✔ PASS Warehouse & Statistical task_102_Q102_equi_depth_dynamic_binning_ntile Scaled: 1M+ Records Ordered: Yes

Dynamic Equi-Depth Histogram Binning via NTILE in Pure SQL

Candidate Latency (1M Rows)

47.93 ms

(1.1x faster than golden)

Golden Latency (1M Rows)

52.28 ms

DuckDB in-memory engine

Underlying Data Volume

1,000,000 rows

19.1 MiB across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 5.1s

✔ 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

Creating balanced feature histograms for ML requires equal-depth binning (each bucket contains an equal number of records) rather than equal-width binning.

⚡ The Frontier Trap (Why LLMs Fail)

Equal-width bins leave high-value tail bins completely empty on skewed power-law distributions.

Prompt / User Request Given to Model

Creating balanced feature histograms for ML requires equal-depth binning (each bucket contains an equal number of records) rather than equal-width binning.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: spend_quartile, customer_count, min_spend_in_bin, max_spend_in_bin, avg_spend_in_bin.
Results should be ordered as specified.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (1,000,000 rows • 19.1 MiB)

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

📊 customer_spend 1,000,000 rows 19.1 MiB Data Volume

customer_id (INTEGER) annual_spend (DECIMAL(10,2))

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

#	customer_id	annual_spend
1	1	20
2	2	35
3	3	50
4	4	150
5	5	300
6	6	500
7	7	1,200
8	8	5,000
9	8	2,339.57
10	9	1,010.32
11	10	2,094.28
12	11	885.98
13	12	0.01
14	13	0.01
15	14	3,009.36

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

⏳ ORDER_BY 0.1%

Latency: 0.15 ms

Rows In/Out: 4

Data Vol: 160 B

📐 PROJECTION 0.0%

Latency: 0.01 ms

Rows In/Out: 4

Data Vol: 160 B

📁 Projections: ['spend_quartile', ...

📊 HASH_GROUP_BY 11.6%

Latency: 12.47 ms

Rows In/Out: 4

Data Vol: 160 B

📐 PROJECTION 0.1%

Latency: 0.09 ms

Rows In/Out: 1,000,000

Data Vol: 30.52 MB

📁 Projections: ['spend_quartile', ...

📐 PROJECTION 0.1%

Latency: 0.07 ms

Rows In/Out: 1,000,000

Data Vol: 15.26 MB

📁 Projections: ['#0', '#1']

🪟 WINDOW 🔥 87.4% Cost

Latency: 93.93 ms

Rows In/Out: 1,000,000

Data Vol: 15.26 MB

📁 Projections: ntile(4) OVER (ORDE...

🔍 TABLE_SCAN 0.7%

Latency: 0.73 ms

Rows In/Out: 1,000,000

Data Vol: 7.63 MB

📁 memory.main.customer_spend

Operator	Cost %	Latency	Processed Rows	Data Volume	Details / Table	Status
WINDOW	87.4%	93.93 ms	1,000,000	15.26 MB	Projections: ntile(4) OVER (ORDER BY annual_spen	🔥 BOTTLENECK
HASH_GROUP_BY	11.6%	12.47 ms	4	0.00 MB	-	Normal
TABLE_SCAN	0.7%	0.73 ms	1,000,000	7.63 MB	memory.main.customer_spend	Normal
ORDER_BY	0.1%	0.15 ms	4	0.00 MB	-	Normal
PROJECTION	0.1%	0.09 ms	1,000,000	30.52 MB	Projections: ['spend_quartile', 'annual_spend',	Normal
PROJECTION	0.1%	0.07 ms	1,000,000	15.26 MB	Projections: ['#0', '#1']	Normal
PROJECTION	0.0%	0.01 ms	4	0.00 MB	Projections: ['spend_quartile', 'customer_count'	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

WITH binned_spend AS
  (SELECT customer_id,
          annual_spend,
          ntile(4) OVER (
                         ORDER BY annual_spend ASC) AS spend_quartile
   FROM customer_spend)
SELECT spend_quartile,
       count(*) AS customer_count,
       min(annual_spend) AS min_spend_in_bin,
       max(annual_spend) AS max_spend_in_bin,
       round(avg(annual_spend), 2) AS avg_spend_in_bin
FROM binned_spend
GROUP BY spend_quartile
ORDER BY spend_quartile ASC;

-- Partition customers into 4 equal-depth spending quartiles (bins)
 WITH binned AS
  (SELECT customer_id,
          annual_spend,
          ntile(4) OVER (
                         ORDER BY annual_spend ASC) AS spend_quartile
   FROM customer_spend)
SELECT spend_quartile,
       count(*) AS customer_count,
       min(annual_spend) AS min_spend_in_bin,
       max(annual_spend) AS max_spend_in_bin,
       round(avg(annual_spend), 2) AS avg_spend_in_bin
FROM binned
GROUP BY spend_quartile
ORDER BY spend_quartile;

CREATE TABLE customer_spend (customer_id INT, annual_spend decimal(10, 2));


INSERT INTO customer_spend
VALUES (1, 20.00),
       (2, 35.00),
       (3, 50.00),
       (4, 150.00),
       (5, 300.00),
       (6, 500.00),
       (7, 1200.00),
       (8, 5000.00);

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (4 rows × 5 cols)

#	spend_quartile	customer_count	min_spend_in_bin	max_spend_in_bin	avg_spend_in_bin
1	1	250,000	0.01	0.01	0.01
2	2	250,000	0.01	906.23	377.29
3	3	250,000	906.23	2,053.43	1,458.74
4	4	250,000	2,053.43	9,162.11	3,067.2

Expected Golden Output (4 rows × 5 cols)

#	spend_quartile	customer_count	min_spend_in_bin	max_spend_in_bin	avg_spend_in_bin
1	1	250,000	0.01	0.01	0.01
2	2	250,000	0.01	906.23	377.29
3	3	250,000	906.23	2,053.43	1,458.74
4	4	250,000	2,053.43	9,162.11	3,067.2

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