feat: Quick and dirty relation skipping

[Rumata888]

Introduces a mechanism to skip accumulating the result of a relation if by checking an appropriate selector we know that the relation is going to result in a zero. The mechanism works during both folding and sumcheck
Removes 3 seconds from the benchmark

[AztecBot]

Benchmark results

Metrics with a significant change:

• batch_insert_into_append_only_tree_16_depth_ms (8): 17.0 (+31%)
• batch_insert_into_append_only_tree_16_depth_hash_ms (8): 0.722 (+31%)

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 13752339 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	259,808	1,019,432	4,060,016
l1_rollup_execution_gas	353,994	1,138,880	4,281,417
l2_block_processing_time_in_ms	1,277	4,813 (+1%)	19,114 (+1%)
note_successful_decrypting_time_in_ms	223 (+2%)	608 (+1%)	2,198 (+2%)
note_trial_decrypting_time_in_ms	40.1 (+45%)	47.3 (+20%)	189 (+1%)
l2_block_building_time_in_ms	21,378	84,686	344,113
l2_block_rollup_simulation_time_in_ms	16,021	63,479	259,499
l2_block_public_tx_process_time_in_ms	5,328 (+1%)	21,129 (+1%)	84,354

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	16,558 (-1%)	29,285 (-9%)
note_history_successful_decrypting_time_in_ms	1,411	2,823 (+4%)
note_history_trial_decrypting_time_in_ms	173 (+7%)	244 (+8%)
node_database_size_in_bytes	18,681,936	36,098,128
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	333	44,664	27,457
private-kernel-ordering	214	45,777	14,627
base-rollup	1,744	175,344	933
root-rollup	83.9 (+1%)	4,192	825
private-kernel-inner	444	73,099	27,457
public-kernel-app-logic	275	32,254	25,379
merge-rollup	7.92 (+2%)	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	10.4	10.9 (+1%)	⚠️ 17.0 (+31%)	17.2 (+1%)	23.5 (+2%)	64.7 (+1%)	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	0.601	0.605 (+1%)	⚠️ 0.722 (+31%)	0.529 (+1%)	0.489 (+1%)	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	75.6 (+1%)	48.3	242	467	922 (+2%)	3,611 (+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	0.466	0.495	0.441	0.436	0.438 (+1%)	0.434 (+1%)
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	106 (+2%)	58.0 (+1%)	357	698	1,383 (+1%)	5,501
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	0.502 (+1%)	0.504	0.485	0.477	0.477	0.477
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	N/A	65.3 (+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	0.562	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 note hashes	1 new note hashes
tx_pxe_processing_time_ms	577 (+1%)	1,505

Metric	0 public data writes	1 public data writes
tx_sequencer_processing_time_ms	0.0290 (-1%)	655

[codygunton]

For sumcheck functionality, this is replaced by #5766. IOU protogalaxy equivalent.