feat: Optimize auxiliary relations slightly

[Rumata888]

We had (-1) * Univariate in some places in auxiliary relation. Multiplication is much heavier than negation, so I replaced those instances. It shaved off a second (~1%) off wasm benchmarks.
WASM benchmark:

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_trial_decrypting_time_in_ms (64): 109 (+82%)

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 881502b4 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	64 txs
l1_rollup_calldata_size_in_bytes	676	676	676
l1_rollup_calldata_gas	6,400	6,400	6,412
l1_rollup_execution_gas	585,733	585,733	585,745
l2_block_processing_time_in_ms	1,298 (-1%)	4,548 (-5%)	9,248 (+1%)
note_successful_decrypting_time_in_ms	263 (-1%)	557 (+5%)	981 (-5%)
note_trial_decrypting_time_in_ms	67.4 (-8%)	77.6 (+54%)	⚠️ 109 (+82%)
l2_block_building_time_in_ms	12,159	43,150 (-4%)	87,372 (-2%)
l2_block_rollup_simulation_time_in_ms	7,190 (-3%)	24,989 (-4%)	49,966 (-2%)
l2_block_public_tx_process_time_in_ms	4,949 (+5%)	18,112 (-3%)	37,311 (-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	15,282 (+11%)	27,984 (+4%)
note_history_successful_decrypting_time_in_ms	1,275 (+7%)	2,479 (+3%)
note_history_trial_decrypting_time_in_ms	102 (+58%)	142 (+6%)
node_database_size_in_bytes	18,694,224	34,918,480
pxe_database_size_in_bytes	29,859	59,414

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	181 (+1%)	44,379	28,214
private-kernel-ordering	167 (+1%)	52,880	14,296
base-parity	3,577 (+4%)	128	311
root-parity	1,236 (-7%)	1,244	311
base-rollup	14,748 (-1%)	165,760	861
root-rollup	48.4 (-1%)	4,359	725
private-kernel-inner	224	73,795	28,214
public-kernel-app-logic	95.5 (+2%)	35,252	28,217
public-kernel-tail	138 (+1%)	40,928	28,217
merge-rollup	8.95 (-7%)	2,568	861
public-kernel-teardown	89.2 (-5%)	35,252	28,217
public-kernel-setup	88.8 (-5%)	35,252	28,217

Tree insertion stats

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

Metric	1 leaves	16 leaves	64 leaves	128 leaves	512 leaves	1024 leaves	2048 leaves	4096 leaves	32 leaves
batch_insert_into_append_only_tree_16_depth_ms	10.0 (+2%)	15.9	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.8	31.6	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.584 (+1%)	0.489	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_32_depth_ms	N/A	N/A	46.2 (+1%)	71.8 (+1%)	226 (-3%)	450 (+4%)	843 (-3%)	1,744 (+1%)	N/A
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	96.0	159	543	1,055	2,079	4,127	N/A
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	0.473	0.442 (+1%)	0.411 (-3%)	0.420 (+4%)	0.401 (-3%)	0.417 (+1%)	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	53.8	105 (-1%)	333 (-1%)	664 (+3%)	1,267 (-3%)	2,547 (-3%)	N/A
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	105	207	691	1,363	2,707	5,395	N/A
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.475 (+1%)	0.474 (-1%)	0.452 (-1%)	0.457 (+3%)	0.441 (-3%)	0.443 (-3%)	N/A
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	60.6 (+1%)
batch_insert_into_indexed_tree_40_depth_hash_count	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	109
batch_insert_into_indexed_tree_40_depth_hash_ms	N/A	N/A	N/A	N/A	N/A	N/A	N/A	N/A	0.529 (+1%)

Miscellaneous

Transaction sizes based on how many contract classes are registered in the tx.

Metric	0 registered classes	1 registered classes
tx_size_in_bytes	14,968	495,320

Transaction size based on fee payment method

Metric	none fee payment method	native fee payment method	fpc_public fee payment method	fpc_private fee payment method
tx_with_fee_size_in_bytes	773	905	1,161	1,377

Transaction processing duration by data writes.

Metric	0 new note hashes	1 new note hashes	2 new note hashes
tx_pxe_processing_time_ms	1,762 (-2%)	1,192 (+1%)	5,544 (-3%)

Metric	0 public data writes	1 public data writes	2 public data writes	3 public data writes	4 public data writes	5 public data writes	8 public data writes
tx_sequencer_processing_time_ms	9.30 (-11%)	580 (+1%)	431 (-6%)	1,138 (-5%)	572 (-3%)	1,974 (-5%)	547 (-5%)

[lucasxia01]

Nice! Can you put the benchmark output in the description?