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:
|   BQ |   BR |   BS |   BT |   BU |   BV |   BW |   BX |   BY |   BZ |   CA |   CB |
|-----:|-----:|-----:|-----:|-----:|-----:|-----:|-----:|-----:|-----:|-----:|-----:|
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    1 |    1 |    0 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    1 |    1 |    0 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    1 |    1 |    0 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    2 |    2 |    0 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    1 |    1 |    0 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    4 |    0 |    0 |    0 |    4 |    0 |    4 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    1 |    1 |    0 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    3 |    0 |    0 |    0 |    3 |    0 |    3 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |    0 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    1 |    1 |    3 |    0 |    0 |    0 |    4 |    0 |    4 |
|    0 |    0 |    0 |    2 |    2 |    4 |    0 |    0 |    0 |    6 |    0 |    6 |
|    0 |    0 |    0 |    1 |    1 |   11 |    0 |    0 |    0 |   12 |    0 |   12 |
|    0 |    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    1 |    0 |    0 |    0 |    1 |    0 |    1 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |
|    0 |    0 |    0 |    0 |    0 |    2 |    0 |    0 |    0 |    2 |    0 |    2 |



label: BY=BW+BX
CB=BZ-CA
labeled_formulas: BY=BW+BX
CB=BZ-CA
BR=BQ*BS
BR=BQ*BT
BR=BQ*BU
BQ=BR*BV
BR=BQ*CA
BQ=BS*BV
BS=BQ*CA
BQ=BS*CB
BU=BQ+BT
BW=BQ*BT
BX=BQ*BT
BY=BQ*BT
BW=BQ*BU
BX=BQ*BU
BY=BQ*BU
BW=BQ*BV
BX=BQ*BV
BY=BQ*BV
BQ=BV*CA
BW=BQ*BZ
BW=BQ*CB
BX=BQ*BZ
BX=BQ*CB
BY=BQ*BZ
BY=BQ*CB
BQ=CA*CB
BS=BR*BT
BS=BR*BU
BR=BS*BV
BS=BR*CA
BR=BS*CB
BU=BR+BT
BW=BR*BT
BX=BR*BT
BY=BR*BT
CA=BR*BT
BW=BR*BU
BX=BR*BU
BY=BR*BU
CA=BR*BU
BW=BR*BV
BX=BR*BV
BY=BR*BV
BR=BV*CA
BW=BR*BZ
BW=BR*CB
BX=BR*BZ
BX=BR*CB
BY=BR*BZ
BY=BR*CB
BR=(BQ*BS)*BT
BR=(BQ*BS)*BU
BR=(BQ*BS)*BV
BR=(BQ*BS)*BZ
CA=(BQ*BR)+BS
BR=(BQ*BS)*CB
BU=(BQ*BR)+BT
BQ=(BR*BT)*BV
BR=(BQ*BT)*BZ
BR=(BQ*BT)*CA
BR=(BQ*BT)*CB
BQ=(BR*BU)*BV
BR=(BQ*BU)*BZ
BR=(BQ*BU)*CA
BR=(BQ*BU)*CB
BQ=(BR*BV)*BZ
BR=(BQ*BV)*CA
BQ=(BR*BV)*CB
BR=(BQ*BZ)*CA
BR=(BZ-CB)*BQ
BR=(BQ*CA)*CB
BU=(BQ*BS)+BT
BQ=(BS*BT)*BV
CA=(BQ+BT)*BS
BQ=(BS*BT)*CB
BQ=(BS*BU)*BV
BQ=(BU-BZ)*BS
BQ=(BS*BU)*CB
BQ=(BS*BV)*BZ
CA=(BQ+BV)*BS
BQ=(BS*BV)*CB
CA=(BQ+BZ)*BS
BS=(BZ-CB)*BQ
CA=(BQ+CB)*BS
BQ=(BT-BU)*BV
BU=(BQ*BZ)+BT
BU=(BQ*CA)+BT
BQ=(BT-BU)*CB
BW=(BQ*BT)*BV
BX=(BQ*BT)*BV
BY=(BQ*BT)*BV
BZ=(BQ+BT)+BV
BQ=(BT*BV)*CA
CB=(BQ+BT)+BV
BW=(BQ*BT)*BZ
BW=(BQ*BT)*CB
BX=(BQ*BT)*BZ
BX=(BQ*BT)*CB
BY=(BQ*BT)*BZ
BY=(BQ*BT)*CB
output: {"Arithmetic-Relationship": ["BY=BW+BX", "CB=BZ-CA"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_205488___xlsx_fb4348457d700fea0faafb37f41a851462bc2913.xlsx___line_708