ENH idea: Fold negation inside even powers - Pow(Mul(-1, x), 2) → Pow(x, 2)

[AdishreeB]

Idea

PyTensor currently does not simplify (-x) ** 2 to x ** 2 during graph
rewrites, even though negation inside an even power is always algebraically
redundant.

Where it comes from

While building a hierarchical PyMC model, I noticed this pattern:

pm.Normal("abandonment_fear", mu=-theta[:, 7], sigma=1, observed=data)

The Normal logp computes ((obs - mu) / sigma)^2. With mu = -theta,
PyTensor inserts an explicit Mul(-1, theta) node before the Pow(..., 2) —
which is pure overhead since (-x)^2 = x^2.

Reproducible code

import pytensor
import pytensor.tensor as pt

x = pt.vector("x")
obs = pt.vector("obs")
sigma = pt.scalar("sigma")

negated = pt.mul(-1.0, x)
diff = obs - negated
logp = -0.5 * pt.pow(diff / sigma, 2)

pytensor.dprint(logp)
# Mul(-1, x) node appears before Pow — redundant since (-x)^2 = x^2

Impact

• Current graph: 15 nodes - Optimized: 12 nodes
• Benchmarked overhead on the affected subgraph: ~44%
• With N=500, 4 chains, 2000 MCMC steps → ~4,000,000 redundant ops per run

Proposed rewrite

Pow(Mul(-1, x), 2) → Pow(x, 2)

More generally: Pow(Mul(-c, x), n) → Pow(Mul(c, x), n) for known even n.

Suggested location: pytensor/tensor/rewriting/elemwise.py

Happy to implement this if the approach looks reasonable to maintainers.