feat: compile base rollup as a circuit

[sirasistant]

This PR adds a variant of the base rollup that is a circuit. This makes sure that PRs don't break compilation as a circuit of the base rollup and tracks its constraint count.
After the last noir pull, thanks to @TomAFrench compilation is now much faster, allowing to compile the base rollup as a circuit in a reasonable time (prev. it took 5 minutes, now some seconds)

[github-actions]

Changes to circuit sizes

Generated at commit: 8f51b189461285dacf13236899413967d806f463, compared to commit: 62a17a4758264c62bb7a9273bf95263dcfea930c

🧾 Summary (100% most significant diffs)

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
rollup_base	+855,345 ❌	+85534500.00%	+4,034,524 ❌	+11527211.43%

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Full diff report 👇

Program	ACIR opcodes (+/-)	%	Circuit size (+/-)	%
rollup_base	855,346 (+855,345)	+85534500.00%	4,034,559 (+4,034,524)	+11527211.43%

[AztecBot]

Benchmark results

Metrics with a significant change:

• note_history_trial_decrypting_time_in_ms (5): 150 (+76%)

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 a60b71a5 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	222,948	868,196	3,449,336
l1_rollup_execution_gas	842,035	3,595,304	22,204,998
l2_block_processing_time_in_ms	1,348 (+1%)	5,084 (-1%)	21,080 (-1%)
note_successful_decrypting_time_in_ms	348 (+1%)	1,253 (+13%)	3,803 (-1%)
note_trial_decrypting_time_in_ms	59.5 (+12%)	38.2 (+2%)	139 (+1%)
l2_block_building_time_in_ms	13,569	53,863	217,335
l2_block_rollup_simulation_time_in_ms	10,009	39,805	161,050
l2_block_public_tx_process_time_in_ms	3,529	13,982	56,015

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	15,715 (-2%)	29,380
note_history_successful_decrypting_time_in_ms	2,710 (+7%)	5,084
note_history_trial_decrypting_time_in_ms	⚠️ 150 (+76%)	150 (+7%)
node_database_size_in_bytes	3,915,013	4,259,347
pxe_database_size_in_bytes	29,940	59,499

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	201 (+1%)	43,109	20,441
private-kernel-ordering	115	25,833	9,689
base-rollup	2,062	244,144	881
root-rollup	85.9 (-3%)	4,088	889
private-kernel-inner	262 (+1%)	64,516	20,441
public-kernel-private-input	172	25,203	20,441
public-kernel-non-first-iteration	171	25,245	20,441
merge-rollup	9.70 (-15%)	2,608	881

Miscellaneous

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

Metric	0 deployed contracts	1 deployed contracts
tx_size_in_bytes	10,323	26,309