Those algorithms are actually surprisingly simple to code most of the time, if you're using a high-level language and aren't worried about scaling. Scaling them is hard, but for that you can already find good, scalable implementations out there of the basic building blocks.

In my experience coding machine learning algorithms is actually easier than the hairier sorts of programming (multithreaded, distributed, very low-level, etc) if you do the math first. Most errors are come from doing the math worngly (or not doing it at all) and most slowness are due to missing very obvious optimizations (which a good programmer will pick up on sometimes even if it's not explicit in the papers that describe the technique; some papers unfortunately assume you will pick up on the obvious optimizations yourself).

That's been my experience so far as well. The algorithms are surprisingly straightforward. Understanding the underlying theory well enough to get good results is the hard part.