✔ PASS Sessionization (Gaps & Islands) task_112_dual_constraint_sessionization Scaled: 1M+ Records Ordered: Yes

Dual-Constraint Sessionization: 30-min Inactivity AND 4-Hour Absolute Hard Cap

Candidate Latency (1M Rows)
194.48 ms
(1.2x faster than golden)
Golden Latency (1M Rows)
225.76 ms
DuckDB in-memory engine
Underlying Data Volume
1,000,000 rows
11.4 MiB across 1 table
Evaluated Model
gemini-3.8-flash-low
Gen Latency: 37.5s
✔ Correctness Verified on 1M+ Records
Candidate SQL output matches ground truth golden query across all multiset rows and numeric tolerances (tol=1e-3). Zero data skew or anti-patterns detected on full dataset scale.

1. Analytical Significance & What It Means

Scenario & Frontier Trap
Business Scenario & Problem

Groups web clickstream events into sessions. A new session starts if: 1) more than 30 minutes pass between consecutive events, OR 2) more than 4 hours have elapsed since the session genesis event.

⚡ The Frontier Trap (Why LLMs Fail)

Frontier models only check the consecutive step lag (> 30 min). When an automated bot or persistent user emits events every 15 minutes continuously for 12 hours, the naive query leaves them in a single endless session, completely violating the 4-hour max session cap constraint.

Prompt / User Request Given to Model
Segment user event stream into deterministic sessions under dual constraints:
1. An inactivity gap of > 30 minutes begins a new session.
2. An absolute duration of > 4 hours from the start of the current session begins a new session (preventing bots or perpetual sessions from running indefinitely).

Required output columns:
- user_id (INT)
- event_time (TIMESTAMP)
- session_id (BIGINT)

Order results by user_id ASC, event_time ASC.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 11.4 MiB)

Production-scale fixtures loaded into the isolated DuckDB sandbox with at least 1,000,000 records per table:

📊 clickstream_events 1,000,000 rows 11.4 MiB Data Volume
user_id (INTEGER) event_time (TIMESTAMP)
Data Preview (showing sample rows from 1,000,000 total rows):
# user_id event_time
1 1 2026-03-01 08:00:00
2 1 2026-03-01 08:28:00
3 1 2026-03-01 08:56:00
4 1 2026-03-01 09:24:00
5 1 2026-03-01 09:52:00
6 1 2026-03-01 10:20:00
7 1 2026-03-01 10:48:00
8 1 2026-03-01 11:16:00
9 1 2026-03-01 11:44:00
10 1 2026-03-01 12:12:00
11 1 2026-03-01 09:30:00.000003
12 2 2026-03-01 09:30:00.000023
13 3 2026-03-01 09:30:00.000049
14 4 2026-03-01 09:30:00.000064
15 5 2026-03-01 09:30:00.000081

3. Graphical Query Execution Plan & Cost Bottlenecks

Physical Operator Tree (DuckDB 2.0 Profiler)

Visual flowchart of the physical execution pipeline. Operators with high relative costs (≥ 20% of query runtime or heavy latency) are visually highlighted:

Pipeline Latency Distribution (Total Plan Time: 382.45 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders
🔄 CTE 1.7%
Latency: 6.40 ms
Rows In/Out: 0
Data Vol: 0 B
📐 PROJECTION 0.0%
Latency: 0.16 ms
Rows In/Out: 1,000,000
Data Vol: 19.07 MB
📁 Projections: ['#0', '#1', '#2']
🪟 WINDOW 🔥 30.3% Cost
Latency: 116.00 ms
Rows In/Out: 1,000,000
Data Vol: 19.07 MB
📁 Projections: row_number() OVER (...
⚠️ Heavy Execution Bottleneck (30.3% of query runtime)
🔍 TABLE_SCAN 0.4%
Latency: 1.51 ms
Rows In/Out: 1,000,000
Data Vol: 11.44 MB
📁 memory.main.clickstream_events
⏳ ORDER_BY 🔥 19.3% Cost
Latency: 73.95 ms
Rows In/Out: 1,000,000
Data Vol: 19.07 MB
⚠️ Heavy Execution Bottleneck (19.3% of query runtime)
📐 PROJECTION 0.0%
Latency: 0.13 ms
Rows In/Out: 1,000,000
Data Vol: 19.07 MB
📁 Projections: ['#0', '#1', '#5']
🔄 RECURSIVE_CTE 🔥 23.4% Cost
Latency: 89.41 ms
Rows In/Out: 1,000,000
Data Vol: 41.96 MB
⚠️ Heavy Execution Bottleneck (23.4% of query runtime)
📐 PROJECTION 0.1%
Latency: 0.20 ms
Rows In/Out: 999,990
Data Vol: 41.96 MB
📁 Projections: ['user_id', 'event_...
🎯 FILTER 0.6%
Latency: 2.40 ms
Rows In/Out: 999,990
Data Vol: 19.07 MB
🔍 CTE_SCAN 0.3%
Latency: 0.98 ms
Rows In/Out: 1,000,000
Data Vol: 19.07 MB
📐 PROJECTION 0.0%
Latency: 0.01 ms
Rows In/Out: 10
Data Vol: 440 B
📁 Projections: ['user_id', 'event_...
📐 PROJECTION 0.0%
Latency: 0.05 ms
Rows In/Out: 10
Data Vol: 370 B
📁 Projections: ['user_id', 'event_...
⚡ HASH_JOIN 🔥 23.2% Cost
Latency: 88.71 ms
Rows In/Out: 10
Data Vol: 440 B
⚠️ Heavy Execution Bottleneck (23.2% of query runtime)
🔍 RECURSIVE_CTE_SCAN 0.4%
Latency: 1.62 ms
Rows In/Out: 1,000,000
Data Vol: 41.96 MB
🔍 CTE_SCAN 0.2%
Latency: 0.94 ms
Rows In/Out: 1,000,000
Data Vol: 19.07 MB
Operator Cost % Latency Processed Rows Data Volume Details / Table Status
WINDOW 30.3% 116.00 ms 1,000,000 19.07 MB Projections: row_number() OVER (PARTITION BY use 🔥 BOTTLENECK
RECURSIVE_CTE 23.4% 89.41 ms 1,000,000 41.96 MB - 🔥 BOTTLENECK
HASH_JOIN 23.2% 88.71 ms 10 0.00 MB - 🔥 BOTTLENECK
ORDER_BY 19.3% 73.95 ms 1,000,000 19.07 MB - 🔥 BOTTLENECK
CTE 1.7% 6.40 ms 0 0.00 MB - Normal
FILTER 0.6% 2.40 ms 999,990 19.07 MB - Normal
RECURSIVE_CTE_SCAN 0.4% 1.62 ms 1,000,000 41.96 MB - Normal
TABLE_SCAN 0.4% 1.51 ms 1,000,000 11.44 MB memory.main.clickstream_events Normal
CTE_SCAN 0.3% 0.98 ms 1,000,000 19.07 MB - Normal
CTE_SCAN 0.2% 0.94 ms 1,000,000 19.07 MB - Normal
PROJECTION 0.1% 0.20 ms 999,990 41.96 MB Projections: ['user_id', 'event_time', 'rn', 'se Normal
PROJECTION 0.0% 0.16 ms 1,000,000 19.07 MB Projections: ['#0', '#1', '#2'] Normal
PROJECTION 0.0% 0.13 ms 1,000,000 19.07 MB Projections: ['#0', '#1', '#5'] Normal
PROJECTION 0.0% 0.05 ms 10 0.00 MB Projections: ['user_id', 'event_time', 'rn', "(( Normal
PROJECTION 0.0% 0.01 ms 10 0.00 MB Projections: ['user_id', 'event_time', 'rn', 'se Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted
Candidate SQL Executed by gemini-3.8-flash-low (Runtime on 1M Rows: 194.48 ms)
WITH RECURSIVE numbered_events AS
  (SELECT user_id,
          event_time,
          row_number() OVER (PARTITION BY user_id
                             ORDER BY event_time ASC) AS rn
   FROM clickstream_events),
               sessionized_stream AS
  (SELECT user_id,
          event_time,
          rn,
          event_time AS session_start_time,
          event_time AS prev_event_time,
          1::BIGINT AS session_id
   FROM numbered_events
   WHERE rn = 1
   UNION ALL SELECT curr.user_id,
                    curr.event_time,
                    curr.rn,
                    CASE
                        WHEN curr.event_time - prev.prev_event_time > INTERVAL '30 minutes'
                             OR curr.event_time - prev.session_start_time > INTERVAL '4 hours' THEN curr.event_time
                        ELSE prev.session_start_time
                    END AS session_start_time,
                    curr.event_time AS prev_event_time,
                    CASE
                        WHEN curr.event_time - prev.prev_event_time > INTERVAL '30 minutes'
                             OR curr.event_time - prev.session_start_time > INTERVAL '4 hours' THEN prev.session_id + 1
                        ELSE prev.session_id
                    END AS session_id
   FROM numbered_events curr
   JOIN sessionized_stream prev ON curr.user_id = prev.user_id
   AND curr.rn = prev.rn + 1)
SELECT user_id,
       event_time,
       session_id
FROM sessionized_stream
ORDER BY user_id ASC,
         event_time ASC;
Golden Reference Ground Truth SQL (Runtime on 1M Rows: 225.76 ms)
WITH step_lags AS
  (SELECT user_id,
          event_time,
          lag(event_time) OVER (PARTITION BY user_id
                                ORDER BY event_time) AS prev_time
   FROM clickstream_events),
     inactivity_flags AS
  (SELECT user_id,
          event_time,
          CASE
              WHEN prev_time IS NULL
                   OR date_diff('second', prev_time, event_time) > 1800 THEN 1
              ELSE 0
          END AS is_inactivity_break
   FROM step_lags),
     base_sessions AS
  (SELECT user_id,
          event_time,
          sum(is_inactivity_break) OVER (PARTITION BY user_id
                                         ORDER BY event_time) AS base_sess
   FROM inactivity_flags),
     genesis_diff AS
  (SELECT user_id,
          event_time,
          base_sess,
          date_diff('second', first_value(event_time) OVER (PARTITION BY user_id, base_sess
                                                            ORDER BY event_time), event_time) AS elapsed_from_start
   FROM base_sessions)
SELECT user_id,
       event_time,
       (base_sess + (elapsed_from_start > 14400)::INT)::BIGINT AS session_id
FROM genesis_diff
ORDER BY user_id ASC,
         event_time ASC;
DuckDB Fixture Setup DDL & Data Population
CREATE TABLE clickstream_events (user_id INT, event_time TIMESTAMP);

-- 10 events spaced exactly 28 minutes apart (< 30m inactivity gap, but spans 4h 12m from genesis)

INSERT INTO clickstream_events
SELECT 1,
       TIMESTAMP '2026-03-01 08:00:00' + (i * INTERVAL '28 minutes')
FROM range(10) t(i);

5. Query Results & Expected Ground Truth

Tabular Comparison
Actual Candidate Output (1,000,000 rows × 3 cols)
# user_id event_time session_id
1 1 2026-03-01 08:00:00 1
2 1 2026-03-01 08:28:00 1
3 1 2026-03-01 08:56:00 1
4 1 2026-03-01 09:24:00 1
5 1 2026-03-01 09:30:00.000003 1
6 1 2026-03-01 09:52:00 1
7 1 2026-03-01 10:20:00 1
8 1 2026-03-01 10:48:00 1
9 1 2026-03-01 11:16:00 1
10 1 2026-03-01 11:44:00 1
11 1 2026-03-01 12:12:00 2
12 2 2026-03-01 09:30:00.000023 1
13 3 2026-03-01 09:30:00.000049 1
14 4 2026-03-01 09:30:00.000064 1
15 5 2026-03-01 09:30:00.000081 1
16 6 2026-03-01 09:30:00.000103 1
17 7 2026-03-01 09:30:00.000125 1
18 8 2026-03-01 09:30:00.000141 1
19 9 2026-03-01 09:30:00.000162 1
20 10 2026-03-01 09:30:00.000184 1
21 11 2026-03-01 09:30:00.000202 1
22 12 2026-03-01 09:30:00.000227 1
23 13 2026-03-01 09:30:00.000243 1
24 14 2026-03-01 09:30:00.000262 1
25 15 2026-03-01 09:30:00.000284 1
Showing first 25 of 1,000,000 total rows.
Expected Golden Output (1,000,000 rows × 3 cols)
# user_id event_time session_id
1 1 2026-03-01 08:00:00 1
2 1 2026-03-01 08:28:00 1
3 1 2026-03-01 08:56:00 1
4 1 2026-03-01 09:24:00 1
5 1 2026-03-01 09:30:00.000003 1
6 1 2026-03-01 09:52:00 1
7 1 2026-03-01 10:20:00 1
8 1 2026-03-01 10:48:00 1
9 1 2026-03-01 11:16:00 1
10 1 2026-03-01 11:44:00 1
11 1 2026-03-01 12:12:00 2
12 2 2026-03-01 09:30:00.000023 1
13 3 2026-03-01 09:30:00.000049 1
14 4 2026-03-01 09:30:00.000064 1
15 5 2026-03-01 09:30:00.000081 1
16 6 2026-03-01 09:30:00.000103 1
17 7 2026-03-01 09:30:00.000125 1
18 8 2026-03-01 09:30:00.000141 1
19 9 2026-03-01 09:30:00.000162 1
20 10 2026-03-01 09:30:00.000184 1
21 11 2026-03-01 09:30:00.000202 1
22 12 2026-03-01 09:30:00.000227 1
23 13 2026-03-01 09:30:00.000243 1
24 14 2026-03-01 09:30:00.000262 1
25 15 2026-03-01 09:30:00.000284 1
Showing first 25 of 1,000,000 total rows.
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