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                  |   K | L       | M       | N                  |        O | P                  | Q                  | R                  | S                  | T                  |
|:-----|----:|----:|----:|----:|----:|----:|-----:|:--------|:-------------------|----:|:--------|:--------|:-------------------|---------:|:-------------------|:-------------------|:-------------------|:-------------------|:-------------------|
| 1L1  |   1 |   1 |   1 |   1 |   1 |   1 | 1    | 100     | 100                |   1 | 100     | 10000   | 4800               | 0        | 100                | 100                | 100                | 100                | 100                |
| 1L2  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 50      | 43.478260869565219 |   1 | 50      | 2500    | 907.37240075614363 | 0.929012 | 57.818337596569329 | 60.386473429951693 | 60.386473429951693 | 69.444444444444443 | 69.444444444444443 |
| 1L3  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | False   | 21.739130434782609 |   1 | 0       | 0       | 226.84310018903591 | 0.929012 | 14.516888117214222 | 30.193236714975846 | 30.193236714975846 | 0                  | 0                  |
| 2L1  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 20      | 20                 |   1 | 20      | 400     | 192                | 0.929012 | 24.049332015055437 | 27.777777777777779 | 27.777777777777779 | 27.777777777777779 | 27.777777777777779 |
| 2L2  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 20      | 20                 |   1 | 20      | 400     | 192                | 0.929012 | 24.049332015055437 | 27.777777777777779 | 27.777777777777779 | 27.777777777777779 | 27.777777777777779 |
| 2L3  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 20      | 20                 |   1 | 20      | 400     | 192                | 0.929012 | 24.049332015055437 | 27.777777777777779 | 27.777777777777779 | 27.777777777777779 | 27.777777777777779 |
| 3L1  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 6       | 3.4782608695652173 |   1 | 6       | 36      | 5.807183364839319  | 0.929012 | 6.4338903502902127 | 4.8309178743961354 | 6.4338903502902127 | 8.3333333333333339 | 8.3333333333333339 |
| 3L2  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 6       | 3.4782608695652173 |   1 | 6       | 36      | 5.807183364839319  | 0.929012 | 6.4338903502902127 | 4.8309178743961354 | 6.4338903502902127 | 8.3333333333333339 | 8.3333333333333339 |
| 3L3  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 6       | 1                  |   1 | 6       | 36      | 0.48               | 0.929012 | 6.0370461258736405 | 1.3888888888888888 | 6.0370461258736405 | 8.3333333333333339 | 8.3333333333333339 |
| 8L1  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 8L2  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 8L3  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 9L1  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 9L2  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 9L3  |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 10L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 10L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 10L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 11L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 11L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 11L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 12L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 12L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 12L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 13L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 13L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 13L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 14L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 14L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 14L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 15L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 15L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 15L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 16L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 16L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 16L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 17L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 17L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 17L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 18L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 18L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 18L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 19L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 19L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 19L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 20L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 20L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 20L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 21L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 21L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 21L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 22L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 22L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 22L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |
| 23L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 23L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 23L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 24L1 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 24L2 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | 0       | 0                  |   1 | 0       | 0       | 0                  | 0.929012 | 0                  | 0                  | 0                  | 0                  | 0                  |
| 24L3 |   1 |   1 |   1 |   1 |   1 |   1 | 0.72 | #VALUE! | #VALUE!            |   1 | #VALUE! | #VALUE! | #VALUE!            | 0.929012 | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            | #VALUE!            |



labeled_formulas: D=B*C
G=B*C
G=B*D
E=C*D
F=C*D
G=C*E
G=C*F
G=D*E
G=D*F
G=(B+C)-D
G=(C+D)-E
G=(C+D)-F
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_147324___xlsx_5dd5b4ac4ad0528a4ab64b3542b430b3c2268d46.xlsx___line_606