Optimise find_optimal_atomics

[pbrubeck]

The sum factorization algorithm involves finding the optimal set of common subexpressions via a brute-force search. Previously, the search spent most of the time comparing sets of "atomic" gem.Node instances (the so-called monomials). The set comparisons were hashing the same gem.Node instances over and over again. Instead, we make sure that the hashing only occurs when preprocessing all unique atomics into a list, and we solve the optimisation problem using the index into that list.

We also introduce a better initial guess by recursively sorting the subset of monomials that intersect with each other.

As a benchmark, we generate code for assembling

from firedrake import *
from firedrake.tsfc_interface import compile_form
V = FunctionSpace(UnitTetrahedronMesh(), "JM", 1)
v = TestFunction(V)
u = TrialFunction(V)
form = (inner(u, v) + inner(div(u), div(v))) * dx
kernels = compile_form(form, "stokes", parameters={"mode": "spectral"})

Notice that the (div, div) term is not integrated with dx(degree=0).

Before: 143 seconds

After: 79 seconds

[connorjward]

I can have a think about further optimisations as a separate piece of work. Think this is fine to go.