feat(docs): Historical trees docs

[catmcgee]

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• If the pull request requires a cryptography review (e.g. cryptographic algorithm implementations) I have added the 'crypto' tag.
• I have reviewed my diff in github, line by line and removed unexpected formatting changes, testing logs, or commented-out code.
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[AztecBot]

Benchmark results

Metrics with a significant change:

• batch_insert_into_append_only_tree_32_depth_ms (512): 412 (+62%)
• batch_insert_into_append_only_tree_32_depth_hash_ms (512): 0.643 (+44%)

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 6dac6504 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	45,412	179,524	716,068
l1_rollup_calldata_gas	221,536	866,368	3,448,384
l1_rollup_execution_gas	313,955	984,040	3,667,973
l2_block_processing_time_in_ms	1,556 (+11%)	5,221 (-3%)	20,645
note_successful_decrypting_time_in_ms	286 (-1%)	841 (-5%)	3,208
note_trial_decrypting_time_in_ms	96.1 (-4%)	66.0 (-41%)	137 (-7%)
l2_block_building_time_in_ms	16,064 (-1%)	63,783	255,419
l2_block_rollup_simulation_time_in_ms	11,691 (-1%)	46,502 (-1%)	186,463
l2_block_public_tx_process_time_in_ms	4,339	17,191	68,665

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	15,963 (-7%)	30,124 (-3%)
note_history_successful_decrypting_time_in_ms	1,948 (-3%)	3,825 (-1%)
note_history_trial_decrypting_time_in_ms	124 (-27%)	235
node_database_size_in_bytes	3,518,270	3,553,910
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	214	44,681	25,561
private-kernel-ordering	167 (+1%)	43,753	14,809
base-rollup	1,208 (+1%)	128,338	881
root-rollup	80.8 (+2%)	4,088	677
private-kernel-inner	294 (+1%)	71,208	25,561
public-kernel-private-input	207	31,863	25,561
public-kernel-non-first-iteration	204	31,905	25,561
merge-rollup	7.65	2,608	881

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	12.3 (+1%)	18.4 (-10%)	13.2 (-2%)	19.3 (-2%)	24.4 (-4%)	68.8 (+5%)	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	0.630 (+1%)	0.670 (-3%)	0.538 (-1%)	0.539 (-2%)	0.482 (-1%)	0.443	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	82.6 (-4%)	51.6	⚠️ 412 (+62%)	478 (-1%)	910 (-1%)	3,552 (-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	0.476 (-3%)	0.498	⚠️ 0.643 (+44%)	0.437 (-1%)	0.428 (-1%)	0.426
batch_insert_into_indexed_tree_20_depth_ms	N/A	N/A	N/A	N/A	N/A	118 (-1%)	61.9 (-1%)	367 (-2%)	765 (-5%)	1,424 (-4%)	5,610
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	0.512	0.504	0.476 (-2%)	0.486 (-4%)	0.472 (-2%)	0.473
batch_insert_into_indexed_tree_40_depth_ms	N/A	N/A	N/A	67.1 (-1%)	N/A	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	94.1	N/A	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	0.596 (-1%)	N/A	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	15,455	32,223

Transaction processing duration by data writes.

Metric	0 new commitments	1 new commitments
tx_pxe_processing_time_ms	375 (+1%)	1,089

Metric	1 public data writes
tx_sequencer_processing_time_ms	537

[benesjan]

Looks good. But the naming needs to be aligned with yellow paper.

[critesjosh]

Some minor nits and just need to update those dead links.

[benesjan]

Looks good. Just a nit.

resovled