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 |
|:-----------|:-----|----:|----:|----:|----------:|----:|----:|----:|----:|----:|
| Bertelsen  | LA   |  21 |   3 | 298 | 14.1905   |  43 |   0 |   0 |   1 |   1 |
| McGill     | SF   |  15 |   0 | 167 | 11.1333   |  33 |   0 |   4 |   1 |   1 |
| Scott      | Mia  |  22 |   3 | 235 | 10.6818   |  25 |   0 |   1 |   1 |   1 |
| Laird      | Bal  |  22 |  12 | 228 | 10.3636   |  40 |   0 |   0 |   1 |   1 |
| Edwards    | Pitt |  21 |  22 | 212 | 10.0952   |  31 |   0 |   6 |   1 |   1 |
| Casanova   | Cin  |  32 |  19 | 309 |  9.65625  |  38 |   0 |   0 |   1 |   1 |
| Vactor     | Was  |  19 |  13 | 176 |  9.26316  |  38 |   0 |   6 |   1 |   1 |
| Houston    | Hou  |  23 |   7 | 204 |  8.86957  |  38 |   0 |   2 |   1 |   1 |
| West       | Min  |  20 |   6 | 176 |  8.8      |  49 |   0 |   4 |   1 |   1 |
| Wyatt      | Buf  |  15 |  11 | 129 |  8.6      |  36 |   0 |   0 |   1 |   1 |
| Dunlap     | SD   |  26 |   6 | 216 |  8.30769  |  28 |   0 |   3 |   1 |   1 |
| Belton     | Atl  |  27 |   3 | 220 |  8.14815  |  19 |   0 |   5 |   1 |   1 |
| Atkinson   | Oak  |  18 |   1 | 133 |  7.38889  |  49 |   0 |   1 |   1 |   1 |
| Sherman    | Den  |  17 |  10 | 122 |  7.17647  |  26 |   0 |   0 |   1 |   1 |
| Willingham | StL  |  18 |   7 | 128 |  7.11111  |  62 |   0 |   2 |   1 |   1 |
| Marshall   | KC   |  26 |   7 | 160 |  6.15385  |  28 |   0 |   1 |   1 |   1 |
| Smith      | Chi  |  42 |   2 | 233 |  5.54762  |  33 |   0 |   4 |   1 |   1 |
| Taylor     | SF   |  19 |   8 | 105 |  5.52632  |  31 |   0 |   0 |   1 |   1 |
| Harris     | Dal  |  21 |  22 | 109 |  5.19048  |  28 |   0 |   0 |   1 |   1 |
| Grim       | NYG  |  18 |  24 |  85 |  4.72222  |  54 |   0 |   3 |   1 |   1 |
| Wehrli     | StL  |  15 |   3 |  64 |  4.26667  |  16 |   0 |   2 |   1 |   1 |
| Bradley    | Phi  |  17 |   4 |  71 |  4.17647  |  17 |   0 |   2 |   1 |   1 |
| Myers      | NO   |  15 |  20 |  59 |  3.93333  |  11 |   0 |   0 |   1 |   1 |
| Branch     | Oak  |  27 |   9 |  93 |  3.44444  |  49 |   0 |   1 |   1 |   1 |
| Podolak    | KC   |  16 |  11 |  45 |  2.8125   |  14 |   0 |   2 |   1 |   1 |
| Ellis      | Atl  |   1 |   0 |  26 | 26        |  26 |   0 |   0 |   0 |   1 |
| Thompson   | Den  |   4 |   1 |  74 | 18.5      |  40 |   0 |   0 |   0 |   1 |
| Logan      | Bal  |   5 |   0 |  90 | 18        |  38 |   0 |   1 |   0 |   1 |
| Staggers   | GB   |   8 |  26 |  99 | 12.375    |  23 |   0 |   1 |   0 |   1 |
| Turner     | NYJ  |   3 |   3 |  35 | 11.6667   |  23 |   0 |   0 |   0 |   1 |
| Kelly      | Clev |   5 |   3 |  50 | 10        |  17 |   0 |   0 |   0 |   1 |
| Gordon     | LA   |   3 |   0 |  30 | 10        |  18 |   0 |   1 |   0 |   1 |
| Hill       | Buf  |   3 |   2 |  29 |  9.66667  |  16 |   0 |   0 |   0 |   1 |
| Simone     | Den  |   1 |   0 |   9 |  9        |   9 |   0 |   0 |   0 |   1 |
| Little     | Den  |  12 |   3 | 101 |  8.41667  |  33 |   0 |   0 |   0 |   1 |
| Duncan     | Was  |   6 |   2 |  50 |  8.33333  |  20 |   0 |   0 |   0 |   1 |
| Greene     | Buf  |   3 |   2 |  24 |  8        |  12 |   0 |   0 |   0 |   1 |
| Fuller     | SF   |   1 |   0 |   8 |  8        |   8 |   0 |   0 |   0 |   1 |
| Majors     | Clev |   9 |   4 |  71 |  7.88889  |  34 |   0 |   0 |   0 |   1 |
| Lewis      | Pitt |  12 |   1 |  93 |  7.75     |  23 |   0 |   2 |   0 |   1 |
| Duhon      | NYG  |   2 |   2 |  14 |  7        |   8 |   0 |   0 |   0 |   1 |
| Athas      | NYG  |  12 |  11 |  78 |  6.5      |  17 |   0 |   0 |   0 |   1 |
| Cole       | Buf  |   6 |   2 |  38 |  6.33333  |  14 |   0 |   3 |   0 |   1 |
| Maxwell    | Oak  |   3 |   0 |  19 |  6.33333  |   9 |   0 |   0 |   0 |   1 |
| Volk       | Bal  |   1 |   9 |   6 |  6        |   6 |   0 |   0 |   0 |   1 |
| Brown      | Atl  |  11 |  12 |  59 |  5.36364  |  13 |   0 |   0 |   0 |   1 |
| Clemons    | Chi  |   2 |   4 |  10 |  5        |  10 |   0 |   1 |   0 |   1 |
| Gibbs      | Phi  |   1 |   0 |   5 |  5        |   5 |   0 |   0 |   0 |   1 |
| Krieg      | Den  |   1 |   0 |   5 |  5        |   5 |   0 |   0 |   0 |   1 |
| Hicks      | NYJ  |   1 |   0 |   5 |  5        |   5 |   0 |   0 |   0 |   1 |
| Gladieux   | NE   |   4 |   6 |  19 |  4.75     |  18 |   0 |   0 |   0 |   1 |
| Waters     | Dal  |  10 |   8 |  46 |  4.6      |  10 |   0 |   0 |   0 |   1 |
| Homan      | KC   |   2 |   0 |   9 |  4.5      |   9 |   0 |   0 |   0 |   1 |
| Garrett    | NE   |   8 |   1 |  35 |  4.375    |  20 |   0 |   1 |   0 |   1 |
| Pearson    | Pitt |   5 |   0 |  21 |  4.2      |   7 |   0 |   0 |   0 |   1 |
| Bleier     | Pitt |  11 |   0 |  43 |  3.90909  |  29 |   0 |   3 |   0 |   1 |
| Harris     | NE   |   7 |   2 |  26 |  3.71429  |  16 |   0 |   1 |   0 |   1 |
| Elmendorf  | LA   |   3 |  10 |  11 |  3.66667  |   6 |   0 |   0 |   0 |   1 |
| Walton,L   | Det  |   3 |   6 |  10 |  3.33333  |  17 |   0 |   1 |   0 |   1 |
| Bryant     | Min  |  11 |   9 |  33 |  3        |   9 |   0 |   0 |   0 |   1 |
| Hudson     | GB   |   6 |   4 |  18 |  3        |  18 |   0 |   0 |   0 |   1 |
| Harrison   | Buf  |   1 |   2 |   3 |  3        |   3 |   0 |   0 |   0 |   1 |
| Johnson,E  | Cin  |   1 |   0 |   3 |  3        |   3 |   0 |   0 |   0 |   1 |
| Anderson   | Mia  |   7 |   2 |   9 |  1.28571  |   4 |   0 |   1 |   0 |   1 |
| Love       | LA   |   7 |   2 |   7 |  1        |   8 |   0 |   1 |   0 |   1 |
| Reardon    | KC   |   1 |   0 |   1 |  1        |   1 |   0 |   0 |   0 |   1 |
| Darden     | Clev |  11 |   8 |   5 |  0.454545 |   2 |   0 |   0 |   0 |   1 |
| Walik      | Phi  |   6 |   0 |   2 |  0.333333 |  12 |   0 |   1 |   0 |   1 |
| Adkins     | NO   |   9 |   1 |   0 |  0        |   5 |   0 |   1 |   0 |   1 |
| Taylor     | SD   |   2 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   1 |
| Small      | Atl  |   1 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   1 |
| Johnson,A  | Hou  |   5 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   1 |
| Mooers     | NO   |   1 |   0 |   0 |  0        |   0 |   0 |   1 |   0 |   1 |
| McLinton   | Was  |   1 |   0 |   0 |  0        |   0 |   0 |   1 |   0 |   1 |
| Mendenhall | NYG  |   1 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   1 |
| Sampson    | Hou  |   1 |   0 |   0 |  0        |   0 |   0 |   1 |   0 |   1 |
| Glass      | GB   |   1 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   1 |
| Haymond    | Was  |   6 |   1 |  -2 | -0.333333 |   1 |   0 |   1 |   0 |   1 |
| Garrett    | SD   |   2 |   1 |  -1 | -0.5      |   0 |   0 |   0 |   0 |   1 |
| Moore      | Hou  |   4 |   2 |  -3 | -0.75     |   0 |   0 |   2 |   0 |   1 |
| Carwell    | NE   |   6 |   1 |  -5 | -0.833333 |   4 |   0 |   1 |   0 |   1 |
| Gray       | StL  |   5 |   1 | -26 | -5.2      |   0 |   0 |   0 |   0 |   1 |
| Detwiler   | SD   |   0 |   6 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |
| Davis      | Oak  |   0 |   4 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |
| Sumner     | Clev |   0 |   2 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |
| Severson   | Was  |   0 |   2 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |
| Sullivan   | Phi  |   0 |   1 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |
| Winfield   | Phi  |   0 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |
| LeVias     | SD   |   0 |   0 |   0 |  0        |   0 |   0 |   0 |   0 |   0 |



labeled_formulas: E=(C*F)+H
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_189178___xlsx_c840fa0b39d44d74a3ea6bdd5dcfb6db136e8511.xlsx___line_556