I imagine you could do most or all of this with yacas, which is actually a computer algebra system (GPL).

From the linked post: 'A "computer algebra system" would have accomplished a similar goal, but been much slower and much more complicated'

Writing a CAS from scratch would've been much more complicated.

Reusing an existing one? Maybe not.

Yes, it would likely be slower, but is a 1ms vs. 10ms response time in the calculator app really such a big deal? entering a correct calculation / formula on the smartphone likely takes much longer.

He was not working on the iOS Calculator.