✔ PASS Temporal & Time-Series task_021_Q21_temporal_gap_detection Scaled: 1M+ Records Ordered: Yes

Continuous Asset Lease Unallocated Gap Discovery

Candidate Latency (1M Rows)

46.28 ms

(1.1x slower than golden)

Golden Latency (1M Rows)

41.04 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: 17.3s

✔ 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

Fleet managers track commercial vehicles to find idle 'unrented' gaps between back-to-back rental contracts for fleet utilization auditing.

⚡ The Frontier Trap (Why LLMs Fail)

Comparing each row with LEAD without filtering where next_start > current_end misses adjacent non-overlapping bookings.

Prompt / User Request Given to Model

Fleet managers track commercial vehicles to find idle 'unrented' gaps between back-to-back rental contracts for fleet utilization auditing.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: vehicle_id, gap_start, gap_end, idle_days.
Results should be ordered as specified.

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:

📊 vehicle_leases 1,000,000 rows 11.4 MiB Data Volume

vehicle_id (INTEGER) lease_start (DATE) lease_end (DATE)

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

#	vehicle_id	lease_start	lease_end
1	55	2026-01-01 00:00:00	2026-01-10 00:00:00
2	55	2026-01-15 00:00:00	2026-01-20 00:00:00
3	55	2026-01-20 00:00:00	2026-01-30 00:00:00
4	55	2026-01-01 00:00:00	2026-01-01 00:00:00
5	56	2026-01-02 00:00:00	2026-01-02 00:00:00
6	57	2026-01-03 00:00:00	2026-01-03 00:00:00
7	58	2026-01-04 00:00:00	2026-01-04 00:00:00
8	59	2026-01-05 00:00:00	2026-01-05 00:00:00
9	60	2026-01-06 00:00:00	2026-01-06 00:00:00
10	61	2026-01-07 00:00:00	2026-01-07 00:00:00
11	62	2026-01-08 00:00:00	2026-01-08 00:00:00
12	63	2026-01-09 00:00:00	2026-01-09 00:00:00
13	64	2026-01-10 00:00:00	2026-01-10 00:00:00
14	65	2026-01-11 00:00:00	2026-01-11 00:00:00
15	66	2026-01-12 00:00:00	2026-01-12 00:00:00

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

⏳ ORDER_BY 0.3%

Latency: 0.56 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: ['vehicle_id', 'gap...

📐 PROJECTION 0.0%

Latency: 0.00 ms

Rows In/Out: 1

Data Vol: 12 B

📁 Projections: ['#0', '#1', '#3']

🎯 FILTER 0.5%

Latency: 0.79 ms

Rows In/Out: 1

Data Vol: 16 B

📐 PROJECTION 0.1%

Latency: 0.20 ms

Rows In/Out: 1,000,000

Data Vol: 15.38 MB

📁 Projections: ['#0', '#1', '#2', ...

🪟 WINDOW 🔥 98.3% Cost

Latency: 173.13 ms

Rows In/Out: 1,000,000

Data Vol: 15.38 MB

📁 Projections: lead(lease_start, 1...

🔍 TABLE_SCAN 0.8%

Latency: 1.38 ms

Rows In/Out: 1,000,000

Data Vol: 11.44 MB

📁 memory.main.vehicle_leases

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
WINDOW	98.3%	173.13 ms	1,000,000	15.38 MB	Projections: lead(lease_start, 1, NULL::DATE) OV	🔥 BOTTLENECK
TABLE_SCAN	0.8%	1.38 ms	1,000,000	11.44 MB	memory.main.vehicle_leases	Normal
FILTER	0.5%	0.79 ms	1	0.00 MB	-	Normal
ORDER_BY	0.3%	0.56 ms	1	0.00 MB	-	Normal
PROJECTION	0.1%	0.20 ms	1,000,000	15.38 MB	Projections: ['#0', '#1', '#2', '#3']	Normal
PROJECTION	0.0%	0.00 ms	1	0.00 MB	Projections: ['vehicle_id', 'gap_start', 'gap_en	Normal
PROJECTION	0.0%	0.00 ms	1	0.00 MB	Projections: ['#0', '#1', '#3']	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH lease_boundaries AS
  (SELECT vehicle_id,
          lease_end AS gap_start,
          lead(lease_start) OVER (PARTITION BY vehicle_id
                                  ORDER BY lease_start) AS gap_end
   FROM vehicle_leases)
SELECT vehicle_id,
       gap_start,
       gap_end,
       (gap_end - gap_start) AS idle_days
FROM lease_boundaries
WHERE gap_end IS NOT NULL
  AND gap_end > gap_start
ORDER BY vehicle_id,
         gap_start;

-- Identify idle intervals between vehicle leases
 WITH lease_boundaries AS
  (SELECT vehicle_id,
          lease_end AS gap_start,
          lead(lease_start) OVER (PARTITION BY vehicle_id
                                  ORDER BY lease_start) AS gap_end
   FROM vehicle_leases)
SELECT vehicle_id,
       gap_start,
       gap_end,
       (gap_end - gap_start) AS idle_days
FROM lease_boundaries
WHERE gap_end IS NOT NULL
  AND gap_end > gap_start
ORDER BY vehicle_id,
         gap_start;

CREATE TABLE vehicle_leases (vehicle_id INT, lease_start DATE, lease_end DATE);


INSERT INTO vehicle_leases
VALUES (55, '2026-01-01', '2026-01-10'),
       (55, '2026-01-15', '2026-01-20'),
       -- 5 day gap (Jan 10 - Jan 15)
 (55, '2026-01-20', '2026-01-30'); -- contiguous

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (1 rows × 4 cols)

#	vehicle_id	gap_start	gap_end	idle_days
1	55	2026-01-10 00:00:00	2026-01-15 00:00:00	5

Expected Golden Output (1 rows × 4 cols)

#	vehicle_id	gap_start	gap_end	idle_days
1	55	2026-01-01 00:00:00	2026-01-15 00:00:00	14

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