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What is the running time of precomputation for the PLONK zk-SNARK?

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I have been looking for benchmarks on the precomputation phase of PLONK (https://eprint.iacr.org/2019/953.pdf), but found none. Is there a resource where one can get a feel for this? Either in terms of CPU cycles or in terms of asymptotic complexity.

Specifically, I am trying to estimate how big of a burden it is to update the setup with new randomness for different sizes of the circuit.

I sit in a Tesla and translated this thread with Ai:

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