feat(docs): Document slow update tree

[catmcgee]

Closes #3374

Documents the slow update tree - how, when, why

Explanation in concepts & how-to in syntax page

Checklist:

Remove the checklist to signal you've completed it. Enable auto-merge if the PR is ready to merge.

• 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.
• Every change is related to the PR description.
• I have linked this pull request to relevant issues (if any exist).

[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.

Values are compared against data from master at commit 9c9b561f 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	223,092	868,280	3,449,384
l1_rollup_execution_gas	842,179	3,595,388	22,204,753
l2_block_processing_time_in_ms	2,069	7,980	33,048
note_successful_decrypting_time_in_ms	316 (+1%)	908 (-1%)	3,318 (-1%)
note_trial_decrypting_time_in_ms	26.4 (+8%)	35.6 (-18%)	198 (-1%)
l2_block_building_time_in_ms	20,440 (+1%)	81,134	325,788
l2_block_rollup_simulation_time_in_ms	16,895 (+1%)	67,138	269,952
l2_block_public_tx_process_time_in_ms	3,497	13,849	55,287 (-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	23,058 (+1%)	44,716 (+1%)
note_history_successful_decrypting_time_in_ms	2,212 (+2%)	4,213 (+1%)
note_history_trial_decrypting_time_in_ms	164 (+1%)	232
node_database_size_in_bytes	3,304,835	3,650,095
pxe_database_size_in_bytes	29,748	59,307

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	199	43,077	20,441
private-kernel-ordering	115	25,833	9,689
base-rollup	2,966	664,108	873
root-rollup	93.7 (+4%)	4,072	1,097
private-kernel-inner	259	64,484	20,441
public-kernel-private-input	171	25,203	20,441
public-kernel-non-first-iteration	168	25,245	20,441
merge-rollup	11.5 (+4%)	2,592	873

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	25,938

[critesjosh]

These links dont go anywhere.

[rahul-kothari]

Ship it!

addressed comments