✖ VALUE_MISMATCH Graph & Hierarchy task_087_Q87_circular_fx_arbitrage_triangle Scaled: 1M+ Records Ordered: No

Triangular FX Currency Arbitrage Detection (Loop Profitability)

Candidate Latency (1M Rows)

0.26 ms

(1.1x faster than golden)

Golden Latency (1M Rows)

0.28 ms

DuckDB in-memory engine

Underlying Data Volume

3 rows

144 B across 1 table

Evaluated Model

gemini-3.8-flash-low

Gen Latency: 4.3s

⚠️ Failure Analysis (VALUE_MISMATCH)

Reason: Data discrepancy: DataFrame.iloc[:, 5] (column name="profit_margin_pct") are different

Data discrepancy: DataFrame.iloc[:, 5] (column name="profit_margin_pct") are different

1. Analytical Significance & What It Means

Scenario & Frontier Trap

Business Scenario & Problem

High-frequency FX trading bots scan for triangular arbitrage where converting USD -> EUR -> JPY -> USD yields more than 1.00 USD after exchange rates.

⚡ The Frontier Trap (Why LLMs Fail)

Missing currency conversion bid-ask spreads causes false positive arbitrage signals that lose money in practice.

Prompt / User Request Given to Model

High-frequency FX trading bots scan for triangular arbitrage where converting USD -> EUR -> JPY -> USD yields more than 1.00 USD after exchange rates.

Execute the required analytical SQL calculation in DuckDB.
Expected output columns: curr_start, curr_mid1, curr_mid2, curr_end, loop_multiplier, profit_margin_pct.
Row order does not matter.

2. Underlying Tables, Row Counts & Data Volume

1 Tables (3 rows • 144 B)

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

📊 fx_pairs 3 rows 144 B Data Volume

from_curr (VARCHAR) to_curr (VARCHAR) exchange_rate (DOUBLE)

Data Preview (showing sample rows from 3 total rows):

#	from_curr	to_curr	exchange_rate
1	USD	EUR	0.92
2	EUR	JPY	160
3	JPY	USD	0.0069

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

📐 PROJECTION 3.2%

Latency: 0.01 ms

Rows In/Out: 3

Data Vol: 240 B

📁 Projections: ['curr_start', 'cur...

📐 PROJECTION 1.8%

Latency: 0.00 ms

Rows In/Out: 3

Data Vol: 168 B

📁 Projections: ['curr_start', 'cur...

⚡ HASH_JOIN 44.8%

Latency: 0.12 ms

Rows In/Out: 3

Data Vol: 216 B

⚡ HASH_JOIN 37.2%

Latency: 0.10 ms

Rows In/Out: 3

Data Vol: 192 B

🔍 TABLE_SCAN 5.0%

Latency: 0.01 ms

Rows In/Out: 3

Data Vol: 120 B

📁 memory.main.fx_pairs

🔍 TABLE_SCAN 4.0%

Latency: 0.01 ms

Rows In/Out: 3

Data Vol: 120 B

📁 memory.main.fx_pairs

🔍 TABLE_SCAN 4.1%

Latency: 0.01 ms

Rows In/Out: 3

Data Vol: 120 B

📁 memory.main.fx_pairs

Operator	Cost %	Latency	Processed Rows	Details / Table	Status
HASH_JOIN	44.8%	0.12 ms	3	-	Normal
HASH_JOIN	37.2%	0.10 ms	3	-	Normal
TABLE_SCAN	5.0%	0.01 ms	3	memory.main.fx_pairs	Normal
TABLE_SCAN	4.1%	0.01 ms	3	memory.main.fx_pairs	Normal
TABLE_SCAN	4.0%	0.01 ms	3	memory.main.fx_pairs	Normal
PROJECTION	3.2%	0.01 ms	3	Projections: ['curr_start', 'curr_mid1', 'curr_m	Normal
PROJECTION	1.8%	0.00 ms	3	Projections: ['curr_start', 'curr_mid1', 'curr_m	Normal

4. Queries Executed (Candidate vs Golden Ground Truth)

Beautified & Syntax Highlighted

SELECT leg1.from_curr AS curr_start,
       leg1.to_curr AS curr_mid1,
       leg2.to_curr AS curr_mid2,
       leg3.to_curr AS curr_end,
       leg1.exchange_rate * leg2.exchange_rate * leg3.exchange_rate AS loop_multiplier,
       (leg1.exchange_rate * leg2.exchange_rate * leg3.exchange_rate - 1.0) * 100.0 AS profit_margin_pct
FROM fx_pairs AS leg1
JOIN fx_pairs AS leg2 ON leg1.to_curr = leg2.from_curr
JOIN fx_pairs AS leg3 ON leg2.to_curr = leg3.from_curr
WHERE leg1.from_curr = leg3.to_curr
  AND leg1.exchange_rate * leg2.exchange_rate * leg3.exchange_rate > 1.0;

-- Detect 3-hop triangular arbitrage opportunities where effective rate > 1.005

SELECT a.from_curr AS curr_start,
       a.to_curr AS curr_mid1,
       b.to_curr AS curr_mid2,
       c.to_curr AS curr_end,
       round(a.exchange_rate * b.exchange_rate * c.exchange_rate, 4) AS loop_multiplier,
       round((a.exchange_rate * b.exchange_rate * c.exchange_rate - 1.0) * 100, 2) AS profit_margin_pct
FROM fx_pairs a
JOIN fx_pairs b ON a.to_curr = b.from_curr
JOIN fx_pairs c ON b.to_curr = c.from_curr
AND c.to_curr = a.from_curr
WHERE (a.exchange_rate * b.exchange_rate * c.exchange_rate) > 1.005;

CREATE TABLE fx_pairs (from_curr VARCHAR, to_curr VARCHAR, exchange_rate DOUBLE);


INSERT INTO fx_pairs
VALUES ('USD', 'EUR', 0.92),
       ('EUR', 'JPY', 160.0),
       ('JPY', 'USD', 0.0069); -- Arbitrage loop: 0.92 * 160 * 0.0069 = 1.01568 (+1.5% profit)

5. Query Results & Expected Ground Truth

Tabular Comparison

Actual Candidate Output (3 rows × 6 cols)

#	curr_start	curr_mid1	curr_mid2	curr_end	loop_multiplier	profit_margin_pct
1	JPY	USD	EUR	JPY	1.0157	1.568
2	USD	EUR	JPY	USD	1.0157	1.568
3	EUR	JPY	USD	EUR	1.0157	1.568

Expected Golden Output (3 rows × 6 cols)

#	curr_start	curr_mid1	curr_mid2	curr_end	loop_multiplier	profit_margin_pct
1	JPY	USD	EUR	JPY	1.0157	1.57
2	USD	EUR	JPY	USD	1.0157	1.57
3	EUR	JPY	USD	EUR	1.0157	1.57

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