Task: Arithmetic-Relationship (source dataset: Auto-Relate)

You are given a table with numerical values in multiple columns. Your task is to analyze the data and identify semantic relationships, expressed in arithmetic relationships, that exist between columns.

These relationships may involve any combination of the following operations: addition (+), subtraction (−), multiplication (*), and division (/). The expressions can involve two or more columns and may be nested (e.g., B = (A + C) / D).

Please only identify arithmetic relationships that hold semantically based on the data, and do not return relationships that are likely spurious, e.g., (A = B * 0), where A is an all 0 column. Please only return minimal atomic relationships, e.g., if A = B + C and D = E + F, then there is no need to return A = B + C + E + F - D.

No explanation, return all the formula(s) in JSON format: {"Arithmetic-Relationship": [<list-of-formulas>]}. If no relationship is found, return {"Arithmetic-Relationship": []}.

Input Table:
|   J |   K |   L |
|----:|----:|----:|
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |
|   0 |   0 |   0 |



label: L=J+K
labeled_formulas: L=J+K
output: {"Arithmetic-Relationship": ["L=J+K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_619103___xlsx_562b15428099b1dc2d502f4891cefc19b1d69f93.xlsx___line_375