p.p.s. Your multiple dispatch signature for broadcasted dimensions is
actually not quite right: should be
(n|1),(n|1)->() ===>

(n),(n)->() | (n),(1)->() | (1),(n)->() | (n),() -> () | (),(n)->()

This is becoming quite verbose... (and perhaps become somewhat slow).
Though arguably one could always allow missing dimensions to be 1 for this
case, so that one could drop the last two.
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