What is the exact number of multiplication operations and addition operations needed to calculate the permanent in Ryser's formula (both original and the Gray coded version)?
I am looking reference for an exact count. It seems Cramer rule always is inferior or just par with the Gray coded version. Also Scott Aaronson has a calculation for $4 \times 4$ determinant where he uses Gaussian elimination. He mentions estimating the precise gap between permanent and determinant calculation for $4 \times 4$ is already a notorious open problem.
I am also looking for counts for other calculations/formulas of Permanent.