How Does the ‘Constant Sum’ Formula Differ from the ‘Constant Product’ Formula in AMMs?

The Constant Product formula ($x y=k$) ensures that the product of the reserve quantities ($x$ and $y$) remains constant, which results in a smooth but exponentially increasing price impact (slippage) for large trades. The Constant Sum formula ($x+y=k$) aims to keep the sum of the reserves constant, resulting in a linear, near-zero slippage price for trades.

This formula is primarily used for stablecoin pairs that should trade at a 1:1 ratio.