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:
| A   |   B |   C | D   |   E |   F |   G |   H |   I | J   |
|:----|----:|----:|:----|----:|----:|----:|----:|----:|:----|
| 0   |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   0 |   0 |   0 | --  |
| --  |   0 |   0 | --  |   0 |   0 |   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: I=G+H
labeled_formulas: I=G+H
output: {"Arithmetic-Relationship": ["I=G+H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_503106___xlsx_9604f15c9b3fe1ef659458721b8f90f3b193a19d.xlsx___line_404