chore: add pow poly bench and link optimization issues

[lucasxia01]

Adds the pow poly bench. This PR was supposed to also optimize the pow poly computation, but I measured that it takes around 45ms of the whole 6-iter client IVC benchmark, so its not worth doing for now.

Links a couple of optimization issues to the codebase: AztecProtocol/barretenberg#857 and AztecProtocol/barretenberg#864.

[AztecBot]

Benchmark results

No metrics with a significant change found.

Detailed 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 8c697ce1 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	54,212	214,436	855,332
l1_rollup_calldata_gas	259,880	1,019,816	4,060,064
l1_rollup_execution_gas	354,066	1,139,264	4,281,465
l2_block_processing_time_in_ms	1,283	4,811	18,985 (-1%)
note_successful_decrypting_time_in_ms	223 (+3%)	608	2,188
note_trial_decrypting_time_in_ms	34.9 (+11%)	51.9 (+10%)	191 (+2%)
l2_block_building_time_in_ms	21,532 (+1%)	85,514 (+1%)	345,874
l2_block_rollup_simulation_time_in_ms	16,155 (+1%)	64,003 (+1%)	260,609
l2_block_public_tx_process_time_in_ms	5,350 (+1%)	21,431 (+1%)	85,013 (+1%)

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	16,123 (-3%)	31,684 (-5%)
note_history_successful_decrypting_time_in_ms	1,402 (-4%)	2,729 (-3%)
note_history_trial_decrypting_time_in_ms	173 (-44%)	218 (-16%)
node_database_size_in_bytes	18,718,800	35,852,368 (-1%)
pxe_database_size_in_bytes	29,923	59,478

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	334	44,664	27,457
private-kernel-ordering	215	45,777	14,627
base-rollup	1,749	175,344	933
root-rollup	84.0	4,192	825
private-kernel-inner	445	73,099	27,457
public-kernel-app-logic	276	32,254	25,379
merge-rollup	7.82 (-1%)	2,712	933

Tree insertion stats

The duration to insert a fixed batch of leaves into each tree type.

Metric	1 leaves	2 leaves	8 leaves	16 leaves	32 leaves	128 leaves	64 leaves	512 leaves	1024 leaves	2048 leaves	8192 leaves
batch_insert_into_append_only_tree_16_depth_ms	10.3 (-1%)	10.8 (-5%)	13.1 (-1%)	17.5 (-2%)	23.4	64.6	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.9	17.5	23.0	31.6	47.0	143	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.597 (-1%)	0.598 (-5%)	0.553 (-1%)	0.539 (-1%)	0.487	0.446	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	N/A	N/A	N/A	75.4 (-1%)	48.0 (-1%)	242	466 (-2%)	923 (-1%)	3,588 (-1%)
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	N/A	N/A	N/A	159	96.0	543	1,055	2,079	8,223
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	0.465 (-1%)	0.491 (-1%)	0.442	0.436 (-1%)	0.439 (-1%)	0.432
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	105 (-1%)	57.6 (-1%)	359 (+1%)	693 (-1%)	1,380 (-1%)	5,467 (-1%)
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	N/A	N/A	N/A	197	104	691	1,363	2,707	10,771
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	0.500	0.503 (-1%)	0.486 (+1%)	0.476 (-1%)	0.476 (-1%)	0.476 (-1%)
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	N/A	64.8 (-1%)	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_count	N/A	N/A	N/A	N/A	110	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_indexed_tree_40_depth_hash_ms	N/A	N/A	N/A	N/A	0.560 (-1%)	N/A	N/A	N/A	N/A	N/A	N/A

Miscellaneous

Transaction sizes based on how many contracts are deployed in the tx.

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	15,388	36,001

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	579	1,507

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	0.0292 (-4%)	657

[ledwards2225]

LGTM