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 |    7 |    5 |    7 |    0 |    0 |    0 |    0 |    7 |    7 |    0 |
|    0 |    0 |    4 |    2 |    5 |    0 |    0 |    0 |    0 |    5 |    4 |    1 |
|    0 |    1 |    6 |    2 |    6 |    0 |    0 |    0 |    0 |    7 |    6 |    1 |
|    0 |    0 |    4 |    5 |    6 |    1 |    0 |    0 |    0 |    7 |    4 |    3 |
|    0 |    2 |    4 |    3 |    5 |    0 |    0 |    0 |    0 |    7 |    4 |    3 |
|    0 |    0 |    8 |    7 |   12 |    0 |    0 |    0 |    0 |   12 |    8 |    4 |
|    0 |    0 |    4 |    3 |    5 |    1 |    0 |    0 |    0 |    6 |    4 |    2 |
|    0 |    0 |    5 |    4 |    7 |    0 |    0 |    0 |    0 |    7 |    5 |    2 |
|    0 |    0 |    6 |    5 |    7 |    0 |    0 |    0 |    0 |    7 |    6 |    1 |
|    0 |    0 |    7 |    5 |    8 |    1 |    0 |    0 |    0 |    9 |    7 |    2 |
|    0 |    2 |    6 |    6 |    8 |    1 |    0 |    0 |    0 |   11 |    6 |    5 |
|    0 |    0 |   10 |    9 |   12 |    1 |    0 |    0 |    0 |   13 |   10 |    3 |
|    0 |    0 |   13 |    8 |   14 |    0 |    0 |    0 |    0 |   14 |   13 |    1 |
|    0 |    1 |    8 |    4 |    9 |    0 |    1 |    0 |    1 |   11 |    9 |    2 |
|    0 |    1 |   11 |    9 |   13 |    0 |    2 |    0 |    2 |   16 |   13 |    3 |
|    0 |    1 |    9 |    7 |   10 |    2 |    0 |    0 |    0 |   13 |    9 |    4 |
|    0 |    0 |   10 |    6 |   12 |    1 |    0 |    0 |    0 |   13 |   10 |    3 |
|    0 |    0 |    5 |    5 |    7 |    0 |    1 |    0 |    1 |    8 |    6 |    2 |
|    0 |    0 |    0 |    0 |    0 |    0 |    1 |    0 |    1 |    1 |    1 |    0 |
|    0 |    1 |    2 |    4 |    4 |    0 |    1 |    0 |    1 |    6 |    3 |    3 |
|    0 |    0 |    5 |    6 |    7 |    1 |    0 |    0 |    0 |    8 |    5 |    3 |
|    0 |    0 |    3 |    2 |    3 |    2 |    0 |    0 |    0 |    5 |    3 |    2 |
|    0 |    1 |    3 |    4 |    4 |    0 |    0 |    0 |    0 |    5 |    3 |    2 |
|    0 |    0 |    1 |    1 |    1 |    0 |    0 |    0 |    0 |    1 |    1 |    0 |
|    0 |    1 |    3 |    3 |    3 |    0 |    0 |    0 |    0 |    4 |    3 |    1 |
|    0 |    2 |    3 |    3 |    3 |    0 |    1 |    0 |    1 |    6 |    4 |    2 |
|    0 |    1 |    4 |    5 |    5 |    5 |    0 |    0 |    0 |   11 |    4 |    7 |
|    0 |    0 |    9 |    5 |    9 |    7 |    0 |    0 |    0 |   16 |    9 |    7 |
|    0 |    1 |    8 |    8 |   11 |   13 |    0 |    0 |    0 |   25 |    8 |   17 |
|    0 |    2 |    5 |    6 |    7 |   13 |    0 |    0 |    0 |   22 |    6 |   16 |
|    0 |    0 |    2 |    2 |    2 |   12 |    0 |    0 |    0 |   14 |    2 |   12 |
|    0 |    0 |    2 |    6 |    6 |   11 |    0 |    0 |    0 |   17 |    2 |   15 |
|    0 |    1 |    2 |    2 |    2 |   11 |    0 |    0 |    0 |   14 |    2 |   12 |
|    0 |    2 |    3 |    2 |    3 |   14 |    0 |    0 |    0 |   19 |    4 |   15 |
|    0 |    1 |    3 |    3 |    3 |   12 |    0 |    0 |    0 |   16 |    3 |   13 |
|    0 |    0 |    1 |    1 |    1 |   12 |    0 |    0 |    0 |   13 |    1 |   12 |
|    0 |    1 |    2 |    2 |    2 |   12 |    0 |    0 |    0 |   15 |    3 |   12 |
|    0 |    2 |    5 |    7 |    7 |   14 |    1 |    0 |    1 |   24 |    7 |   17 |
|    0 |    1 |    7 |    5 |    8 |   13 |    2 |    0 |    2 |   24 |    9 |   15 |
|    0 |    1 |    6 |    5 |    7 |   12 |    1 |    0 |    1 |   21 |    7 |   14 |
|    0 |    0 |    4 |    4 |    4 |   12 |    0 |    0 |    0 |   16 |    4 |   12 |
|    0 |    0 |    3 |    3 |    3 |   11 |    2 |    0 |    2 |   16 |    5 |   11 |
|    0 |    0 |    3 |    2 |    3 |   11 |    1 |    0 |    1 |   15 |    4 |   11 |
|    0 |    0 |    2 |    2 |    2 |    9 |    1 |    0 |    1 |   12 |    3 |    9 |
|    0 |    0 |    2 |    2 |    2 |    9 |    1 |    0 |    1 |   12 |    3 |    9 |
|    0 |    0 |    3 |    3 |    4 |    9 |    1 |    0 |    1 |   14 |    4 |   10 |
|    0 |    0 |    7 |    6 |    8 |    7 |    1 |    0 |    1 |   16 |    8 |    8 |
|    0 |    0 |    9 |    7 |    9 |    8 |    1 |    0 |    1 |   18 |   10 |    8 |
|    0 |    0 |    5 |    4 |    6 |    8 |    1 |    0 |    1 |   15 |    6 |    9 |
|    0 |    0 |    2 |    2 |    2 |    7 |    0 |    0 |    0 |    9 |    2 |    7 |
|    0 |    1 |    5 |    4 |    6 |    8 |    0 |    0 |    0 |   15 |    6 |    9 |
|    0 |    1 |    5 |    3 |    5 |    8 |    0 |    0 |    0 |   14 |    5 |    9 |
|    0 |    1 |    4 |    4 |    4 |    8 |    0 |    0 |    0 |   13 |    4 |    9 |
|    0 |    0 |    5 |    4 |    5 |    8 |    0 |    0 |    0 |   13 |    5 |    8 |
|    0 |    2 |    7 |    5 |    8 |   10 |    0 |    0 |    0 |   20 |    7 |   13 |
|    0 |    0 |    4 |    4 |    4 |    8 |    0 |    0 |    0 |   12 |    4 |    8 |
|    0 |    0 |    6 |    6 |    7 |    9 |    0 |    0 |    0 |   16 |    6 |   10 |
|    0 |    3 |    5 |    3 |    5 |    7 |    1 |    0 |    1 |   16 |    6 |   10 |
|    0 |    2 |    3 |    3 |    3 |    6 |    0 |    0 |    0 |   11 |    4 |    7 |
|    0 |    0 |    4 |    3 |    4 |    6 |    0 |    0 |    0 |   10 |    4 |    6 |
|    0 |    0 |    4 |    2 |    4 |    7 |    0 |    0 |    0 |   11 |    4 |    7 |
|    0 |    3 |    2 |    2 |    2 |    5 |    1 |    0 |    1 |   11 |    4 |    7 |
|    0 |    2 |    3 |    5 |    5 |    4 |    1 |    0 |    1 |   12 |    4 |    8 |
|    0 |    3 |    5 |    6 |    7 |    3 |    1 |    0 |    1 |   14 |    6 |    8 |
|    0 |    4 |    3 |    3 |    3 |    4 |    2 |    0 |    2 |   13 |    7 |    6 |
|    1 |    4 |    2 |    2 |    2 |    4 |    0 |    0 |    0 |   11 |    3 |    8 |
|    1 |    3 |    6 |    5 |    7 |    4 |    1 |    0 |    1 |   16 |    8 |    8 |
|    2 |    0 |    7 |    5 |    8 |    4 |    0 |    0 |    0 |   14 |    7 |    7 |
|    2 |    1 |    4 |    3 |    5 |    5 |    0 |    0 |    0 |   13 |    4 |    9 |
|    2 |    1 |    2 |    1 |    2 |    4 |    0 |    0 |    0 |    9 |    3 |    6 |
|    2 |    1 |    5 |    2 |    5 |    4 |    0 |    0 |    0 |   12 |    5 |    7 |
|    0 |    1 |    2 |    1 |    2 |    4 |    0 |    0 |    0 |    7 |    2 |    5 |
|    0 |    2 |    1 |    1 |    1 |    6 |    0 |    0 |    0 |    9 |    2 |    7 |
|    0 |    1 |    2 |    1 |    2 |    8 |    3 |    0 |    3 |   14 |    6 |    8 |
|    0 |    2 |    1 |    1 |    1 |    9 |    1 |    0 |    1 |   13 |    4 |    9 |
|    0 |    1 |    1 |    2 |    2 |    9 |    1 |    0 |    1 |   13 |    3 |   10 |
|    1 |    1 |    3 |    3 |    4 |   12 |    2 |    0 |    2 |   20 |    6 |   14 |
|    3 |    2 |    4 |    6 |    7 |   11 |    1 |    0 |    1 |   24 |    5 |   19 |
|    1 |    3 |    4 |    6 |    6 |   11 |    1 |    0 |    1 |   22 |    5 |   17 |
|    1 |    1 |    3 |    4 |    4 |   11 |    1 |    0 |    1 |   18 |    5 |   13 |
|    1 |    1 |    2 |    3 |    4 |   11 |    1 |    0 |    1 |   18 |    4 |   14 |
|    1 |    1 |    2 |    2 |    3 |   11 |    1 |    0 |    1 |   17 |    3 |   14 |
|    0 |    2 |    2 |    1 |    2 |   11 |    1 |    0 |    1 |   16 |    4 |   12 |
|    0 |    3 |    0 |    0 |    0 |   10 |    1 |    0 |    1 |   14 |    2 |   12 |
|    0 |    2 |    0 |    0 |    0 |   10 |    1 |    0 |    1 |   13 |    2 |   11 |
|    0 |    1 |    1 |    1 |    2 |   14 |    0 |    0 |    0 |   17 |    2 |   15 |
|    0 |    1 |    0 |    0 |    0 |    6 |    1 |    0 |    1 |    8 |    1 |    7 |
|    0 |    0 |    0 |    0 |    0 |    6 |    0 |    0 |    0 |    6 |    0 |    6 |
|    0 |    1 |    1 |    1 |    1 |    6 |    0 |    0 |    0 |    8 |    1 |    7 |
|    0 |    0 |    3 |    2 |    3 |    7 |    0 |    0 |    0 |   10 |    3 |    7 |
|    1 |    0 |    1 |    1 |    1 |   12 |    0 |    0 |    0 |   14 |    1 |   13 |
|    0 |    0 |    3 |    6 |    6 |   13 |    1 |    0 |    1 |   20 |    4 |   16 |
|    0 |    3 |    1 |    1 |    1 |    9 |    1 |    0 |    1 |   14 |    2 |   12 |
|    0 |    3 |    2 |    2 |    2 |   11 |    2 |    0 |    2 |   18 |    5 |   13 |
|    0 |    5 |    2 |    2 |    2 |    8 |    1 |    0 |    1 |   16 |    4 |   12 |
|    0 |    0 |    2 |    2 |    2 |    6 |    0 |    0 |    0 |    8 |    2 |    6 |
|    0 |    1 |    2 |    3 |    3 |    4 |    0 |    0 |    0 |    8 |    2 |    6 |
|    0 |    2 |    4 |    5 |    5 |    6 |    1 |    0 |    1 |   14 |    5 |    9 |
|    0 |    3 |    2 |    2 |    2 |    6 |    0 |    0 |    0 |   11 |    2 |    9 |
|    0 |    0 |    2 |    2 |    2 |    6 |    0 |    0 |    0 |    8 |    2 |    6 |
|    0 |    1 |    3 |    2 |    3 |    8 |    0 |    0 |    0 |   12 |    3 |    9 |
|    0 |    5 |    2 |    1 |    2 |    8 |    0 |    0 |    0 |   15 |    3 |   12 |
|    0 |    2 |    1 |    0 |    1 |    7 |    1 |    0 |    1 |   11 |    2 |    9 |
|    1 |    0 |    0 |    0 |    0 |    9 |    0 |    0 |    0 |   10 |    0 |   10 |
|    1 |    0 |    0 |    0 |    0 |    8 |    0 |    0 |    0 |    9 |    0 |    9 |
|    0 |    0 |    0 |    0 |    0 |    7 |    0 |    0 |    0 |    7 |    0 |    7 |
|    0 |    0 |    0 |    0 |    0 |    7 |    1 |    0 |    1 |    8 |    1 |    7 |
|    1 |    1 |    4 |    4 |    6 |    8 |    2 |    0 |    2 |   18 |    7 |   11 |
|    0 |    4 |    1 |    1 |    1 |    9 |    1 |    0 |    1 |   15 |    2 |   13 |
|    0 |    0 |    0 |    0 |    0 |    7 |    0 |    0 |    0 |    7 |    0 |    7 |
|    0 |    0 |    0 |    0 |    0 |    5 |    0 |    0 |    0 |    5 |    0 |    5 |
|    0 |    3 |    0 |    0 |    0 |    6 |    0 |    0 |    0 |    9 |    0 |    9 |
|    0 |    0 |    0 |    0 |    0 |    6 |    1 |    0 |    1 |    7 |    1 |    6 |
|    0 |    0 |    0 |    0 |    0 |    4 |    0 |    0 |    0 |    4 |    0 |    4 |
|    0 |    1 |    6 |    3 |    7 |    9 |    2 |    0 |    2 |   19 |    8 |   11 |
|    1 |    1 |    7 |    4 |    9 |    8 |    1 |    0 |    1 |   20 |    8 |   12 |
|    1 |    1 |    7 |    4 |    8 |    7 |    0 |    0 |    0 |   17 |    7 |   10 |
|    2 |    4 |    7 |    8 |   10 |    7 |    1 |    0 |    1 |   24 |   10 |   14 |
|    2 |    6 |   12 |   15 |   18 |    7 |    0 |    0 |    0 |   33 |   13 |   20 |
|    1 |    7 |    8 |    8 |   13 |    9 |    0 |    0 |    0 |   30 |    9 |   21 |
|    2 |    5 |   15 |   16 |   22 |   11 |    2 |    0 |    2 |   42 |   17 |   25 |
|    1 |    3 |   12 |   14 |   19 |    7 |    0 |    0 |    0 |   30 |   12 |   18 |
|    1 |    4 |   12 |   14 |   19 |    7 |    1 |    0 |    1 |   32 |   14 |   18 |
|    1 |    4 |    6 |   14 |   16 |    4 |    0 |    0 |    0 |   25 |    7 |   18 |
|    0 |    3 |    3 |    4 |    6 |    1 |    0 |    0 |    0 |   10 |    3 |    7 |
|    0 |    2 |    5 |    3 |    7 |    4 |    1 |    0 |    1 |   14 |    6 |    8 |
|    0 |    3 |    1 |    3 |    3 |    1 |    1 |    0 |    1 |    8 |    3 |    5 |
|    0 |    3 |    0 |    4 |    4 |    1 |    0 |    0 |    0 |    8 |    0 |    8 |
|    1 |    3 |    3 |    3 |    5 |    6 |    2 |    0 |    2 |   17 |    5 |   12 |
|    1 |    2 |    4 |    4 |    6 |    9 |    3 |    0 |    3 |   21 |    7 |   14 |
|    1 |    1 |    7 |   10 |   15 |   23 |    3 |    0 |    3 |   43 |   10 |   33 |
|    1 |    2 |    6 |   10 |   13 |   22 |    0 |    0 |    0 |   38 |    6 |   32 |
|    0 |    4 |    7 |   11 |   14 |   20 |    1 |    0 |    1 |   39 |    8 |   31 |
|    0 |    2 |   12 |   13 |   17 |   17 |    1 |    0 |    1 |   37 |   13 |   24 |
|    0 |    2 |    9 |   10 |   14 |   18 |    0 |    0 |    0 |   34 |    9 |   25 |
|    0 |    1 |    9 |    9 |   13 |   23 |    0 |    0 |    0 |   37 |    9 |   28 |
|    4 |    4 |   10 |   13 |   17 |   13 |    1 |    0 |    1 |   39 |   11 |   28 |
|    3 |    3 |    9 |   14 |   16 |   15 |    0 |    0 |    0 |   37 |    9 |   28 |
|    4 |    8 |   10 |   13 |   17 |   17 |    0 |    0 |    0 |   46 |   11 |   35 |
|    7 |    6 |   11 |   15 |   18 |   17 |    0 |    0 |    0 |   48 |   12 |   36 |
|    8 |    6 |   12 |   13 |   17 |   12 |    0 |    0 |    0 |   43 |   14 |   29 |
|    1 |    8 |   12 |   12 |   19 |    9 |    0 |    0 |    0 |   37 |   15 |   22 |
|    3 |   10 |   18 |   20 |   28 |   14 |    0 |    0 |    0 |   55 |   21 |   34 |
|    5 |   11 |    8 |   11 |   15 |   11 |    0 |    0 |    0 |   42 |   10 |   32 |
|    5 |   11 |   10 |   10 |   15 |    9 |    0 |    0 |    0 |   40 |   11 |   29 |
|    0 |    4 |    3 |    7 |    9 |    8 |    0 |    0 |    0 |   21 |    4 |   17 |
|    0 |    2 |    3 |    8 |    9 |    8 |    0 |    0 |    0 |   19 |    3 |   16 |
|    0 |    4 |    3 |    7 |    7 |   10 |    0 |    0 |    0 |   21 |    3 |   18 |
|    0 |    4 |    1 |    5 |    5 |    6 |    0 |    0 |    0 |   15 |    1 |   14 |
|    1 |    3 |    1 |    6 |    6 |    5 |    0 |    0 |    0 |   15 |    1 |   14 |
|    0 |    2 |    2 |    9 |   10 |    9 |    0 |    0 |    0 |   21 |    2 |   19 |
|    5 |    3 |    1 |    6 |    6 |   13 |    0 |    0 |    0 |   27 |    1 |   26 |
|    3 |    1 |    2 |    7 |    7 |    7 |    0 |    0 |    0 |   18 |    2 |   16 |
|    1 |    1 |    3 |    5 |    6 |    4 |    0 |    0 |    0 |   12 |    3 |    9 |
|    0 |    1 |    1 |    4 |    4 |    6 |    0 |    0 |    0 |   11 |    1 |   10 |
|    1 |    5 |    1 |    4 |    4 |    9 |    0 |    0 |    0 |   19 |    2 |   17 |
|    3 |    3 |    2 |    3 |    4 |   11 |    0 |    0 |    0 |   21 |    2 |   19 |
|    1 |    2 |    1 |    3 |    3 |   11 |    0 |    0 |    0 |   17 |    1 |   16 |
|    3 |    1 |    0 |    4 |    4 |   12 |    0 |    0 |    0 |   20 |    0 |   20 |
|    3 |    4 |    0 |    2 |    2 |    7 |    0 |    0 |    0 |   16 |    0 |   16 |
|    2 |    2 |    0 |    1 |    1 |    8 |    1 |    0 |    1 |   14 |    1 |   13 |
|    2 |    3 |    0 |    1 |    1 |    3 |    0 |    0 |    0 |    9 |    0 |    9 |
|    2 |    3 |    0 |    2 |    2 |   10 |    1 |    0 |    1 |   18 |    1 |   17 |
|    2 |    1 |    0 |    1 |    1 |    7 |    0 |    0 |    0 |   11 |    0 |   11 |
|    4 |    6 |    0 |    2 |    2 |    8 |    0 |    0 |    0 |   20 |    0 |   20 |
|    7 |    1 |    6 |    8 |    9 |   14 |    0 |    0 |    0 |   31 |    6 |   25 |
|    4 |    1 |    2 |    5 |    6 |   12 |    0 |    0 |    0 |   23 |    2 |   21 |
|    7 |    5 |    2 |    6 |    7 |   16 |    0 |    0 |    0 |   35 |    3 |   32 |
|    5 |    4 |    3 |    7 |    7 |   23 |    0 |    0 |    0 |   39 |    3 |   36 |
|   11 |    8 |    5 |   14 |   14 |   41 |    1 |    0 |    1 |   75 |    6 |   69 |
|   13 |    7 |    3 |    9 |    9 |   47 |    1 |    0 |    1 |   77 |    4 |   73 |
|   23 |    5 |    7 |   21 |   22 |   29 |    0 |    0 |    0 |   79 |    8 |   71 |
|   27 |    5 |    5 |   16 |   18 |   28 |    0 |    0 |    0 |   78 |    6 |   72 |
|   23 |    5 |    4 |   18 |   19 |   35 |    0 |    0 |    0 |   82 |    5 |   77 |
|   18 |    6 |    0 |   11 |   11 |   29 |    0 |    0 |    0 |   64 |    1 |   63 |
|   17 |   12 |    0 |   11 |   11 |   18 |    0 |    0 |    0 |   58 |    1 |   57 |
|   13 |    8 |    1 |   12 |   12 |   17 |    0 |    0 |    0 |   50 |    2 |   48 |
|   14 |    5 |    1 |    9 |    9 |   13 |    0 |    0 |    0 |   41 |    2 |   39 |
|   11 |    5 |    0 |    2 |    2 |   18 |    1 |    0 |    1 |   37 |    1 |   36 |
|   12 |    3 |    0 |    1 |    1 |   13 |    1 |    0 |    1 |   30 |    1 |   29 |
|    9 |    2 |    0 |    0 |    0 |   10 |    0 |    0 |    0 |   21 |    0 |   21 |
|    9 |    2 |    9 |    6 |   10 |    7 |    0 |    0 |    0 |   28 |    9 |   19 |
|    7 |    2 |    0 |    0 |    0 |    3 |    0 |    0 |    0 |   12 |    0 |   12 |
|    7 |    1 |    1 |    1 |    1 |    0 |    1 |    0 |    1 |   10 |    2 |    8 |
|    6 |    2 |   14 |   16 |   20 |    4 |    0 |    0 |    0 |   32 |   15 |   17 |
|    5 |    1 |   12 |    9 |   14 |    5 |    1 |    0 |    1 |   26 |   13 |   13 |
|    5 |    2 |   10 |   10 |   14 |    5 |    0 |    0 |    0 |   26 |   10 |   16 |
|    4 |    2 |   11 |   10 |   13 |    4 |    0 |    0 |    0 |   23 |   11 |   12 |
|    4 |    2 |   11 |   14 |   17 |   10 |    0 |    0 |    0 |   33 |   12 |   21 |



label: BY=BW+BX
CB=BZ-CA
labeled_formulas: BY=BW+BX
CB=BZ-CA
BY=(BQ*BX)+BW
BY=(BR*BX)+BW
BY=(BS*BX)+BW
BY=(BT*BX)+BW
BY=(BU*BX)+BW
BY=(BV*BX)+BW
BX=(BW-BY)*BZ
BX=(BW-BY)*CA
BX=(BW-BY)*CB
CB=(BX+BZ)-CA
output: {"Arithmetic-Relationship": ["BY=BW+BX", "CB=BZ-CA"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_205478___xlsx_fb4348457d700fea0faafb37f41a851462bc2913.xlsx___line_707