✔ PASS Temporal & Time-Series task_004_Q04_dual_bound_session_capping Scaled: 1M+ Records Ordered: Yes

Sliding Sessionization with Absolute Maximum Duration Cap

Candidate Latency (1M Rows)
408.07 ms
(1.0x slower than golden)
Golden Latency (1M Rows)
399.69 ms
DuckDB in-memory engine
Underlying Data Volume
1,000,000 rows
30.5 MiB across 1 table
Evaluated Model
gemini-3.8-flash-low
Gen Latency: 18.8s
✔ 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

Real-world web sessions often need dual constraints: a 30-minute inactivity timeout AND a strict maximum 4-hour absolute session duration to prevent bots from maintaining endless sessions.

⚡ The Frontier Trap (Why LLMs Fail)

A simple inactivity check keeps sessions alive indefinitely if events happen every 10 minutes. Tracking session origin requires window frames with state.

Prompt / User Request Given to Model
Real-world web sessions often need dual constraints: a 30-minute inactivity timeout AND a strict maximum 4-hour absolute session duration to prevent bots from maintaining endless sessions.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: user_id, event_time, action, raw_session_id, minutes_since_session_start.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 30.5 MiB)

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

📊 bot_events 1,000,000 rows 30.5 MiB Data Volume
user_id (INTEGER) event_time (TIMESTAMP) action (VARCHAR)
Data Preview (showing sample rows from 1,000,000 total rows):
# user_id event_time action
1 1 2026-03-01 00:00:00 ping
2 1 2026-03-01 02:00:00 ping
3 1 2026-03-01 04:30:00 ping
4 1 2026-03-01 04:45:00 ping
5 1 2026-03-01 09:30:00.000010 click
6 2 2026-03-01 09:30:00.000025 view
7 3 2026-03-01 09:30:00.000056 add_to_cart
8 4 2026-03-01 09:30:00.000062 checkout
9 5 2026-03-01 09:30:00.000098 search
10 6 2026-03-01 09:30:00.000106 click
11 7 2026-03-01 09:30:00.000123 view
12 8 2026-03-01 09:30:00.000145 add_to_cart
13 9 2026-03-01 09:30:00.000163 checkout
14 10 2026-03-01 09:30:00.000182 search
15 11 2026-03-01 09:30:00.000217 click

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: 924.62 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders
📐 PROJECTION 0.8%
Latency: 7.18 ms
Rows In/Out: 1,000,000
Data Vol: 49.59 MB
📁 Projections: ['#0', '#1', '__int...
⏳ ORDER_BY 🔥 12.4% Cost
Latency: 114.20 ms
Rows In/Out: 1,000,000
Data Vol: 49.59 MB
⚠️ Heavy Execution Bottleneck (12.4% of query runtime)
📐 PROJECTION 1.0%
Latency: 9.52 ms
Rows In/Out: 1,000,000
Data Vol: 49.59 MB
📁 Projections: ['#0', '#1', '__int...
📐 PROJECTION 0.5%
Latency: 4.84 ms
Rows In/Out: 1,000,000
Data Vol: 49.59 MB
📁 Projections: ['user_id', 'event_...
📐 PROJECTION 0.0%
Latency: 0.26 ms
Rows In/Out: 1,000,000
Data Vol: 49.59 MB
📁 Projections: ['#0', '#1', '#2', ...
🪟 WINDOW 🔥 33.9% Cost
Latency: 313.54 ms
Rows In/Out: 1,000,000
Data Vol: 49.59 MB
📁 Projections: first_value(event_t...
⚠️ Heavy Execution Bottleneck (33.9% of query runtime)
📐 PROJECTION 0.0%
Latency: 0.13 ms
Rows In/Out: 1,000,000
Data Vol: 41.96 MB
📁 Projections: ['user_id', 'event_...
📐 PROJECTION 0.0%
Latency: 0.25 ms
Rows In/Out: 1,000,000
Data Vol: 45.78 MB
📁 Projections: ['#0', '#1', '#2', ...
🪟 WINDOW 🔥 25.0% Cost
Latency: 231.58 ms
Rows In/Out: 1,000,000
Data Vol: 45.78 MB
📁 Projections: sum_no_overflow(gap...
⚠️ Heavy Execution Bottleneck (25.0% of query runtime)
📐 PROJECTION 0.2%
Latency: 1.80 ms
Rows In/Out: 1,000,000
Data Vol: 30.52 MB
📁 Projections: ['user_id', 'event_...
📐 PROJECTION 0.0%
Latency: 0.16 ms
Rows In/Out: 1,000,000
Data Vol: 34.45 MB
📁 Projections: ['#0', '#1', '#2', ...
🪟 WINDOW 🔥 24.6% Cost
Latency: 227.19 ms
Rows In/Out: 1,000,000
Data Vol: 34.45 MB
📁 Projections: lag(event_time, 1, ...
⚠️ Heavy Execution Bottleneck (24.6% of query runtime)
🔍 TABLE_SCAN 1.5%
Latency: 13.97 ms
Rows In/Out: 1,000,000
Data Vol: 26.70 MB
📁 memory.main.bot_events
Operator Cost % Latency Processed Rows Data Volume Details / Table Status
WINDOW 33.9% 313.54 ms 1,000,000 49.59 MB Projections: first_value(event_time) OVER (PARTI 🔥 BOTTLENECK
WINDOW 25.0% 231.58 ms 1,000,000 45.78 MB Projections: sum_no_overflow(gap_split) OVER (PA 🔥 BOTTLENECK
WINDOW 24.6% 227.19 ms 1,000,000 34.45 MB Projections: lag(event_time, 1, NULL::TIMESTAMP) 🔥 BOTTLENECK
ORDER_BY 12.4% 114.20 ms 1,000,000 49.59 MB - 🔥 BOTTLENECK
TABLE_SCAN 1.5% 13.97 ms 1,000,000 26.70 MB memory.main.bot_events Normal
PROJECTION 1.0% 9.52 ms 1,000,000 49.59 MB Projections: ['#0', '#1', '__internal_compress_s Normal
PROJECTION 0.8% 7.18 ms 1,000,000 49.59 MB Projections: ['#0', '#1', '__internal_decompress Normal
PROJECTION 0.5% 4.84 ms 1,000,000 49.59 MB Projections: ['user_id', 'event_time', 'action', Normal
PROJECTION 0.2% 1.80 ms 1,000,000 30.52 MB Projections: ['user_id', 'event_time', 'action', Normal
PROJECTION 0.0% 0.26 ms 1,000,000 49.59 MB Projections: ['#0', '#1', '#2', '#3', '#4'] Normal
PROJECTION 0.0% 0.25 ms 1,000,000 45.78 MB Projections: ['#0', '#1', '#2', '#3', '#4'] Normal
PROJECTION 0.0% 0.16 ms 1,000,000 34.45 MB Projections: ['#0', '#1', '#2', '#3'] Normal
PROJECTION 0.0% 0.13 ms 1,000,000 41.96 MB Projections: ['user_id', 'event_time', 'action', 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: 408.07 ms)
-- Partition sessions by inactivity (>30m) OR exceeding 4 hours from session start
WITH ranked_events AS
  (SELECT user_id,
          event_time,
          action,
          lag(event_time) OVER (PARTITION BY user_id
                                ORDER BY event_time) AS prev_time
   FROM bot_events),
     step_flags AS
  (SELECT user_id,
          event_time,
          action,
          CASE
              WHEN prev_time IS NULL THEN 1
              WHEN date_diff('minute', prev_time, event_time) > 30 THEN 1
              ELSE 0
          END AS gap_split
   FROM ranked_events),
     base_sessions AS
  (SELECT *,
          sum(gap_split) OVER (PARTITION BY user_id
                               ORDER BY event_time) AS raw_session_id
   FROM step_flags)
SELECT user_id,
       event_time,
       action,
       raw_session_id, -- Measure elapsed minutes from session genesis
 date_diff('minute', first_value(event_time) OVER (PARTITION BY user_id, raw_session_id
                                                   ORDER BY event_time), event_time) AS minutes_since_session_start
FROM base_sessions
ORDER BY user_id,
         event_time;
Golden Reference Ground Truth SQL (Runtime on 1M Rows: 399.69 ms)
-- Partition sessions by inactivity (>30m) OR exceeding 4 hours from session start
 WITH ranked_events AS
  (SELECT user_id,
          event_time,
          action,
          lag(event_time) OVER (PARTITION BY user_id
                                ORDER BY event_time) AS prev_time
   FROM bot_events),
      step_flags AS
  (SELECT user_id,
          event_time,
          action,
          CASE
              WHEN prev_time IS NULL THEN 1
              WHEN date_diff('minute', prev_time, event_time) > 30 THEN 1
              ELSE 0
          END AS gap_split
   FROM ranked_events),
      base_sessions AS
  (SELECT *,
          sum(gap_split) OVER (PARTITION BY user_id
                               ORDER BY event_time) AS raw_session_id
   FROM step_flags)
SELECT user_id,
       event_time,
       action,
       raw_session_id, -- Measure elapsed minutes from session genesis
 date_diff('minute', first_value(event_time) OVER (PARTITION BY user_id, raw_session_id
                                                   ORDER BY event_time), event_time) AS minutes_since_session_start
FROM base_sessions
ORDER BY user_id,
         event_time;
DuckDB Fixture Setup DDL & Data Population
CREATE TABLE bot_events (user_id INT, event_time TIMESTAMP, action VARCHAR);


INSERT INTO bot_events
VALUES (1, '2026-03-01 00:00:00', 'ping'),
       (1, '2026-03-01 02:00:00', 'ping'),
       -- +2 hrs
 (1, '2026-03-01 04:30:00', 'ping'),
 -- +4.5 hrs (exceeds 4h cap)
 (1, '2026-03-01 04:45:00', 'ping');

5. Query Results & Expected Ground Truth

Tabular Comparison
Actual Candidate Output (1,000,000 rows × 5 cols)
# user_id event_time action raw_session_id minutes_since_session_start
1 1 2026-03-01 00:00:00 ping 1 0
2 1 2026-03-01 02:00:00 ping 2 0
3 1 2026-03-01 04:30:00 ping 3 0
4 1 2026-03-01 04:45:00 ping 3 15
5 1 2026-03-01 09:30:00.000010 click 4 0
6 2 2026-03-01 09:30:00.000025 view 1 0
7 3 2026-03-01 09:30:00.000056 add_to_cart 1 0
8 4 2026-03-01 09:30:00.000062 checkout 1 0
9 5 2026-03-01 09:30:00.000098 search 1 0
10 6 2026-03-01 09:30:00.000106 click 1 0
11 7 2026-03-01 09:30:00.000123 view 1 0
12 8 2026-03-01 09:30:00.000145 add_to_cart 1 0
13 9 2026-03-01 09:30:00.000163 checkout 1 0
14 10 2026-03-01 09:30:00.000182 search 1 0
15 11 2026-03-01 09:30:00.000217 click 1 0
16 12 2026-03-01 09:30:00.000224 view 1 0
17 13 2026-03-01 09:30:00.000242 add_to_cart 1 0
18 14 2026-03-01 09:30:00.000271 checkout 1 0
19 15 2026-03-01 09:30:00.000290 search 1 0
20 16 2026-03-01 09:30:00.000303 click 1 0
21 17 2026-03-01 09:30:00.000329 view 1 0
22 18 2026-03-01 09:30:00.000340 add_to_cart 1 0
23 19 2026-03-01 09:30:00.000368 checkout 1 0
24 20 2026-03-01 09:30:00.000386 search 1 0
25 21 2026-03-01 09:30:00.000403 click 1 0
Showing first 25 of 1,000,000 total rows.
Expected Golden Output (1,000,000 rows × 5 cols)
# user_id event_time action raw_session_id minutes_since_session_start
1 1 2026-03-01 00:00:00 ping 1 0
2 1 2026-03-01 02:00:00 ping 2 0
3 1 2026-03-01 04:30:00 ping 3 0
4 1 2026-03-01 04:45:00 ping 3 15
5 1 2026-03-01 09:30:00.000010 click 4 0
6 2 2026-03-01 09:30:00.000025 view 1 0
7 3 2026-03-01 09:30:00.000056 add_to_cart 1 0
8 4 2026-03-01 09:30:00.000062 checkout 1 0
9 5 2026-03-01 09:30:00.000098 search 1 0
10 6 2026-03-01 09:30:00.000106 click 1 0
11 7 2026-03-01 09:30:00.000123 view 1 0
12 8 2026-03-01 09:30:00.000145 add_to_cart 1 0
13 9 2026-03-01 09:30:00.000163 checkout 1 0
14 10 2026-03-01 09:30:00.000182 search 1 0
15 11 2026-03-01 09:30:00.000217 click 1 0
16 12 2026-03-01 09:30:00.000224 view 1 0
17 13 2026-03-01 09:30:00.000242 add_to_cart 1 0
18 14 2026-03-01 09:30:00.000271 checkout 1 0
19 15 2026-03-01 09:30:00.000290 search 1 0
20 16 2026-03-01 09:30:00.000303 click 1 0
21 17 2026-03-01 09:30:00.000329 view 1 0
22 18 2026-03-01 09:30:00.000340 add_to_cart 1 0
23 19 2026-03-01 09:30:00.000368 checkout 1 0
24 20 2026-03-01 09:30:00.000386 search 1 0
25 21 2026-03-01 09:30:00.000403 click 1 0
Showing first 25 of 1,000,000 total rows.
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