TAOCP is meant to be a textbook, a reference, and a historical account of algorithm development. I find it most rewarding to pick the most interesting part to me at the moment to read. I also ignore the MMIX code (even though I did work through the MMIXware book) and focus on first intuition, then code, and then the math that teaches me new ideas or new methods.

I find the MMIX code less relevant to my line of work now as getting down to machine-level optimization requires a whole new different suite of tools. The ensuing optimizations on modern CPUs seem deviated from what the MMIX code can help.