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 |
|:-------------------|---------:|------:|------:|---------:|--------:|--------:|----:|--------:|----:|
| UNIT 23 BACK       | 189.569  | 13    | 29.25 | 190.125  | 379.694 | 35.2747 |  10 | 352.747 | 360 |
| UNIT 22 BACK       | 174.936  | 13    | 29.25 | 190.125  | 365.061 | 33.9153 |  10 | 339.153 | 340 |
| UNIT 21 BACK       | 174.936  | 13    | 29.25 | 190.125  | 365.061 | 33.9153 |  10 | 339.153 | 340 |
| UNIT 20 BACK       | 174.936  | 13    | 29.25 | 190.125  | 365.061 | 33.9153 |  10 | 339.153 | 340 |
| UNIT 19 BACK       | 174.936  | 13    | 29.25 | 190.125  | 365.061 | 33.9153 |  10 | 339.153 | 340 |
| UNIT 18 BACK       | 174.936  | 13    | 29.25 | 190.125  | 365.061 | 33.9153 |  10 | 339.153 | 340 |
| UNIT 17 BACK       | 218.457  | 15    | 29.25 | 219.375  | 437.832 | 40.676  |  10 | 406.76  | 410 |
| UNIT 23 FRONT      | 303.205  | 20.9  | 29.25 | 305.663  | 608.868 | 56.5657 |  10 | 565.657 | 570 |
| UNIT 22 FRONT      | 189.708  | 13    | 29.25 | 190.125  | 379.833 | 35.2877 |  10 | 352.877 | 360 |
| UNIT 21 FRONT      | 189.708  | 13    | 29.25 | 190.125  | 379.833 | 35.2877 |  10 | 352.877 | 360 |
| UNIT 20 FRONT      | 189.708  | 13    | 29.25 | 190.125  | 379.833 | 35.2877 |  10 | 352.877 | 360 |
| UNIT 19 FRONT      | 189.708  | 13    | 29.25 | 190.125  | 379.833 | 35.2877 |  10 | 352.877 | 360 |
| UNIT 18 FRONT      | 189.708  | 13    | 29.25 | 190.125  | 379.833 | 35.2877 |  10 | 352.877 | 360 |
| UNIT 17 FRONT      | 189.708  | 13    | 29.25 | 190.125  | 379.833 | 35.2877 |  10 | 352.877 | 360 |
| EAST WEST PATH 1   | 119.238  |  0    |  0    |   0      | 119.238 | 11.0776 |  10 | 110.776 | 120 |
| EAST WEST PATH 2   | 108.137  |  0    |  0    |   0      | 108.137 | 10.0462 |  10 | 100.462 | 110 |
| EAST WEST PATH 3   | 113.214  |  0    |  0    |   0      | 113.214 | 10.518  |  10 | 105.18  | 110 |
| EAST WEST PATH 4   | 456.281  |  0    |  0    |   0      | 456.281 | 42.39   |  10 | 423.9   | 430 |
| UNIT 1 SIDE        | 271.307  | 31    | 29.25 | 453.375  | 724.682 | 67.3252 |  10 | 673.252 | 680 |
| UNIT 1/2 BACK      | 165.731  | 20.5  | 29.25 | 299.812  | 465.544 | 43.2505 |  10 | 432.505 | 440 |
| UNIT 2/3 BACK      |  92.4587 | 11    | 29.25 | 160.875  | 253.334 | 23.5355 |  10 | 235.355 | 240 |
| UNIT 3/4 BACK      |  96.9969 | 15    | 29.25 | 219.375  | 316.372 | 29.3919 |  10 | 293.919 | 300 |
| UNIT 4/5 BACK      |  59.4654 | 11    | 29.25 | 160.875  | 220.34  | 20.4703 |  10 | 204.703 | 210 |
| UNIT 5/6 BACK      |  74.4943 | 15    | 29.25 | 219.375  | 293.869 | 27.3014 |  10 | 273.014 | 280 |
| UNIT 6/7 BACK      |  59.4654 | 11    | 29.25 | 160.875  | 220.34  | 20.4703 |  10 | 204.703 | 210 |
| UNIT 7/8 BACK      |  74.4943 | 15    | 29.25 | 219.375  | 293.869 | 27.3014 |  10 | 273.014 | 280 |
| UNIT 9 BACK        |  80.4006 |  7.5  | 29.25 | 109.688  | 190.088 | 17.6598 |  10 | 176.598 | 180 |
| NORTH SOUTH PATH 1 | 169.41   | 26.25 | 29.25 | 383.906  | 553.316 | 51.4048 |  10 | 514.048 | 520 |
| NORTH SOUTH PATH 2 | 159.839  |  0    |  0    |   0      | 159.839 | 14.8496 |  10 | 148.496 | 150 |
| NORTH SOUTH PATH 3 | 160.273  | 27.1  | 29.25 | 396.337  | 556.61  | 51.7108 |  10 | 517.108 | 520 |
| UNIT 1 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 2 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 3 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 4 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 5 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 6 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 7 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 8 FRONT       | 194.281  | 13    | 29.25 | 190.125  | 384.406 | 35.7125 |  10 | 357.125 | 360 |
| UNIT 9 FRONT       | 213.33   | 13    | 29.25 | 190.125  | 403.455 | 37.4822 |  10 | 374.822 | 380 |
| ACCESS PARKING     | 298.361  |  0    |  0    |   0      | 298.361 | 27.7187 |  10 | 277.187 | 280 |
| UNIT 16 SIDE       | 340.056  | 31.5  | 29.25 | 460.688  | 800.743 | 74.3915 |  10 | 743.915 | 750 |
| NORTH WEST CORNER  | 157.131  |  0    |  0    |   0      | 157.131 | 14.5979 |  10 | 145.979 | 150 |
| UNIT 16 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| UNIT 15 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| UNIT 14 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| UNIT 13 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| UNIT 12 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| UNIT 11 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| UNIT 10 FRONT      | 190.75   | 13    | 29.25 | 190.125  | 380.875 | 35.3845 |  10 | 353.845 | 360 |
| SOUTH WEST CORNER  | 201.017  |  2.25 | 29.25 |  32.9062 | 233.923 | 21.7322 |  10 | 217.322 | 220 |
| UNIT 10 SIDE       | 388.358  | 29.6  | 29.25 | 432.9    | 821.258 | 76.2974 |  10 | 762.974 | 770 |
| UNIT 10 BACK       | 151.667  | 13    | 29.25 | 190.125  | 341.792 | 31.7535 |  10 | 317.535 | 320 |
| UNIT 11 BACK       | 151.667  | 13    | 29.25 | 190.125  | 341.792 | 31.7535 |  10 | 317.535 | 320 |
| UNIT 12 BACK       | 151.667  | 13    | 29.25 | 190.125  | 341.792 | 31.7535 |  10 | 317.535 | 320 |
| UNIT 13 BACK       | 151.667  | 13    | 29.25 | 190.125  | 341.792 | 31.7535 |  10 | 317.535 | 320 |
| UNIT 14 BACK       | 151.667  | 13    | 29.25 | 190.125  | 341.792 | 31.7535 |  10 | 317.535 | 320 |
| UNIT 15 BACK       | 151.667  | 13    | 29.25 | 190.125  | 341.792 | 31.7535 |  10 | 317.535 | 320 |
| UNIT 16 BACK       | 130.494  | 13    | 29.25 | 190.125  | 320.619 | 29.7865 |  10 | 297.865 | 300 |



label: F=B+E
I=G*H
labeled_formulas: F=B+E
I=G*H
output: {"Arithmetic-Relationship": ["F=B+E", "I=G*H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_589380___xlsx_51b8be1d1896ba8032c5f00de64ff10eec6847d2.xlsx___line_240