✔ PASS Strict Funnel Precedence task_06_funnel_precedence Scaled: 1M+ Records Ordered: No

Sequential Multi-Stage User Onboarding Conversion Funnel

Candidate Latency (1M Rows)

43.89 ms

(1.6x faster than golden)

Golden Latency (1M Rows)

71.44 ms

DuckDB in-memory engine

Underlying Data Volume

1,000,000 rows

34.3 MiB across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 5.2s

✔ 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

Calculates user conversion through a multi-step sequence where events must strictly obey chronological order.

⚡ The Frontier Trap (Why LLMs Fail)

Frontier models frequently calculate funnel conversions using independent conditional aggregations (COUNT DISTINCT CASE WHEN event = 'purchase'). This completely ignores the chronological order requirement (t_view < t_cart < t_purchase), mistakenly counting users who purchased via separate shortcuts or had events recorded out of sequence as successful sequential conversions.

Prompt / User Request Given to Model

Analyze user conversion across a 3-step marketing funnel using `user_journey_events`:
1. Step 1 (View): The user viewed an item (`event_name = 'view_item'`).
2. Step 2 (Cart): The user added an item to cart (`event_name = 'add_to_cart'`) strictly AFTER their initial view event.
3. Step 3 (Purchase): The user completed a purchase (`event_name = 'purchase'`) strictly AFTER their cart event.

Calculate the count of distinct users reaching each sequential stage in the funnel.

Required output columns:
- total_viewers (BIGINT or INT): Distinct users who viewed an item
- converted_cart (BIGINT or INT): Distinct users who added to cart after viewing
- converted_purchase (BIGINT or INT): Distinct users who purchased after adding to cart

Only a single summary row is returned.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 34.3 MiB)

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

📊 user_journey_events 1,000,000 rows 34.3 MiB Data Volume

event_id (INTEGER) user_id (INTEGER) event_name (VARCHAR) event_time (TIMESTAMP)

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

#	event_id	user_id	event_name	event_time
1	1	1	view_item	2025-01-01 10:00:00
2	2	1	add_to_cart	2025-01-01 10:05:00
3	3	1	purchase	2025-01-01 10:10:00
4	4	2	view_item	2025-01-01 11:00:00
5	5	2	add_to_cart	2025-01-01 11:15:00
6	6	3	view_item	2025-01-01 12:00:00
7	7	4	purchase	2025-01-01 08:00:00
8	8	4	view_item	2025-01-01 09:00:00
9	8	4	click	2026-03-01 09:30:00.000005
10	9	5	view	2026-03-01 09:30:00.000023
11	10	6	add_to_cart	2026-03-01 09:30:00.000050
12	11	7	checkout	2026-03-01 09:30:00.000061
13	12	8	search	2026-03-01 09:30:00.000085
14	13	9	click	2026-03-01 09:30:00.000119
15	14	10	view	2026-03-01 09:30:00.000121

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

📊 UNGROUPED_AGGREGATE 0.0%

Latency: 0.01 ms

Rows In/Out: 1

Data Vol: 24 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 1,344 B

📁 Projections: ['first_cart_time',...

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 1,344 B

📁 Projections: ['first_cart_time',...

📊 HASH_GROUP_BY 0.1%

Latency: 0.24 ms

Rows In/Out: 4

Data Vol: 1,360 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 1,360 B

📁 Projections: ['user_id', 'first_...

⚡ HASH_JOIN 0.1%

Latency: 0.25 ms

Rows In/Out: 4

Data Vol: 1,360 B

🔍 TABLE_SCAN 0.1%

Latency: 0.22 ms

Rows In/Out: 1

Data Vol: 12 B

📁 memory.main.user_journey_events

📊 HASH_GROUP_BY 0.2%

Latency: 0.28 ms

Rows In/Out: 4

Data Vol: 592 B

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 592 B

📁 Projections: ['user_id', 'first_...

⚡ HASH_JOIN 0.1%

Latency: 0.17 ms

Rows In/Out: 4

Data Vol: 592 B

🔍 TABLE_SCAN 0.2%

Latency: 0.28 ms

Rows In/Out: 2

Data Vol: 24 B

📁 memory.main.user_journey_events

🎯 FILTER 1.0%

Latency: 1.68 ms

Rows In/Out: 4

Data Vol: 48 B

📊 HASH_GROUP_BY 🔥 82.6% Cost

Latency: 139.15 ms

Rows In/Out: 999,995

Data Vol: 11.57 MB

📐 PROJECTION 1.6%

Latency: 2.63 ms

Rows In/Out: 1,000,000

Data Vol: 11.56 MB

📁 Projections: ['user_id', "CASE ...

🔍 TABLE_SCAN 14.0%

Latency: 23.50 ms

Rows In/Out: 1,000,000

Data Vol: 26.70 MB

📁 memory.main.user_journey_events

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
HASH_GROUP_BY	82.6%	139.15 ms	999,995	11.57 MB	-	🔥 BOTTLENECK
TABLE_SCAN	14.0%	23.50 ms	1,000,000	26.70 MB	memory.main.user_journey_events	Normal
PROJECTION	1.6%	2.63 ms	1,000,000	11.56 MB	Projections: ['user_id', "CASE WHEN ((event_nam	Normal
FILTER	1.0%	1.68 ms	4	0.00 MB	-	Normal
TABLE_SCAN	0.2%	0.28 ms	2	0.00 MB	memory.main.user_journey_events	Normal
HASH_GROUP_BY	0.2%	0.28 ms	4	0.00 MB	-	Normal
HASH_JOIN	0.1%	0.25 ms	4	0.00 MB	-	Normal
HASH_GROUP_BY	0.1%	0.24 ms	4	0.00 MB	-	Normal
TABLE_SCAN	0.1%	0.22 ms	1	0.00 MB	memory.main.user_journey_events	Normal
HASH_JOIN	0.1%	0.17 ms	4	0.00 MB	-	Normal
UNGROUPED_AGGREGATE	0.0%	0.01 ms	1	0.00 MB	-	Normal
PROJECTION	0.0%	0.00 ms	4	0.00 MB	Projections: ['user_id', 'first_cart_time', 'eve	Normal
PROJECTION	0.0%	0.00 ms	4	0.00 MB	Projections: ['user_id', 'first_view_time', 'eve	Normal
PROJECTION	0.0%	0.00 ms	4	0.00 MB	Projections: ['first_cart_time', 'first_purchase	Normal
PROJECTION	0.0%	0.00 ms	4	0.00 MB	Projections: ['first_cart_time', 'first_purchase	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH user_funnel AS
  (SELECT user_id,
          min(CASE
                  WHEN event_name = 'view_item' THEN event_time
              END) AS first_view_time
   FROM user_journey_events
   GROUP BY user_id
   HAVING min(CASE
                  WHEN event_name = 'view_item' THEN event_time
              END) IS NOT NULL),
     cart_events AS
  (SELECT f.user_id,
          f.first_view_time,
          min(e.event_time) AS first_cart_time
   FROM user_funnel f
   LEFT JOIN user_journey_events e ON f.user_id = e.user_id
   AND e.event_name = 'add_to_cart'
   AND e.event_time > f.first_view_time
   GROUP BY f.user_id,
            f.first_view_time),
     purchase_events AS
  (SELECT c.user_id,
          c.first_cart_time,
          min(e.event_time) AS first_purchase_time
   FROM cart_events c
   LEFT JOIN user_journey_events e ON c.user_id = e.user_id
   AND e.event_name = 'purchase'
   AND c.first_cart_time IS NOT NULL
   AND e.event_time > c.first_cart_time
   GROUP BY c.user_id,
            c.first_cart_time)
SELECT count(user_id) AS total_viewers,
       count(first_cart_time) AS converted_cart,
       count(first_purchase_time) AS converted_purchase
FROM purchase_events;

WITH user_stages AS
  (SELECT user_id,
          min(CASE
                  WHEN event_name = 'view_item' THEN event_time
              END) AS view_time,
          min(CASE
                  WHEN event_name = 'add_to_cart' THEN event_time
              END) AS cart_time,
          min(CASE
                  WHEN event_name = 'purchase' THEN event_time
              END) AS purchase_time
   FROM user_journey_events
   GROUP BY user_id)
SELECT count(CASE
                 WHEN view_time IS NOT NULL THEN 1
             END) AS total_viewers,
       count(CASE
                 WHEN view_time IS NOT NULL
                      AND cart_time > view_time THEN 1
             END) AS converted_cart,
       count(CASE
                 WHEN view_time IS NOT NULL
                      AND cart_time > view_time
                      AND purchase_time > cart_time THEN 1
             END) AS converted_purchase
FROM user_stages;

CREATE TABLE user_journey_events (event_id INT, user_id INT, event_name VARCHAR, event_time TIMESTAMP);


INSERT INTO user_journey_events
VALUES -- User 1: valid sequence (view -> cart -> purchase)
(1, 1, 'view_item', '2025-01-01 10:00:00'),
                                                           (2, 1, 'add_to_cart', '2025-01-01 10:05:00'),
                                                           (3, 1, 'purchase', '2025-01-01 10:10:00'),
                                                           -- User 2: abandoned after cart (view -> cart)
(4, 2, 'view_item', '2025-01-01 11:00:00'),
                                                                                                         (5, 2, 'add_to_cart', '2025-01-01 11:15:00'),
                                                                                                         -- User 3: viewed only
(6, 3, 'view_item', '2025-01-01 12:00:00'),
                                                                                                                               -- User 4: out of order! Purchased before viewing (1-click reorder)
(7, 4, 'purchase', '2025-01-01 08:00:00'),
                                                                                                                                                                                                  (8, 4, 'view_item', '2025-01-01 09:00:00');

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (1 rows × 3 cols)

#	total_viewers	converted_cart	converted_purchase
1	4	2	1

Expected Golden Output (1 rows × 3 cols)

#	total_viewers	converted_cart	converted_purchase
1	4	2	1

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