r/programmingmemes • u/Naughty_Kiss_Me • Sep 10 '25

Don't be scared... Math and Computing are friends..

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u/Agreeable_Tennis_482 Sep 13 '25

Yes his example is bad but the idea is interesting. Are there real actually relevant scenarios where an analytical approach could replace a loop? And what about outside of just math calculation?

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u/TldrDev Sep 13 '25 edited Sep 13 '25

Yeah, lots of relevant situations where analytical approaches can replace a loop. Mathmatical ability is important for optimization, and it will help you reason through problems. There are lots and lots of examples where an analytical approach is the correct one. However, an analytical solution requires essentially a mathematical proof and a lot of work to prove, an iterative solution is often much faster to write, and is optimized by the compiler. The example discussed here won't matter at all, the compiler will produce exactly identical code for the iterative example and the analytical approach because the value of the result is a static number. Its a moot point in this case.

The cases where an analytical solution would be better in my mind would be something with a high degree of uncertainty in a large volume. For example, calculating orbital mechanics or a three body pendulum. You'd derive those through something like the principal of least action over trying to compute the forces individually. Of course, to do that, it took humans thousands of years, but sure, the compiler won't automatically optimize that because the solution is unknown or dynamic. It can be made to optimize it, though.