✔ PASS Graph & Hierarchy task_076_Q76_bill_of_materials_recursive_rollup Scaled: 1M+ Records Ordered: Yes

Hierarchical Bill of Materials (BOM) Cost Rollup via Recursive CTE

Candidate Latency (1M Rows)

0.76 ms

(1.1x faster than golden)

Golden Latency (1M Rows)

0.83 ms

DuckDB in-memory engine

Underlying Data Volume

4 rows

240 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 11.3s

✔ 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

Manufacturing an electric vehicle requires thousands of nested parts (Car -> Battery Pack -> Cell Module -> Lithium Cathode). Calculating unit cost requires rolling up quantities across arbitrary depth levels.

⚡ The Frontier Trap (Why LLMs Fail)

Fixed joins only support fixed depth hierarchies (e.g. 3 levels max). If an assembly has 6 levels, fixed joins miss the lowest-tier parts entirely.

Prompt / User Request Given to Model

Manufacturing an electric vehicle requires thousands of nested parts (Car -> Battery Pack -> Cell Module -> Lithium Cathode). Calculating unit cost requires rolling up quantities across arbitrary depth levels.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: child_part, total_qty, depth.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (4 rows • 240 B)

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

📊 bom_parts 4 rows 240 B Data Volume

parent_part (VARCHAR) child_part (VARCHAR) quantity_needed (INTEGER) unit_cost (DECIMAL(10,2))

Data Preview (showing sample rows from 4 total rows):

#	parent_part	child_part	quantity_needed	unit_cost
1	EV_CAR	CHASSIS	1	5,000
2	EV_CAR	BATTERY_PACK	1	0
3	BATTERY_PACK	BATTERY_MODULE	4	0
4	BATTERY_MODULE	LITHIUM_CELL	100	15

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

⏳ ORDER_BY 15.8%

Latency: 0.12 ms

Rows In/Out: 4

Data Vol: 4,192 B

🔄 RECURSIVE_CTE 65.2%

Latency: 0.50 ms

Rows In/Out: 4

Data Vol: 96 B

📐 PROJECTION 0.1%

Latency: 0.00 ms

Rows In/Out: 2

Data Vol: 48 B

📁 Projections: ['child_part', 'tot...

🔍 TABLE_SCAN 2.4%

Latency: 0.02 ms

Rows In/Out: 2

Data Vol: 40 B

📁 memory.main.bom_parts

📐 PROJECTION 1.2%

Latency: 0.01 ms

Rows In/Out: 2

Data Vol: 4,144 B

📁 Projections: ['child_part', 'tot...

⚡ HASH_JOIN 14.0%

Latency: 0.11 ms

Rows In/Out: 2

Data Vol: 4,152 B

🔍 RECURSIVE_CTE_SCAN 0.5%

Latency: 0.00 ms

Rows In/Out: 4

Data Vol: 96 B

🔍 TABLE_SCAN 0.8%

Latency: 0.01 ms

Rows In/Out: 4

Data Vol: 144 B

📁 memory.main.bom_parts

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
RECURSIVE_CTE	65.2%	0.50 ms	4	-	Normal
ORDER_BY	15.8%	0.12 ms	4	-	Normal
HASH_JOIN	14.0%	0.11 ms	2	-	Normal
TABLE_SCAN	2.4%	0.02 ms	2	memory.main.bom_parts	Normal
PROJECTION	1.2%	0.01 ms	2	Projections: ['child_part', 'total_qty', 'depth'	Normal
TABLE_SCAN	0.8%	0.01 ms	4	memory.main.bom_parts	Normal
RECURSIVE_CTE_SCAN	0.5%	0.00 ms	4	-	Normal
PROJECTION	0.1%	0.00 ms	2	Projections: ['child_part', 'total_qty', 'depth'	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH RECURSIVE bom_tree AS
  (-- Anchor: Top-level components of EV_CAR
 SELECT parent_part,
        child_part,
        quantity_needed AS total_qty,
        1 AS depth
   FROM bom_parts
   WHERE parent_part = 'EV_CAR'
   UNION ALL -- Recursive: Multiply quantity down the hierarchy tree
 SELECT t.child_part AS parent_part,
        b.child_part,
        t.total_qty * b.quantity_needed AS total_qty,
        t.depth + 1 AS depth
   FROM bom_tree t
   JOIN bom_parts b ON t.child_part = b.parent_part)
SELECT child_part,
       total_qty,
       depth
FROM bom_tree
ORDER BY depth,
         child_part;

-- Recursively expand BOM tree to compute total quantity of base components
 WITH RECURSIVE bom_tree AS
  (-- Anchor: Top-level components of EV_CAR
 SELECT parent_part,
        child_part,
        quantity_needed AS total_qty,
        1 AS depth
   FROM bom_parts
   WHERE parent_part = 'EV_CAR'
   UNION ALL -- Recursive: Multiply quantity down the hierarchy tree
 SELECT t.child_part AS parent_part,
        b.child_part,
        t.total_qty * b.quantity_needed AS total_qty,
        t.depth + 1 AS depth
   FROM bom_tree t
   JOIN bom_parts b ON t.child_part = b.parent_part)
SELECT child_part,
       total_qty,
       depth
FROM bom_tree
ORDER BY depth,
         child_part;

CREATE TABLE bom_parts (parent_part VARCHAR, child_part VARCHAR, quantity_needed INT, unit_cost decimal(10, 2));


INSERT INTO bom_parts
VALUES ('EV_CAR', 'CHASSIS', 1, 5000.00),
       ('EV_CAR', 'BATTERY_PACK', 1, 0.00),
       ('BATTERY_PACK', 'BATTERY_MODULE', 4, 0.00),
       ('BATTERY_MODULE', 'LITHIUM_CELL', 100, 15.00);

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (4 rows × 3 cols)

#	child_part	total_qty	depth
1	BATTERY_PACK	1	1
2	CHASSIS	1	1
3	BATTERY_MODULE	4	2
4	LITHIUM_CELL	400	3

Expected Golden Output (4 rows × 3 cols)

#	child_part	total_qty	depth
1	BATTERY_PACK	1	1
2	CHASSIS	1	1
3	BATTERY_MODULE	4	2
4	LITHIUM_CELL	400	3

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