What Is the Constant Sum Formula (X+y=k) and Why Is It Not Used Alone?

The constant sum formula x plus y equals k maintains a perfectly linear exchange rate between the two tokens. This would result in zero slippage and a constant price regardless of trade size.

However, if the external market price of one token deviates from the other (e.g. a stablecoin de-pegs), arbitrageurs would drain the pool of the more valuable token entirely, leaving LPs with only the worthless one. This high risk of pool depletion makes it unusable for most pairs.