Speed up sol[UnaryExpr] via C-level math and refactor UnaryExpr

[Zeroto521]

This branch is 1.45x faster than master.

• this branch: 2.9803s
• master branch: 4.3398s

from timeit import timeit

from pyscipopt import Model, sqrt

m = Model()

n = 1000
x = m.addMatrixVar(n, lb=0, ub=1, vtype="C", name="x")
e = sqrt(x)
obj = m.addVar(lb=0, ub=None, vtype="C", name="obj")
m.addCons(obj == e.sum())

m.setObjective(obj, "maximize")
m.hideOutput()
m.optimize()
sol = m.getBestSol()

number = 10_000
cost = timeit(lambda: sol[e], number=number)
print(f"Cost of squaring an expression over {number:,} runs: {cost:.4f} seconds")

[Joao-Dionisio]

By the way, @Zeroto521 , out of curiosity. Are you also using PySCIPOpt for your work, or are you just speeding things up for fun?

[Zeroto521]

80% of the OR problems I encounter use commercial solvers or our closure algorithms for large-scale, speed-critical cases, while the rest use open-source ones for small tasks and research.

[Joao-Dionisio]

I see @Zeroto521 , thank you! We're actually in the process of collecting users of SCIP "in the wild", particularly in industry. Would it be possible for us to reference the work you're doing? We can talk via email, if you prefer: joao.goncalves.dionisio@gmail.com

[Joao-Dionisio]

Hey @Zeroto521 , just wanted to let you know that I'm going to be quite busy until the end of August, but by then I will be able to take a proper look at the repo. Are there other changes you're planning on making?

[Zeroto521]

Hey @Zeroto521 , just wanted to let you know that I'm going to be quite busy until the end of August, but by then I will be able to take a proper look at the repo. Are there other changes you're planning on making?

Yeah, I've already finished the basic version (drop OP, Split Variable and Expr). But they depend on this PR, so I haven't submitted it yet.

[Copilot]

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[Joao-Dionisio]

Thank you once again @Zeroto521 ! Very happy to see that #1074 is nearly finished, great job!