docs: Initial pg-stat-analysis project

[johnjcsmith]

Adds an Inferable demonstration for analysing a Postgres DB and recommending index creation

Example output

{
  "summary": "After analyzing the database access patterns through pg_stat_statements, I've identified several potential performance improvements. The analysis shows that the most time-consuming queries are primarily related to job status updates and machine status management.",
  "suggestions": [
    {
      "name": "Add index on jobs.executing_machine_id, status, and remaining_attempts",
      "explanation": "One of the most time-consuming queries updates job status based on machine status and remaining attempts. This compound index would improve the performance of this frequently executed query.",
      "impactedQueries": [
        "UPDATE jobs as j SET status = $1 FROM machines as m WHERE j.status = $2 AND j.executing_machine_id = m.id AND m.status = $3 AND j.cluster_id = m.cluster_id AND j.remaining_attempts > $4"
      ],
      "remediation": "CREATE INDEX idx_jobs_exec_machine_status_attempts ON jobs(executing_machine_id, status, remaining_attempts);",
      "impact": 8
    },
    {
      "name": "Add partial index on jobs for timeout conditions",
      "explanation": "The most time-consuming query involves updating timed-out jobs. A partial index would improve the performance of this specific operation.",
      "impactedQueries": [
        "update \"jobs\" set \"status\" = $1 where (\"jobs\".\"status\" = $2 and \"jobs\".\"last_retrieved_at\" < now() - interval $4 * timeout_interval_seconds and \"jobs\".\"timeout_interval_seconds\" is not null and (\"jobs\".\"approval_requested\" = $3 or \"jobs\".\"approved\" is not null))"
      ],
      "remediation": "CREATE INDEX idx_jobs_timeout_conditions ON jobs(status, last_retrieved_at) WHERE timeout_interval_seconds IS NOT NULL;",
      "impact": 9
    }
  ]
}