Optimize `Sum`s of `MakeVector`s and `Join`s

[ricardoV94]

Please describe the purpose of filing this issue

Not a drastic improvement by any means, but something we can keep in mind:

reduce(at.concatenate(*tensors)) -> reduce(reduce(tensor) for tensor in tensors)

Ignoring any axis complexities

import pytensor
import pytensor.tensor as pt
import numpy as np

x = pt.vector("x")
y = pt.vector("y")

f1 = pytensor.function([x, y], pt.sum(pt.concatenate((x, y))))
f2 = pytensor.function([x, y], pt.sum((pt.sum(x), pt.sum(y))))
f3 = pytensor.function([x, y], pt.add(pt.sum(x), pt.sum(y)))

pytensor.dprint(f1)
print()
pytensor.dprint(f2)
print()
pytensor.dprint(f3)

x_val = np.random.rand(100_000)
y_val = np.random.rand(200_000)

%timeit f1(x_val, y_val)
%timeit f2(x_val, y_val)
%timeit f3(x_val, y_val)

Sum{acc_dtype=float64} [id A] ''   1
 |Join [id B] ''   0
   |TensorConstant{0} [id C]
   |x [id D]
   |y [id E]

Sum{acc_dtype=float64} [id A] ''   3
 |MakeVector{dtype='float64'} [id B] ''   2
   |Sum{acc_dtype=float64} [id C] ''   1
   | |x [id D]
   |Sum{acc_dtype=float64} [id E] ''   0
     |y [id F]

Elemwise{Add}[(0, 0)] [id A] ''   2
 |Sum{acc_dtype=float64} [id B] ''   1
 | |x [id C]
 |Sum{acc_dtype=float64} [id D] ''   0
   |y [id E]
544 µs ± 27.5 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
270 µs ± 5.11 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)
270 µs ± 8.86 µs per loop (mean ± std. dev. of 7 runs, 1,000 loops each)