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Partial proofs
If a large part of your witness is constant (or changing infrequently), you can precalculate a significant portion of the proof.
See this forum post for more details.
This is essentially free (the overhead is minimal, so already when doing 2 proofs with same shared part of the witness, it's worth do it).
A more advanced version, but one which also comes with a heavy trade-off, is developed in
groth16/dynamic.