be solved exactly even though it was commonly approximated by simulation.
This is another example of trying the simplest thing that might work. But it’s also an example of conflicting ideas of simplicity. It’s simpler, in a sense, to do what you’ve always done than to do something new.
It’s also an example of a conflict between a programmer’s idea of simplicity versus a user’s idea of simplicity. For this problem, the slower and less accurate code requires less work. It’s more straightforward and more likely to be correct. The exact solution takes less code but more thought, and I didn’t get it right the first time. But from a user’s perspective, having exact results is simpler in several ways: no need to specify a number of replications, no need to wait for results, no need to argue over what’s real and what’s simulation noise, etc. In this case I’m the programmer and the user so I feel the tug in both directions.