feat: Goblin Translator Permutation relation (Goblin Translator part 2)

[Rumata888]

This PR adds the goblin translator permutation relation (proves that the set of values is 5 polynomials is equivalent to values in other 5 polynomials) as well as tests for consistency. Correctness tests require flavor, so will be added later and separately.

Checklist:

Remove the checklist to signal you've completed it. Enable auto-merge if the PR is ready to merge.

• If the pull request requires a cryptography review (e.g. cryptographic algorithm implementations) I have added the 'crypto' tag.
• I have reviewed my diff in github, line by line and removed unexpected formatting changes, testing logs, or commented-out code.
• Every change is related to the PR description.
• I have linked this pull request to relevant issues (if any exist).

[AztecBot]

Benchmark results

All benchmarks are run on txs on the Benchmarking contract on the repository. Each tx consists of a batch call to create_note and increment_balance, which guarantees that each tx has a private call, a nested private call, a public call, and a nested public call, as well as an emitted private note, an unencrypted log, and public storage read and write.

This benchmark source data is available in JSON format on S3 here.

Values are compared against data from master at commit b30839e9 and shown if the difference exceeds 1%.

L2 block published to L1

Each column represents the number of txs on an L2 block published to L1.

Metric	8 txs	32 txs	128 txs
l1_rollup_calldata_size_in_bytes	45,444	179,588	716,132
l1_rollup_calldata_gas	222,804	868,400	3,449,660
l1_rollup_execution_gas	841,891	3,595,508	22,205,029
l2_block_processing_time_in_ms	1,007	3,818 (-2%)	15,120 (-2%)
note_successful_decrypting_time_in_ms	319 (-2%)	964 (-2%)	3,554 (-4%)
note_trial_decrypting_time_in_ms	⚠️ 23.0 (-21%)	⚠️ 73.0 (-24%)	138 (+1%)
l2_block_building_time_in_ms	8,857 (-2%)	35,340 (-2%)	149,140 (-1%)
l2_block_rollup_simulation_time_in_ms	6,583 (-1%)	26,331 (-2%)	104,790 (-1%)
l2_block_public_tx_process_time_in_ms	2,230 (-2%)	8,887 (-3%)	43,699

L2 chain processing

Each column represents the number of blocks on the L2 chain where each block has 16 txs.

Metric	5 blocks	10 blocks
node_history_sync_time_in_ms	14,803 (-9%)	32,006 (-9%)
note_history_successful_decrypting_time_in_ms	⚠️ 2,396 (-19%)	⚠️ 4,891 (-20%)
note_history_trial_decrypting_time_in_ms	121 (-3%)	148 (-6%)
node_database_size_in_bytes	1,647,252	1,193,445
pxe_database_size_in_bytes	27,188	54,187

Circuits stats

Stats on running time and I/O sizes collected for every circuit run across all benchmarks.

Circuit	circuit_simulation_time_in_ms	circuit_input_size_in_bytes	circuit_output_size_in_bytes
private-kernel-init	44.0 (-9%)	56,577	14,745
private-kernel-ordering	21.6 (-10%)	20,137	8,089
base-rollup	854 (-10%)	631,605	811
root-rollup	37.9 (-10%)	4,072	1,097
private-kernel-inner	36.8 (-10%)	72,288	14,745
public-kernel-private-input	46.8 (-10%)	37,359	14,745
public-kernel-non-first-iteration	28.2 (-10%)	37,401	14,745
merge-rollup	⚠️ 0.964 (-16%)	2,592	873

[codygunton]

Thanks for breaking this into a small and manageable piece. To explain one part of my master merge: rather than using unnamed scopes in accumulate wrapped those blocks in an immediately-executed lambda to avoid a clang-format bug.