Rewrite assumes x^n is same type as x * x

[odow]

See:

MutableArithmetics.jl/src/rewrite.jl

Lines 573 to 590 in 01cae64

	# An expression like `base ^ exponent`, where the `base` is a
	# non-trivial expression that also needs to be re-written. We need
	# `!vectorized` otherwise `A .+ (A + A)^2` would be rewritten as
	# `broadcast!!(add_mul, x, AA, AA)` where `AA` is `A + A`.
	MulType = :($promote_operation(
	*,
	typeof($(inner_factor.args[2])),
	typeof($(inner_factor.args[2])),
	))
	if inner_factor.args[3] == 0
	# If the exponent is 0, rewrite
	# new_var = base^0
	# as
	# new_var = 1
	return _rewrite(
	vectorized,
	minus,
	:(one($MulType)),

This is not always true, for example, in jump-dev/JuMP.jl#3474.

[odow]

Closing as won't fix. This is too disruptive to change in rewrite.jl, and JuMP uses rewrite_generic.jl anyway so it isn't affected by this.