It's hard if:

1. You dont recognise the recursive nature of the problem,

Or

2. You don't recognise the stack-based nature in the problem (shunting yard algo, etc).

IOW, you did it the hard way :-).

Good to know I wasn't alone in writing terrible expression parsers. Since I knew absolutely nothing about parsing, my parser/interpreter consisted of splitting on whitespace, followed by linear scanning to find the most high precedence operation, repeated until a single token remains (basically how a human would do it).