✔ PASS Temporal & Time-Series task_016_Q16_sequential_funnel_precedence Scaled: 1M+ Records Ordered: No

Chronological Multi-Stage Conversion Funnel with Time Boundaries

Candidate Latency (1M Rows)

35.96 ms

(1.2x slower than golden)

Golden Latency (1M Rows)

31.10 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: 22.6s

✔ 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

In product funnels (Signup -> Verify -> Purchase), events must occur in exact chronological order, with each step completed within 24 hours of the previous.

⚡ The Frontier Trap (Why LLMs Fail)

Models join events without checking timestamp ordering (e.g., verifying after purchase), artificially inflating funnel conversion.

Prompt / User Request Given to Model

In product funnels (Signup -> Verify -> Purchase), events must occur in exact chronological order, with each step completed within 24 hours of the previous.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: total_signups, verified_users, completed_purchasers, end_to_end_conversion_pct.
Row order does not matter.

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:

📊 user_actions 1,000,000 rows 30.5 MiB Data Volume

user_id (INTEGER) stage (VARCHAR) action_time (TIMESTAMP)

Data Preview (showing sample rows from 1,000,000 total rows):

#	user_id	stage	action_time
1	1	signup	2026-03-01 10:00:00
2	1	verify	2026-03-01 11:00:00
3	1	purchase	2026-03-01 15:00:00
4	2	signup	2026-03-01 10:00:00
5	2	purchase	2026-03-01 10:30:00
6	2	signup	2026-03-01 09:30:00.000006
7	3	verify	2026-03-01 09:30:00.000024
8	4	purchase	2026-03-01 09:30:00.000046
9	5	signup	2026-03-01 09:30:00.000066
10	6	verify	2026-03-01 09:30:00.000084
11	7	purchase	2026-03-01 09:30:00.000108
12	8	signup	2026-03-01 09:30:00.000139
13	9	verify	2026-03-01 09:30:00.000141
14	10	purchase	2026-03-01 09:30:00.000171
15	11	signup	2026-03-01 09:30:00.000187

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: 61.29 ms) Nodes consuming ≥ 20% of query runtime are highlighted with glowing borders

🔄 CTE 5.1%

Latency: 3.15 ms

Rows In/Out: 0

Data Vol: 0 B

🔍 TABLE_SCAN 🔥 22.1% Cost

Latency: 13.53 ms

Rows In/Out: 333,334

Data Vol: 3.81 MB

📁 memory.main.user_actions

🔄 CTE 0.0%

Latency: 0.00 ms

Rows In/Out: 0

Data Vol: 0 B

📊 HASH_GROUP_BY 0.4%

Latency: 0.22 ms

Rows In/Out: 1

Data Vol: 20 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 20 B

📁 Projections: ['user_id', 'signup...

⚡ HASH_JOIN 🔥 37.1% Cost

Latency: 22.77 ms

Rows In/Out: 1

Data Vol: 20 B

🔍 CTE_SCAN 0.4%

Latency: 0.23 ms

Rows In/Out: 333,334

Data Vol: 3.81 MB

🔍 TABLE_SCAN 🔥 23.6% Cost

Latency: 14.44 ms

Rows In/Out: 333,333

Data Vol: 3.81 MB

📁 memory.main.user_actions

📐 PROJECTION 0.1%

Latency: 0.03 ms

Rows In/Out: 1

Data Vol: 32 B

📁 Projections: ['total_signups', '...

📊 UNGROUPED_AGGREGATE 0.8%

Latency: 0.51 ms

Rows In/Out: 1

Data Vol: 24 B

📐 PROJECTION 0.0%

Latency: 0.03 ms

Rows In/Out: 333,334

Data Vol: 2.62 MB

📁 Projections: ['user_id', 'user_i...

⚡ HASH_JOIN 4.7%

Latency: 2.90 ms

Rows In/Out: 333,334

Data Vol: 2.62 MB

⚡ HASH_JOIN 5.0%

Latency: 3.05 ms

Rows In/Out: 333,334

Data Vol: 2.58 MB

🔍 CTE_SCAN 0.3%

Latency: 0.18 ms

Rows In/Out: 333,334

Data Vol: 3.81 MB

📊 HASH_GROUP_BY 0.2%

Latency: 0.13 ms

Rows In/Out: 1

Data Vol: 20 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 20 B

📁 Projections: ['user_id', 'signup...

⚡ HASH_JOIN 0.1%

Latency: 0.08 ms

Rows In/Out: 1

Data Vol: 20 B

🔍 TABLE_SCAN 0.1%

Latency: 0.03 ms

Rows In/Out: 1

Data Vol: 12 B

📁 memory.main.user_actions

🔍 CTE_SCAN 0.0%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 20 B

🔍 CTE_SCAN 0.0%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 20 B

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
HASH_JOIN	37.1%	22.77 ms	1	0.00 MB	-	🔥 BOTTLENECK
TABLE_SCAN	23.6%	14.44 ms	333,333	3.81 MB	memory.main.user_actions	🔥 BOTTLENECK
TABLE_SCAN	22.1%	13.53 ms	333,334	3.81 MB	memory.main.user_actions	🔥 BOTTLENECK
CTE	5.1%	3.15 ms	0	0.00 MB	-	Normal
HASH_JOIN	5.0%	3.05 ms	333,334	2.58 MB	-	Normal
HASH_JOIN	4.7%	2.90 ms	333,334	2.62 MB	-	Normal
UNGROUPED_AGGREGATE	0.8%	0.51 ms	1	0.00 MB	-	Normal
CTE_SCAN	0.4%	0.23 ms	333,334	3.81 MB	-	Normal
HASH_GROUP_BY	0.4%	0.22 ms	1	0.00 MB	-	Normal
CTE_SCAN	0.3%	0.18 ms	333,334	3.81 MB	-	Normal
HASH_GROUP_BY	0.2%	0.13 ms	1	0.00 MB	-	Normal
HASH_JOIN	0.1%	0.08 ms	1	0.00 MB	-	Normal
PROJECTION	0.1%	0.03 ms	1	0.00 MB	Projections: ['total_signups', 'verified_users',	Normal
TABLE_SCAN	0.1%	0.03 ms	1	0.00 MB	memory.main.user_actions	Normal
PROJECTION	0.0%	0.03 ms	333,334	2.62 MB	Projections: ['user_id', 'user_id']	Normal
CTE	0.0%	0.00 ms	0	0.00 MB	-	Normal
CTE_SCAN	0.0%	0.00 ms	1	0.00 MB	-	Normal
CTE_SCAN	0.0%	0.00 ms	1	0.00 MB	-	Normal
PROJECTION	0.0%	0.00 ms	1	0.00 MB	Projections: ['user_id', 'signup_time', 'action_	Normal
PROJECTION	0.0%	0.00 ms	1	0.00 MB	Projections: ['user_id', 'signup_time', 'verify_	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH step1 AS
  (SELECT user_id,
          action_time AS signup_time
   FROM user_actions
   WHERE stage = 'signup'),
     step2 AS
  (SELECT s1.user_id,
          s1.signup_time,
          min(a.action_time) AS verify_time
   FROM step1 s1
   JOIN user_actions a ON s1.user_id = a.user_id
   AND a.stage = 'verify'
   AND a.action_time >= s1.signup_time
   AND a.action_time <= s1.signup_time + INTERVAL '24 hours'
   GROUP BY s1.user_id,
            s1.signup_time),
     step3 AS
  (SELECT s2.user_id,
          s2.signup_time,
          s2.verify_time,
          min(a.action_time) AS purchase_time
   FROM step2 s2
   JOIN user_actions a ON s2.user_id = a.user_id
   AND a.stage = 'purchase'
   AND a.action_time >= s2.verify_time
   AND a.action_time <= s2.verify_time + INTERVAL '24 hours'
   GROUP BY s2.user_id,
            s2.signup_time,
            s2.verify_time)
SELECT count(s1.user_id) AS total_signups,
       count(s2.user_id) AS verified_users,
       count(s3.user_id) AS completed_purchasers,
       round(count(s3.user_id) * 100.0 / count(s1.user_id), 1) AS end_to_end_conversion_pct
FROM step1 s1
LEFT JOIN step2 s2 ON s1.user_id = s2.user_id
LEFT JOIN step3 s3 ON s1.user_id = s3.user_id;

-- Enforce Signup -> Verify -> Purchase chronological order
 WITH step1 AS
  (SELECT user_id,
          action_time AS signup_time
   FROM user_actions
   WHERE stage = 'signup'),
      step2 AS
  (SELECT s1.user_id,
          s1.signup_time,
          min(a.action_time) AS verify_time
   FROM step1 s1
   JOIN user_actions a ON s1.user_id = a.user_id
   AND a.stage = 'verify'
   AND a.action_time >= s1.signup_time
   AND a.action_time <= s1.signup_time + INTERVAL '24 hours'
   GROUP BY s1.user_id,
            s1.signup_time),
      step3 AS
  (SELECT s2.user_id,
          s2.signup_time,
          s2.verify_time,
          min(a.action_time) AS purchase_time
   FROM step2 s2
   JOIN user_actions a ON s2.user_id = a.user_id
   AND a.stage = 'purchase'
   AND a.action_time >= s2.verify_time
   AND a.action_time <= s2.verify_time + INTERVAL '24 hours'
   GROUP BY s2.user_id,
            s2.signup_time,
            s2.verify_time)
SELECT count(s1.user_id) AS total_signups,
       count(s2.user_id) AS verified_users,
       count(s3.user_id) AS completed_purchasers,
       round(count(s3.user_id) * 100.0 / count(s1.user_id), 1) AS end_to_end_conversion_pct
FROM step1 s1
LEFT JOIN step2 s2 ON s1.user_id = s2.user_id
LEFT JOIN step3 s3 ON s1.user_id = s3.user_id;

CREATE TABLE user_actions (user_id INT, stage VARCHAR, action_time TIMESTAMP);


INSERT INTO user_actions
VALUES (1, 'signup', '2026-03-01 10:00:00'),
       (1, 'verify', '2026-03-01 11:00:00'),
       (1, 'purchase', '2026-03-01 15:00:00'),
       (2, 'signup', '2026-03-01 10:00:00'),
       (2, 'purchase', '2026-03-01 10:30:00'); -- Skipped verify

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (1 rows × 4 cols)

#	total_signups	verified_users	completed_purchasers	end_to_end_conversion_pct
1	333,334	1	1	0

Expected Golden Output (1 rows × 4 cols)

#	total_signups	verified_users	completed_purchasers	end_to_end_conversion_pct
1	333,334	1	1	0

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