Do you actually need the math function on-chain? What makes this function so special and complicated that it can't be simplified with existing gas-efficient libraries? Have you already written up the algo in solidity? (assuming you have since you mentioned hardhat)
Have you considered using an optimistic prover? You can publish a pairing of {inputs,outputs} without actually running the algorithm, and if anyone challenges it, then they can pay the gas to run this complex algorithm (I think this can be done with ZK provers as well) and show the results were wrong. This might require some stake (0.1 ETH?) when people push new {input,output} sets though, since there needs to be a penalty for lying. Of course whoever calls you out for lying should get their gas reimbursed, plus maybe some reward.
To answer your original question, polygon or a rollup may be the right choice. Consider also: Gnosis chain and Celo. Those are fairly cheap at the moment, but still large enough to offer good security. My recent calculations were showing less than 0.03 USD per 1 million gas for all of these chains. Fuse is a very inexpensive EVM chain but is less secure due to low marketcap of the FUSE token, so keep this in mind if you expect your project to have significant TVL.
Finally, note that gas costs are primarily driven by storage reads/writes, which is non-volatile memory. "memory" in the solidity sense is expensive-ish, and that is data that doesn't persist after the transaction finishes. Try to minimize writes/reads of storage first, then memory if possible to reduce your gas costs. Keep in mind one "read/write" is 32 bytes, so you can pack data cleverly to reduce total reads/writes
Yo i already wrote a lot, but i'm curious what you mean by this: