Just getting the grammar straight on the naturally recursive structures can be a trick. They also touch a large portion of the code generation and run time.
Get:
(a + c/2) * sqrt(b)
This is why teaching material should be tailored towards teaching rather than implementing demented stuff from the real world just because it is "there." You can easily implement a parser that ignores precedence and tell the reader that we are using brackets to force precedence instead.
In a real-word parser, you might use something like this[1] or some other home-grown algorithm if you didn't know about it. Doesn't matter as long as the parser works.
[1] Top-Down operator precedence (Pratt) parsing https://eli.thegreenplace.net/2010/01/02/top-down-operator-p...
I never got much farther than that though, I've looked into making a compiler many times and got overwhelmed every time.
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 :-).
https://journal.stuffwithstuff.com/2011/03/19/pratt-parsers-...
(a + c/2) * sqrt(b)
(* (+ a (/ c 2)) (sqrt b))
The alternative is going to an IR and doing full register allocation but then you need to implement Lengauer-Tarjan to get into SSA, all the same parallel load stuff for phi functions/block arguments, out-of-SSA, reconstruct in optimisation passes all the information you discard by going to a linear IR, etc.
If you are saying that constructing SSA following the classical approach is a premature optimisation, perhaps you would prefer Braun et al's retelling of Cliff Click's SSA construction algorithm - which works backwards from uses to place phis and requires no dominance information to be computed.
Why not fully maximal SSA + DCE? I mean, other than timings consideration. Fully maximal does not even need any graph traversal, it is entirely local to each block.
Braun et al's algorithm works backwards from uses (which generate liveness), so you get pruned SSA out. In the case of reducible control flow graphs, you also get minimal SSA. This is all without any liveness or dominance computation beforehand. Granted, you may want those things later, but it's nice that you can construct a decent quality SSA with a fairly intuitive algorithm. Also shown in the paper is that you can incorporate a few light optimisations during SSA construction (constant folding, for example).
I'm always happy to see more accessible resources for compiler writers.
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As an aside: for displaying CFGs on the page, it would be very interesting to emit something somewhat dynamic. SVGs are always a good start, but there is a neat library for doing hierarchical graph layout (dagre, with d3-dagre handling rendering as well). In my own efforts at pedagogy, I've been interested in producing CFGs in-browser whose basic blocks comprise a "unified diff" view of the block (this being achieved in realtime by maintaining a subset of LLVM whose CFGs are persistent). Then it is more obvious what has changed: at least in the case of mem2reg which shouldn't introduce new blocks or move too much around (I forget if it hoists allocas to the entry block or not).
It'd also be cool to distil what underlying ideas you have found to be most useful in your efforts. The constrained scope of them may be useful to me, as I've wanted to create a kind of "advent of compilers" for years (advent of code but with a heavy slant towards compiler tasks/algorithms).