Is there a standard name or standard symbol for the binary operation that combines $x$ and $y$ to give $xy/(x+y)$, or equivalently $1/(1/x+1/y)$? (At least the expressions are equivalent if we ignore the case where $x$ or $y$ is 0.)
One possible name that comes to mind is "harmonic sum", but some might say that the harmonic sum of $x$ and $y$ should be defined as $1/x+1/y$.
Another possibility is "cosum" or "co-sum", since the relationship between this operation and ordinary addition is analogous to (and indeed tropicalizes to) the relationship between the operations min and max.
Anyway, in addition to knowing what to call this operation, I'd also like to know how to write it, if there is some existing notation for it.