[ty] Optimize TDD atom ordering (#20098)
## Summary
While looking at some logging output that I added to
`ReachabilityConstraintBuilder::add_and_constraint` in order to debug
https://github.com/astral-sh/ty/issues/1091, I noticed that it seemed to
suggest that the TDD was built in an imbalanced way for code like the
following, where we have a sequence of non-nested `if` conditions:
```py
def f(t1, t2, t3, t4, …):
x = 0
if t1:
x = 1
if t2:
x = 2
if t3:
x = 3
if t4:
x = 4
…
```
To understand this a bit better, I added some code to the
`ReachabilityConstraintBuilder` to render the resulting TDD. On `main`,
we get a tree that looks like the following, where you can see a pattern
of N sub-trees that grow linearly with N (number of `if` statements).
This results in an overall tree structure that has N² nodes (see graph
below):
<img alt="normal order"
src="https://github.com/user-attachments/assets/aab40ce9-e82a-4fcd-823a-811f05f15f66"
/>
If we zoom in to one of these subgraphs, we can see what the problem is.
When we add new constraints that represent combinations like `t1 AND ~t2
AND ~t3 AND t4 AND …`, they start with the evaluation of "early"
conditions (`t1`, `t2`, …). This means that we have to create new
subgraphs for each new `if` condition because there is little sharing
with the previous structure. We evaluate the Boolean condition in a
right-associative way: `t1 AND (~t2 AND (~t3 AND t4)))`:
<img width="500" align="center"
src="https://github.com/user-attachments/assets/31ea7182-9e00-4975-83df-d980464f545d"
/>
If we change the ordering of TDD atoms, we can change that to a
left-associative evaluation: `(((t1 AND ~t2) AND ~t3) AND t4) …`. This
means that we can re-use previous subgraphs `(t1 AND ~t2)`, which
results in a much more compact graph structure overall (note how "late"
conditions are now at the top, and "early" conditions are further down
in the graph):
<img alt="reverse order"
src="https://github.com/user-attachments/assets/96a6b7c1-3d35-4192-a917-0b2d24c6b144"
/>
If we count the number of TDD nodes for a growing number if `if`
statements, we can see that this change results in a slower growth. It's
worth noting that the growth is still superlinear, though:
<img width="800" height="600" alt="plot"
src="https://github.com/user-attachments/assets/22e8394f-e74e-4a9e-9687-0d41f94f2303"
/>
On the actual code from the referenced ticket (the `t_main.py` file
reduced to its main function, with the main function limited to 2000
lines instead of 11000 to allow the version on `main` to run to
completion), the effect is much more dramatic. Instead of 26 million TDD
nodes (`main`), we now only create 250 thousand (this branch), which is
slightly less than 1%.
The change in this PR allows us to build the semantic index and
type-check the problematic `t_main.py` file in
https://github.com/astral-sh/ty/issues/1091 in 9 seconds. This is still
not great, but an obvious improvement compared to running out of memory
after *minutes* of execution.
An open question remains whether this change is beneficial for all kinds
of code patterns, or just this linear sequence of `if` statements. It
does not seem unreasonable to think that referring to "earlier"
conditions is generally a good idea, but I learned from Doug that it's
generally not possible to find a TDD-construction heuristic that is
non-pathological for all kinds of inputs. Fortunately, it seems like
this change here results in performance improvements across *all of our
benchmarks*, which should increase the confidence in this change:
| Benchmark | Improvement |
|---------------------|-------------------------|
| hydra-zen | +13% |
| DateType | +5% |
| sympy (walltime) | +4% |
| attrs | +4% |
| pydantic (walltime) | +2% |
| pandas (walltime) | +2% |
| altair (walltime) | +2% |
| static-frame | +2% |
| anyio | +1% |
| freqtrade | +1% |
| colour-science | +1% |
| tanjun | +1% |
closes https://github.com/astral-sh/ty/issues/1091
---------
Co-authored-by: Douglas Creager <dcreager@dcreager.net>
