Feat: improve tower verifier

[kunxian-xia]

Tower Verifier

Cycle Distribution

The cmd to get the following cycle distribution for a tower verifier with 2 product specs and 5 variables (which has 5 layers, 4 sumcheck proofs to verify) is

RUST_LOG=info cargo test --features "bench-metrics" --release --lib test_prod_tower -- --nocapture

Cycle count

INFO     ┝━ ｉ [info]: ┌╴initial sum
INFO     ┝━ ｉ [info]: └╴183 cycles
INFO     ┝━ ｉ [info]: ┌╴sumcheck verify
INFO     ┝━ ｉ [info]: └╴244 cycles
INFO     ┝━ ｉ [info]: ┌╴check expected evaluation
INFO     ┝━ ｉ [info]: └╴216 cycles
INFO     ┝━ ｉ [info]: ┌╴derive next layer's expected sum
INFO     ┝━ ｉ [info]: └╴432 cycles
INFO     ┝━ ｉ [info]: ┌╴sumcheck verify
INFO     ┝━ ｉ [info]: └╴424 cycles
INFO     ┝━ ｉ [info]: ┌╴check expected evaluation
INFO     ┝━ ｉ [info]: └╴254 cycles
INFO     ┝━ ｉ [info]: ┌╴derive next layer's expected sum
INFO     ┝━ ｉ [info]: └╴444 cycles
INFO     ┝━ ｉ [info]: ┌╴sumcheck verify
INFO     ┝━ ｉ [info]: └╴604 cycles
INFO     ┝━ ｉ [info]: ┌╴check expected evaluation
INFO     ┝━ ｉ [info]: └╴292 cycles
INFO     ┝━ ｉ [info]: ┌╴derive next layer's expected sum
INFO     ┝━ ｉ [info]: └╴456 cycles
INFO     ┝━ ｉ [info]: ┌╴sumcheck verify
INFO     ┝━ ｉ [info]: └╴784 cycles
INFO     ┝━ ｉ [info]: ┌╴check expected evaluation
INFO     ┝━ ｉ [info]: └╴330 cycles
INFO     ┝━ ｉ [info]: ┌╴derive next layer's expected sum
INFO     ┕━ ｉ [info]: └╴462 cycles

Sumcheck

Before this pr, the cycle count is

INFO     ┝━ ｉ [info]: ┌╴IOPVerifierState::verify_round_and_update_state
INFO     ┝━ ｉ [info]: │ ┌╴multi_observe
INFO     ┝━ ｉ [info]: │ └╴11 cycles x4
INFO     ┝━ ｉ [info]: │ ┌╴observe round
INFO     ┝━ ｉ [info]: │ └╴13 cycles x4
INFO     ┝━ ｉ [info]: │ ┌╴sample_ext
INFO     ┝━ ｉ [info]: │ └╴24 cycles x4
INFO     ┝━ ｉ [info]: └╴253 cycles
INFO     ┝━ ｉ [info]: ┌╴IOPVerifierState::check_and_generate_subclaim
INFO     ┝━ ｉ [info]: │ ┌╴extrapolate_uni_poly
INFO     ┝━ ｉ [info]: │ └╴92 cycles x4
INFO     ┕━ ｉ [info]: └╴503 cycles