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 |
|-------:|:-----------------------------------------|-----:|:----|:----|------:|----:|----:|----:|----:|------:|------:|----:|
| 756815 | Blck & Wht      70cl      12X01          | 5010 | BE2 | BTL |     6 |   0 |   0 |   0 |   0 |     6 |     6 |   0 |
| 681175 | Cardhu          70cl  12Y 06X01          | 5010 | BE2 | BTL |    10 |   0 |   0 |   0 |   0 |    10 |    10 |   0 |
| 714032 | Ciroc           1L        12X01          | 5010 | BE2 | BTL |  7507 |   0 |   0 |   0 |   0 |  7507 |  7507 |   0 |
| 688645 | Ciroc           6L        01X01          | 5010 | BE2 | BTL |     5 |   0 |   0 |   0 |   0 |     5 |     5 |   0 |
| 714041 | Ciroc Coconut   1L        06X01          | 5010 | BE2 | BTL |   279 |   0 |   0 |   0 |   0 |   279 |   279 |   0 |
| 713980 | Ciroc Peach     1L        06X01          | 5010 | BE2 | BTL |     1 |   0 |   0 |   0 |   0 |     1 |     1 |   0 |
| 711535 | Ciroc Pineapple 1L        06X01          | 5010 | BE2 | BTL |     6 |   0 |   0 |   0 |   0 |     6 |     6 |   0 |
| 744473 | Ciroc Red Berry 1L        06X01          | 5010 | BE2 | BTL |   581 |   0 |   0 |   0 |   0 |   581 |   581 |   0 |
| 740612 | Ciroc Smr Colda 1L        12X01          | 5010 | BE2 | BTL |     6 |   0 |   0 |   0 |   0 |     6 |     6 |   0 |
| 735458 | CptMrg Spc Gld  70cl      06X01          | 5010 | BE2 | BTL |    53 |   0 |   0 |   0 |   0 |    53 |    53 |   0 |
| 711670 | Don Julio Blanc 75cl      06X01          | 5010 | BE2 | BTL |     6 |   0 |   0 |   0 |   0 |     6 |     6 |   0 |
| 758811 | Dtown - Sngltn  70cl  12Y 06X01          | 5010 | BE2 | BTL |   480 |   0 |   0 |   0 |   0 |   480 |   480 |   0 |
| 647985 | Gordons Dry Gin 20cl      08X06          | 5010 | BE2 | BTL |   573 |   0 |   0 |   0 |   0 |   573 |   573 |   0 |
| 756013 | Gordons Dry Gin 70cl      12X01          | 5010 | BE2 | BTL |  1074 |   0 |   0 |   0 |   0 |  1074 |  1074 |   0 |
| 649606 | J Wlkr Red 20cl 48X01                    | 5010 | BE2 | BTL |  1488 |   0 |   0 |   0 |   0 |  1488 |  1488 |   0 |
| 646731 | J+B Rare        20cl      04X06          | 5010 | BE2 | BTL | 29480 |   0 |   0 |   0 |   0 | 29480 | 29480 |   0 |
| 751281 | J+B Rare        70cl      12X01          | 5010 | BE2 | BTL |    46 |   0 |   0 |   0 |   0 |    46 |    46 |   0 |
| 746799 | JW Aged 18 Yrs  70cl  18Y 06X01          | 5010 | BE2 | BTL |     2 |   0 |   0 |   0 |   0 |     2 |     2 |   0 |
| 678403 | JW Black        1L    12Y 12X01          | 5010 | BE2 | BTL |    11 |   0 |   0 |   0 |   0 |    11 |    11 |   0 |
| 703777 | JW Black        37.5c 12Y 24X01          | 5010 | BE2 | BTL |   248 |   0 |   0 |   0 |   0 |   248 |   248 |   0 |
| 756483 | JW Black        70cl  12Y 12X01          | 5010 | BE2 | BTL |   625 |   0 |   0 |   0 |   0 |   625 |   625 |   0 |
| 760979 | JW Black        70cl  12Y 12X01 icons    | 5010 | BE2 | BTL |   153 |   0 |   0 |   0 |   0 |   153 |   153 |   0 |
| 751894 | JW BlkLbl PcktS 20cl  12Y 04X12          | 5010 | BE2 | BTL |  4272 |   0 |   0 |   0 |   0 |  4272 |  4272 |   0 |
| 756522 | JW Blue         70cl      03X01 VAPRIGID | 5010 | BE2 | BTL |    21 |   0 |   0 |   0 |   0 |    21 |    21 |   0 |
| 688866 | JW Blue         70cl      06X01          | 5010 | BE2 | BTL |    23 |   0 |   0 |   0 |   0 |    23 |    23 |   0 |
| 733837 | JW Gold Rsv     70cl      06X01          | 5010 | BE2 | BTL |     1 |   0 |   0 |   0 |   0 |     1 |     1 |   0 |
| 756377 | JW Gold Rsv     70cl      06X01 VAP F20  | 5010 | BE2 | BTL |    12 |   0 |   0 |   0 |   0 |    12 |    12 |   0 |
| 756119 | JW GOT SngOfFir 70cl      12X01 GOT      | 5010 | BE2 | BTL |   336 |   0 |   0 |   0 |   0 |   336 |   336 |   0 |
| 756120 | JW GOT SngOfIce 70cl      12X01 GOT      | 5010 | BE2 | BTL |   336 |   0 |   0 |   0 |   0 |   336 |   336 |   0 |
| 752462 | JW Red          1L        12X01          | 5010 | BE2 | BTL |    63 |   0 |   0 |   0 |   0 |    63 |    63 |   0 |
| 697171 | JW Red          20cl      24X01          | 5010 | BE2 | BTL |    26 |   0 |   0 |   0 |   0 |    26 |    26 |   0 |
| 713764 | JW Red          3L        03X01 CRADLE   | 5010 | BE2 | BTL |   114 |   0 |   0 |   0 |   0 |   114 |   114 |   0 |
| 756664 | JW Red          70cl      06X01 TUMBLER  | 5010 | BE2 | BTL |    18 |   0 |   0 |   0 |   0 |    18 |    18 |   0 |
| 752425 | JW Red          70cl      12X01          | 5010 | BE2 | BTL | 14830 |   0 |   0 |   0 |   0 | 14830 | 14830 |   0 |
| 717191 | JW Red          70cl      12X01 Electric | 5010 | BE2 | BTL |   176 |   0 |   0 |   0 |   0 |   176 |   176 |   0 |
| 760946 | JW Red          70cl      12X01 ICONS    | 5010 | BE2 | BTL |   329 |   0 |   0 |   0 |   0 |   329 |   329 |   0 |
| 751895 | JW RedLbl PcktS 20cl      04X12          | 5010 | BE2 | BTL |    45 |   0 |   0 |   0 |   0 |    45 |    45 |   0 |
| 714276 | Ketel One Vodka 1L 12X01                 | 5010 | BE2 | BTL |   516 |   0 |   0 |   0 |   0 |   516 |   516 |   0 |
| 711209 | Smir Blue       1L        12X01          | 5010 | BE2 | BTL |    26 |   0 |   0 |   0 |   0 |    26 |    26 |   0 |
| 716654 | Smir Citrus     1L        12X01          | 5010 | BE2 | BTL |   362 |   0 |   0 |   0 |   0 |   362 |   362 |   0 |
| 716884 | Smir Gr Apple   1L        12X01          | 5010 | BE2 | BTL |  1092 |   0 |   0 |   0 |   0 |  1092 |  1092 |   0 |
| 716664 | Smir Orange     1L        12X01          | 5010 | BE2 | BTL |   805 |   0 |   0 |   0 |   0 |   805 |   805 |   0 |
| 716716 | Smir Raspberry  1L        12X01          | 5010 | BE2 | BTL |   439 |   0 |   0 |   0 |   0 |   439 |   439 |   0 |
| 660242 | Smir Red 20cl 08X06                      | 5010 | BE2 | BTL | 10267 |   0 |   0 |   0 |   0 | 10267 | 10267 |   0 |
| 646724 | Tanq Lndn Gin   70cl      06X01          | 5010 | BE2 | BTL |    11 |   0 |   0 |   0 |   0 |    11 |    11 |   0 |
| 697509 | Tanq Ten        70cl      06X01          | 5010 | BE2 | BTL |    27 |   0 |   0 |   0 |   0 |    27 |    27 |   0 |
| 708388 | White Horse Fo  70cl      12X01          | 5010 | BE2 | BTL |  6957 |   0 |   0 |   0 |   0 |  6957 |  6957 |   0 |
| 746673 | Wht Walker JW   70cl      12X01          | 5010 | BE2 | BTL | 32322 |   0 |   0 |   0 |   0 | 32322 | 32322 |   0 |
| 701308 | Zacapa Cent 23  75cl      06X01          | 5010 | BE2 | BTL |   222 |   0 |   0 |   0 |   0 |   222 |   222 |   0 |
| 712907 | Zacapa Cent XO  75cl      06X01          | 5010 | BE2 | BTL |   113 |   0 |   0 |   0 |   0 |   113 |   113 |   0 |



label: M=L-K
labeled_formulas: M=L-K
H=A*G
I=A*G
J=A*G
M=A*G
H=C*G
I=C*G
J=C*G
M=C*G
K=F+H
L=F+H
K=F+I
L=F+I
K=F+J
L=F+J
M=F-K
M=F-L
H=G*K
H=G*L
I=G*K
I=G*L
J=G*K
J=G*L
L=G+K
M=G*K
M=G*L
H=(A+C)*G
I=(A+C)*G
J=(A+C)*G
M=(A+C)*G
K=(A*G)+F
L=(A*G)+F
K=(A*H)+F
L=(A*H)+F
K=(A*I)+F
L=(A*I)+F
K=(A*J)+F
L=(A*J)+F
K=(A*M)+F
L=(A*M)+F
H=(A*G)*K
H=(A*G)*L
I=(A*G)*K
I=(A*G)*L
J=(A*G)*K
J=(A*G)*L
L=(A*G)+K
M=(A*G)*K
M=(A*G)*L
K=(C*G)+F
L=(C*G)+F
K=(C*H)+F
L=(C*H)+F
K=(C*I)+F
L=(C*I)+F
K=(C*J)+F
L=(C*J)+F
K=(C*M)+F
L=(C*M)+F
H=(C*G)*K
H=(C*G)*L
I=(C*G)*K
I=(C*G)*L
J=(C*G)*K
J=(C*G)*L
L=(C*G)+K
M=(C*G)*K
M=(C*G)*L
output: {"Arithmetic-Relationship": ["M=L-K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_108302___xlsx_22510594b1afd3b54e8e93af5a608d1b060223b6.xlsx___line_141