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 |
|:---------|:----|:--------------------------------------------------|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|--------:|
| 2        | -   | EDGEDALE                                          | 427 |   0 |  32 |  16 |   5 |  25 |   6 |   2 |  86 |   0 |   0 |   0 | 20.1405 |
| 3        | -   | EDGEMONT ESTATES                                  | 455 |   0 |  42 |  23 |  11 |  47 |   6 |   4 | 133 |   0 |   0 |   0 | 29.2308 |
| 4        | -   | EDGEMONT BAY                                      | 385 |   1 |  31 |  27 |   4 |  66 |  15 |   1 | 145 |   0 |   0 |   0 | 37.6623 |
| 6        | -   | EDENSTONE                                         | 501 |   2 |  40 |  48 |   7 |  45 |  13 |   6 | 161 |   0 |   0 |   0 | 32.1357 |
| 7        | -   | EDGEWOOD                                          | 421 |   0 |  33 |  19 |   3 |  11 |   2 |   2 |  70 |   0 |   0 |   0 | 16.6271 |
| 8        | -   | EDGELAND                                          | 482 |   0 |  49 |  23 |   6 |  38 |   6 |   2 | 124 |   0 |   0 |   0 | 25.7261 |
| 9        | -   | EDGEBYNE                                          | 325 |   2 |  43 |  26 |   4 |  41 |   4 |   5 | 125 |   0 |   0 |   0 | 38.4615 |
| 10       | -   | EDGEVIEW                                          | 441 |   0 |  30 |  44 |   5 |  59 |  13 |   8 | 159 |   0 |   0 |   0 | 36.0544 |
| 11       | -   | EDFORTH                                           | 523 |   0 |  51 |  47 |  11 |  63 |  16 |  10 | 198 |   0 |   0 |   0 | 37.8585 |
| 12       | -   | EDCATH                                            | 486 |   2 |  46 |  40 |  12 |  63 |   4 |  10 | 177 |   0 |   0 |   0 | 36.4198 |
| 16       | -   | EDGEVALLEY                                        | 488 |   0 |  16 |  40 |   2 |  37 |   9 |  14 | 118 |   0 |   0 |   0 | 24.1803 |
| 17       | -   | EDGEVALLEY LANDING                                | 412 |   1 |  20 |  26 |   3 |  58 |   7 |   7 | 122 |   0 |   0 |   0 | 29.6117 |
| 18       | -   | EDGEBURN                                          | 489 |   1 |  25 |  23 |   2 |  32 |   2 |   8 |  93 |   0 |   0 |   0 | 19.0184 |
| 21       | -   | EDGERIDGE TERRACE                                 | 486 |   1 |  21 |  13 |   2 |  33 |   8 |   6 |  84 |   0 |   0 |   0 | 17.284  |
| 23       | -   | EDGEBROOK COVE                                    | 437 |   0 |  31 |  34 |   3 |  25 |   2 |  20 | 115 |   0 |   0 |   0 | 26.3158 |
| 24       | -   | EDGEBROOK CLOSE                                   | 339 |   0 |  30 |  43 |   6 |  43 |   5 |  10 | 137 |   0 |   0 |   0 | 40.413  |
| 25       | -   | EDGEBROOK PARK                                    | 472 |   0 |  27 |  25 |   4 |  37 |   7 |   3 | 103 |   0 |   0 |   0 | 21.822  |
| 26       | -   | EDGERIDGE VIEW                                    | 499 |   2 |  36 |  36 |   5 |  35 |   6 |  15 | 135 |   0 |   0 |   0 | 27.0541 |
| 29/30    | -   | HIDDEN COVE / HIDDENVALLEY LANDING                | 896 |   1 |  58 |  74 |   5 |  97 |  12 |   6 | 253 |   0 |   0 |   0 | 28.2366 |
| 31/32    | -   | HIDDENVALLEY VALE / HIDDENVALLEY PLACE            | 982 |   2 |  76 |  78 |   3 |  77 |   8 |  12 | 256 |   0 |   0 |   0 | 26.0692 |
| 39/40    | -   | HIDDENRANCH ROAD / HIDDENHILLS PLACE              | 881 |   0 | 109 |  41 |  15 |  54 |  26 |  17 | 262 |   0 |   0 |   0 | 29.7389 |
| 41       | -   | HIDDENHILLS ROAD                                  | 407 |   1 |  35 |  28 |   3 |  25 |  13 |  11 | 116 |   0 |   0 |   0 | 28.5012 |
| 44       | -   | HAMPSTEAD WAY                                     | 522 |   0 |  10 |  23 |   1 |  53 |   4 |   8 |  99 |   0 |   0 |   0 | 18.9655 |
| 45       | -   | HAMPSTEAD CIRCLE                                  | 636 |   0 |  14 |  57 |   2 |  39 |   3 |  12 | 127 |   0 |   0 |   0 | 19.9686 |
| 47/54    | -   | HAMPSHIRE GROVE / CITADEL                         | 857 |   2 |  33 |  44 |   7 |  65 |  10 |  11 | 172 |   0 |   0 |   0 | 20.07   |
| 48       | -   | HAMPTON MEWS                                      | 584 |   0 |  19 |  25 |   3 |  56 |  11 |   8 | 122 |   0 |   0 |   0 | 20.8904 |
| 50       | -   | HAMPTON TERRACE                                   | 483 |   0 |  15 |  22 |   2 |  39 |  13 |   6 |  97 |   0 |   0 |   0 | 20.0828 |
| 51/52    | -   | HAMPTON LINK / HAMPTON HEIGHTS                    | 832 |   0 |  36 |  43 |   7 |  72 |   4 |  10 | 172 |   0 |   0 |   0 | 20.6731 |
| 53       | -   | HAMPTON WAY                                       | 551 |   0 |  18 |  32 |   2 |  59 |   5 |   8 | 124 |   0 |   0 |   0 | 22.5045 |
| 55       | -   | SHERWOOD MEADOW                                   | 627 |   1 |  33 |  23 |   5 |  47 |   1 |   6 | 116 |   0 |   0 |   0 | 18.5008 |
| 56/57    | -   | SHERWOOD CIRCLE / SHERWOOD RISE                   | 890 |   1 |  28 |  36 |   0 |  35 |   2 |  15 | 117 |   0 |   0 |   0 | 13.1461 |
| 58       | -   | KINCORA MANOR                                     | 534 |   0 |  53 |  50 |   3 |  54 |  12 |  10 | 182 |   0 |   0 |   0 | 34.0824 |
| 61/62    | -   | KINCORA POINT / KINCORA GARDEN                    | 851 |   0 |  76 |  46 |   5 |  88 |   8 |  27 | 250 |   0 |   0 |   0 | 29.3772 |
| 63/64/65 | -   | SHERWOOD COMMON / SHERWOOD ROAD / SHERWOOD SQUARE | 616 |   0 |  20 |  16 |   1 |  38 |   1 |  12 |  88 |   0 |   0 |   0 | 14.2857 |
| 67       | -   | KINCORA GLEN                                      | 608 |   0 |  37 |  46 |   4 |  44 |   7 |  13 | 151 |   0 |   0 |   0 | 24.8355 |
| 72/73    | -   | NOLAN MANOR / SAGE BANK SOUTH                     | 394 |   0 |  46 |  15 |   1 |  31 |   7 |   8 | 108 |   0 |   0 |   0 | 27.4112 |
| 74       | -   | SAGE VALLEY GREEN                                 | 358 |   0 |  20 |  17 |   2 |  34 |   4 |   0 |  77 |   0 |   0 |   0 | 21.5084 |
| 75       | -   | SAGEHILL WAY                                      | 466 |   0 |  23 |  11 |   4 |  36 |   7 |   2 |  83 |   0 |   0 |   0 | 17.8112 |
| 76       | -   | SAGEVALLEY CLOSE                                  | 386 |   1 |  16 |  13 |   1 |  29 |   9 |   3 |  72 |   0 |   0 |   0 | 18.6528 |
| 77       | -   | SAGEVALLEY DRIVE                                  | 294 |   0 |  17 |  14 |   1 |  21 |   8 |   4 |  65 |   0 |   0 |   0 | 22.1088 |
| 78/79    | -   | SAGE BANK NORTH / SAGE BERRY                      | 337 |   0 |  28 |  20 |   5 |  20 |   5 |   1 |  79 |   0 |   0 |   0 | 23.4421 |
| 80/81    | -   | NOLANFIELD / NOLAN CLIFF                          | 330 |   1 |  13 |  15 |   3 |  43 |   3 |  10 |  88 |   0 |   0 |   0 | 26.6667 |



labeled_formulas: N=D*M
N=E*M
M=E*O
N=E*O
N=F*M
N=G*M
N=H*M
N=H*O
N=I*M
N=J*M
N=K*M
N=L*M
N=M*P
N=(D*E)*M
M=(D*E)*O
N=(D*E)*O
N=(D+F)*M
N=(D+G)*M
N=(D+H)*M
N=(D*H)*O
N=(D+I)*M
N=(D+J)*M
N=(D+K)*M
N=(D+L)*M
N=(D*M)*P
N=(E*F)*M
M=(E*F)*O
N=(E*F)*O
N=(E*G)*M
M=(E*G)*O
N=(E*G)*O
N=(E*H)*M
M=(E*H)*O
N=(E*H)*O
N=(E*I)*M
M=(E*I)*O
N=(E*I)*O
N=(E*J)*M
M=(E/J)*O
N=(E*J)*O
N=(E*K)*M
M=(E*K)*O
N=(E*K)*O
N=(E*L)*M
M=(E*L)*O
N=(E*L)*O
N=(E*M)*P
M=(E*O)*P
N=(E*O)*P
N=(F+G)*M
N=(F+H)*M
N=(F*H)*O
N=(F+I)*M
N=(F-I)*O
N=(F+J)*M
N=(F+K)*M
N=(F+L)*M
N=(F*M)*P
N=(G+H)*M
N=(G*H)*O
N=(G+I)*M
N=(G+J)*M
N=(G+K)*M
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_714981___xlsx_450e4080f2a14bfdec0dbb2c0d63514da4b8711a.xlsx___line_426