[flym4n]

   I spent three days in coffee shops with a pen and paper taking first and then second derivatives of the Winkel Tripel formula

I felt bad for you reading that. There are loads of tools to do it automatically (matlab, wolfram, etc).

[sanskritabelt]

The stuff coming out of those computer algebra things is not always exactly the form you want to be stuffing in your code. Working it out manually focuses the mind.

[weland]

They also tend to do it quite badly in some non-trivial cases. I've seen Wolfram spewing a three-line result which could be further simplified to a simple expression. It also doesn't always help to simply know the result; a lot of insight about numerical problems can be gained from how the result is derived.

I also spent several days churning formulae in bars. Got a lot of weird looks.