chore: reproduce bug for duplicate lagrange_first commitment

[ledwards2225]

When making an update to the DataBus, I ran into an issue where one of the new databus related polynomials that I added was identical to lagrange_first (and thus has the same commitment) which seemingly leads to failure in the Ultra arithmetized biggroup. This PR minimally reproduces this issue by adding a fake new polynomial that's not actually used in any relations but is otherwise treated as any other polynomial in the proving system. If this polynomial is set to be equal to L_1, we get failures. If not, there is no issue.

[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.

Proof generation

Each column represents the number of threads used in proof generation.

Metric	1 threads	4 threads	16 threads	32 threads	64 threads
proof_construction_time_sha256	5,641	1,538	705	774	769

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	1,412	1,412	1,412
l1_rollup_calldata_gas	9,428	9,476	9,464
l1_rollup_execution_gas	616,069	616,117	616,105
l2_block_processing_time_in_ms	1,301	4,830	9,582
l2_block_building_time_in_ms	44,812	177,365	354,822
l2_block_rollup_simulation_time_in_ms	44,639	176,726	353,549
l2_block_public_tx_process_time_in_ms	24,120	100,546 (+1%)	205,818

L2 chain processing

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

Metric	3 blocks	5 blocks
node_history_sync_time_in_ms	9,523 (-1%)	14,488 (-1%)
node_database_size_in_bytes	14,463,056	21,336,144
pxe_database_size_in_bytes	18,071	29,868

Circuits stats

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

Circuit	simulation_time_in_ms	witness_generation_time_in_ms	proving_time_in_ms	input_size_in_bytes	output_size_in_bytes	proof_size_in_bytes	num_public_inputs	size_in_gates
private-kernel-init	161	3,576	25,040 (-8%)	20,630	64,614	89,536	2,731	1,048,576
private-kernel-inner	625	4,082	50,708 (+1%)	92,318	64,614	89,536	2,731	2,097,152
private-kernel-tail	570	2,794 (-5%)	44,519 (-7%)	96,541	77,498	10,656	266	2,097,152
base-parity	6.44 (-1%)	1,135 (+1%)	2,799 (-5%)	128	64.0	2,208	2.00	131,072
root-parity	50.5 (+2%)	61.2 (-3%)	50,529 (-6%)	27,084	64.0	2,720	18.0	2,097,152
base-rollup	727	2,355	87,022 (-6%)	119,610	756	3,648	47.0	4,194,304
root-rollup	111 (+1%)	80.2 (+2%)	23,708 (-3%)	25,297	620	3,456	41.0	1,048,576
public-kernel-app-logic	522 (-1%)	2,981	53,928 (-4%)	104,941	86,302	114,784	3,520	2,097,152
public-kernel-tail	1,082	23,773	181,260 (-5%)	395,386	7,522	10,656	266	8,388,608
private-kernel-reset-small	593	2,053 (+4%)	50,698 (-11%)	120,733	64,614	89,536	2,731	2,097,152
merge-rollup	28.9	N/A	N/A	16,534	756	N/A	N/A	N/A
public-kernel-setup	662 (+1%)	N/A	N/A	104,941	86,302	N/A	N/A	N/A
public-kernel-teardown	540 (-2%)	N/A	N/A	104,941	86,302	N/A	N/A	N/A
private-kernel-tail-to-public	N/A	8,348 (+1%)	105,439 (-5%)	N/A	N/A	114,784	3,520	4,194,304

Stats on running time collected for app circuits

Function	input_size_in_bytes	output_size_in_bytes	witness_generation_time_in_ms	proof_size_in_bytes	proving_time_in_ms	size_in_gates	num_public_inputs
ContractClassRegisterer:register	1,344	9,944	469	N/A	N/A	N/A	N/A
ContractInstanceDeployer:deploy	1,408	9,944	41.0 (-1%)	N/A	N/A	N/A	N/A
MultiCallEntrypoint:entrypoint	1,920	9,944	1,422 (+1%)	N/A	N/A	N/A	N/A
SchnorrAccount:constructor	1,312	9,944	975	N/A	N/A	N/A	N/A
SchnorrAccount:entrypoint	2,304	9,944	2,085	16,768	55,683 (-5%)	2,097,152	457
Token:privately_mint_private_note	1,280	9,944	1,090	N/A	N/A	N/A	N/A
Token:transfer	1,376	9,944	4,014	16,768	54,530	2,097,152	457
Benchmarking:create_note	1,312	9,944	958 (+1%)	N/A	N/A	N/A	N/A
FPC:fee_entrypoint_public	1,344	9,944	224 (+2%)	N/A	N/A	N/A	N/A
SchnorrAccount:spend_private_authwit	1,280	9,944	78.3 (-2%)	N/A	N/A	N/A	N/A
Token:unshield	1,376	9,944	3,257 (-2%)	N/A	N/A	N/A	N/A
FPC:fee_entrypoint_private	1,376	9,944	4,032 (-2%)	N/A	N/A	N/A	N/A

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	10.4 (-1%)	17.0	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_count	16.7	31.8	N/A	N/A	N/A	N/A	N/A	N/A	N/A
batch_insert_into_append_only_tree_16_depth_hash_ms	0.603 (-1%)	0.520	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	48.5	77.4 (+1%)	247	475 (-1%)	938 (+1%)	1,850	N/A
batch_insert_into_append_only_tree_32_depth_hash_count	N/A	N/A	95.9	159	543	1,055	2,079	4,127	N/A
batch_insert_into_append_only_tree_32_depth_hash_ms	N/A	N/A	0.495	0.477 (+1%)	0.448	0.443 (-1%)	0.443 (+1%)	0.441	N/A
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	58.5	113 (-1%)	357	699 (-1%)	1,389	2,773	N/A
batch_insert_into_indexed_tree_20_depth_hash_count	N/A	N/A	106	208	692	1,363	2,707	5,395	N/A
batch_insert_into_indexed_tree_20_depth_hash_ms	N/A	N/A	0.506	0.507	0.482	0.480 (-1%)	0.480	0.481	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	62.5
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	107
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	0.553

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	83,794	665,117

Transaction size based on fee payment method

| Metric | |
| - | |