pymc-devs
Add rewrite for `log(gamma) -> gammaln`
Description
We're missing this simple rewrite:
import pytensor.tensor as pt
from pytensor.graph import rewrite_graph
x = pt.scalar("x")
out = pt.log(pt.gamma(x))
new_out = rewrite_graph(out, include=("canonicalize", "stabilize", "specialize"))
new_out.dprint()
Can be done easily with PatternNodeRewriter as in
https://github.com/pymc-devs/pytensor/blob/911c6a33c2bea6bf1d5b628154e84c43cbed1c63/pytensor/tensor/rewriting/math.py#L3646-L3651
We could also add rewrites for common combinatorics expressions like
naive_betaln = pt.log((pt.gamma(x) * pt.gamma(y)) / pt.gamma(x + y)
betaln = pt.gammaln(x) + pt.gammaln(y) - pt.gammaln(x + y)
https://github.com/pymc-devs/pytensor/blob/ad55b69f3d13f11c6a9a57823c2a88a966db8b1a/pytensor/tensor/special.py#L799-L804
Or for log(poch): https://github.com/pymc-devs/pytensor/blob/ad55b69f3d13f11c6a9a57823c2a88a966db8b1a/pytensor/tensor/special.py#L767-L772
For these more general cases we can probably use something more flexible than the PatternNodeRewriter. We want to apply as long as we know all the terms inside are factorials/gammas/exps (positive things that easily blow up). This is a narrow/easier subset of https://github.com/pymc-devs/pytensor/discussions/177
