E2E optimizations and tweaks

[frozenspider]

1. In MLE-first approach, when the ideal is zero, the ideal check computation can be skipped - we know that the MLE evaluation is supposed to be 0, so P does not need to compute it: it just sends 0.
   • This only allows skippping MLE evaluation if ALL ideals are 0.
   • In combined polynomial ideal check, this was already handled but with more granularity - all zero ideal constraints were skipped while keeping non-zero ones.
2. Reworked MLE-first approach to handle linear constraints in MLE-first way while the rest are going through the regular combined subroutine. This allows using MLE-first approach for UAIRs with non-linear constraints.
3. Use IPRS code with rate 1/8 instead of 1/4, while also lowering number of column openings to 100 instead of 147.

Overall effect on E2E benchmarks (2^8 vars, parallel mode):

• Prover time (both combined and MLE-first) stayed pretty much the same
• Verifier time worsened by around to ~10%
• Proofs became smaller by ~30-40%, both compressed and uncompressed

[github-actions]

Coverage (base → head): 87.55% → 87.28% ⬇️ 0.27 pp
Only posts when PR coverage is lower than the base branch's latest push (or freshly computed base).

[frozenspider]

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[chatgpt-codex-connector]

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