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        |
|:------------|:----------|:---------------------|:----------|------:|------:|----:|:-------|:---------|
| Abbott      | Cathy     | Abbott, Cathy        | Southeast | 43573 | 43575 |   2 | Single | Hilton   |
| Able        | Aaron     | Able, Aaron          | West      | 43573 | 43576 |   3 | Single | Hilton   |
| Adams       | Donald    | Adams, Donald        | Southeast | 43575 | 43576 |   1 | Single | Marriott |
| Albert      | Maxine    | Albert, Maxine       | Midwest   | 43569 | 43578 |   9 | Single | Sheraton |
| Alexi       | Stephanie | Alexi, Stephanie     | Southeast | 43573 | 43576 |   3 | Single | Sheraton |
| Al-Sabah    | Daoud     | Al-Sabah, Daoud      | West      | 43573 | 43576 |   3 | Single | Sheraton |
| Alstain     | Isolde    | Alstain, Isolde      | West      | 43573 | 43575 |   2 | Single | Hilton   |
| Armel       | Bonny     | Armel, Bonny         | Southwest | 43575 | 43577 |   2 | Double | Sheraton |
| Asonte      | Tony      | Asonte, Tony         | Midwest   | 43571 | 43574 |   3 | Double | Hilton   |
| Bankler     | Rowena    | Bankler, Rowena      | West      | 43573 | 43576 |   3 | Single | Hilton   |
| Barber      | Lisa      | Barber, Lisa         | West      | 43573 | 43577 |   4 | Double | Hilton   |
| Barth       | Sandra    | Barth, Sandra        | Midwest   | 43572 | 43576 |   4 | Single | Hilton   |
| Barton      | Alice     | Barton, Alice        | West      | 43574 | 43576 |   2 | Single | Hilton   |
| Barton      | Eileen    | Barton, Eileen       | Southwest | 43573 | 43576 |   3 | Single | Hilton   |
| Bates       | Lisa      | Bates, Lisa          | West      | 43572 | 43576 |   4 | Single | Sheraton |
| Beech       | Susan     | Beech, Susan         | Southeast | 43572 | 43574 |   2 | Double | Hilton   |
| Bell        | Tom       | Bell, Tom            | Midwest   | 43572 | 43576 |   4 | Single | Hilton   |
| Bellwood    | Frank     | Bellwood, Frank      | Southwest | 43571 | 43574 |   3 | Double | Hilton   |
| Berg        | Bobby     | Berg, Bobby          | Southeast | 43571 | 43576 |   5 | Single | Hilton   |
| Berwick     | Sam       | Berwick, Sam         | Southeast | 43571 | 43573 |   2 | Single | Sheraton |
| Boughton    | Frank     | Boughton, Frank      | Northeast | 43573 | 43574 |   1 | Single | Marriott |
| Brwyne      | Melia     | Brwyne, Melia        | Southwest | 43573 | 43576 |   3 | Single | Hilton   |
| Cane        | Nate      | Cane, Nate           | Northeast | 43571 | 43577 |   6 | Single | Sheraton |
| Cash        | Mary      | Cash, Mary           | Southeast | 43571 | 43577 |   6 | Single | Hilton   |
| Chu         | Steven    | Chu, Steven          | West      | 43573 | 43576 |   3 | Single | Hilton   |
| Constance   | Burt      | Constance, Burt      | Southwest | 43571 | 43575 |   4 | Single | Hilton   |
| Cooper      | Linda     | Cooper, Linda        | Midwest   | 43571 | 43575 |   4 | Double | Marriott |
| Coyne       | Dennis    | Coyne, Dennis        | West      | 43573 | 43574 |   1 | Single | Sheraton |
| Cromwell    | Loni      | Cromwell, Loni       | Northeast | 43575 | 43576 |   1 | Single | Hilton   |
| Cronwith    | Brent     | Cronwith, Brent      | West      | 43571 | 43574 |   3 | Double | Sheraton |
| Cummins     | Dave      | Cummins, Dave        | Midwest   | 43573 | 43574 |   1 | Single | Hilton   |
| Daltes      | Boris     | Daltes, Boris        | Midwest   | 43575 | 43576 |   1 | Single | Hilton   |
| Davison     | Karen     | Davison, Karen       | West      | 43572 | 43576 |   4 | Single | Marriott |
| Dixon-Waite | Sherrie   | Dixon-Waite, Sherrie | West      | 43573 | 43574 |   1 | Single | Sheraton |
| Dorfberg    | Jeremy    | Dorfberg, Jeremy     | Northeast | 43571 | 43574 |   3 | Double | Marriott |
| Dunn        | Byron     | Dunn, Byron          | Southwest | 43574 | 43576 |   2 | Single | Sheraton |
| Farley      | Sam       | Farley, Sam          | Northeast | 43573 | 43576 |   3 | Single | Sheraton |
| Fein        | Caroline  | Fein, Caroline       | Midwest   | 43573 | 43576 |   3 | Single | Sheraton |
| Ferngood    | Jules     | Ferngood, Jules      | Southwest | 43572 | 43576 |   4 | Single | Marriott |
| Fontaine    | Jean      | Fontaine, Jean       | Northeast | 43574 | 43575 |   1 | Single | Marriott |
| Foss        | Felix     | Foss, Felix          | West      | 43570 | 43577 |   7 | Single | Marriott |
| Goldberg    | Malcolm   | Goldberg, Malcolm    | West      | 43573 | 43576 |   3 | Single | Hilton   |
| Gonzales    | George    | Gonzales, George     | Northeast | 43575 | 43577 |   2 | Double | Hilton   |
| Gonzales    | Joe       | Gonzales, Joe        | Southwest | 43570 | 43576 |   6 | Single | Marriott |
| Gorton      | Hazel     | Gorton, Hazel        | Northeast | 43568 | 43577 |   9 | Single | Marriott |
| Hapsbuch    | Kendrick  | Hapsbuch, Kendrick   | Northeast | 43570 | 43577 |   7 | Single | Hilton   |
| Hardy       | Bill      | Hardy, Bill          | Northeast | 43572 | 43573 |   1 | Single | Sheraton |
| Hardy       | Tom       | Hardy, Tom           | Southwest | 43575 | 43576 |   1 | Single | Sheraton |
| Henders     | Mark      | Henders, Mark        | Midwest   | 43570 | 43577 |   7 | Double | Hilton   |
| Hernandez   | Laura     | Hernandez, Laura     | Southwest | 43574 | 43577 |   3 | Single | Marriott |
| Hodge       | Alex      | Hodge, Alex          | Midwest   | 43573 | 43576 |   3 | Single | Hilton   |
| Homes       | Megan     | Homes, Megan         | Midwest   | 43573 | 43576 |   3 | Single | Hilton   |
| Jefferson   | Carla     | Jefferson, Carla     | Midwest   | 43574 | 43576 |   2 | Double | Sheraton |
| Jenkins     | Bob       | Jenkins, Bob         | Northeast | 43574 | 43576 |   2 | Double | Hilton   |
| Johnson     | Miguel    | Johnson, Miguel      | West      | 43574 | 43575 |   1 | Single | Sheraton |
| Kane        | Sheryl    | Kane, Sheryl         | Midwest   | 43570 | 43576 |   6 | Single | Sheraton |
| Kaneko      | Midori    | Kaneko, Midori       | West      | 43572 | 43573 |   1 | Single | Sheraton |
| Kegler      | Pam       | Kegler, Pam          | West      | 43572 | 43576 |   4 | Double | Hilton   |
| Kellerman   | Tommie    | Kellerman, Tommie    | West      | 43572 | 43576 |   4 | Single | Hilton   |
| Kourios     | Theo      | Kourios, Theo        | Southwest | 43572 | 43577 |   5 | Double | Sheraton |
| Lambert     | Octaviano | Lambert, Octaviano   | Southwest | 43574 | 43576 |   2 | Single | Sheraton |
| Lampstone   | Pete      | Lampstone, Pete      | Southwest | 43572 | 43576 |   4 | Single | Hilton   |
| Lark        | Donald    | Lark, Donald         | West      | 43571 | 43577 |   6 | Double | Marriott |
| Lempert     | Alexandra | Lempert, Alexandra   | West      | 43572 | 43576 |   4 | Single | Hilton   |
| Levine      | Eric      | Levine, Eric         | Southwest | 43573 | 43574 |   1 | Double | Marriott |
| Lin         | Michael   | Lin, Michael         | Northeast | 43573 | 43576 |   3 | Single | Sheraton |
| Logan       | David     | Logan, David         | Midwest   | 43575 | 43576 |   1 | Single | Hilton   |
| Long        | Lillian   | Long, Lillian        | West      | 43575 | 43576 |   1 | Single | Marriott |
| Lopez       | Sylvia    | Lopez, Sylvia        | Southwest | 43574 | 43575 |   1 | Single | Hilton   |
| Mann        | Alyssa    | Mann, Alyssa         | West      | 43570 | 43576 |   6 | Single | Hilton   |
| March       | Lucy      | March, Lucy          | Northeast | 43575 | 43576 |   1 | Double | Hilton   |
| McGuire     | Ellen     | McGuire, Ellen       | West      | 43574 | 43575 |   1 | Single | Hilton   |
| McKormick   | Brad      | McKormick, Brad      | Northeast | 43570 | 43577 |   7 | Single | Sheraton |
| Melendez    | Jaime     | Melendez, Jaime      | West      | 43573 | 43574 |   1 | Single | Hilton   |
| Miller      | Janet     | Miller, Janet        | Midwest   | 43573 | 43574 |   1 | Single | Hilton   |
| Morton      | Sara      | Morton, Sara         | West      | 43572 | 43574 |   2 | Single | Sheraton |
| Mueller     | Ursula    | Mueller, Ursula      | Southwest | 43573 | 43578 |   5 | Single | Hilton   |
| Nelson      | Ed        | Nelson, Ed           | West      | 43573 | 43575 |   2 | Double | Marriott |
| North       | Robert    | North, Robert        | Midwest   | 43571 | 43576 |   5 | Single | Sheraton |
| Olson       | Sean      | Olson, Sean          | Southwest | 43575 | 43576 |   1 | Single | Hilton   |
| Pearson     | Lynn      | Pearson, Lynn        | Southwest | 43575 | 43576 |   1 | Double | Hilton   |
| Plant       | Allen     | Plant, Allen         | Southwest | 43570 | 43577 |   7 | Single | Hilton   |
| Preston     | Liza      | Preston, Liza        | Northeast | 43568 | 43577 |   9 | Single | Hilton   |
| Price       | David     | Price, David         | West      | 43572 | 43576 |   4 | Single | Hilton   |
| Price       | Ellen     | Price, Ellen         | Southwest | 43570 | 43577 |   7 | Single | Hilton   |
| Price       | Ralph     | Price, Ralph         | Midwest   | 43575 | 43577 |   2 | Single | Hilton   |
| Quan        | Karen     | Quan, Karen          | Northeast | 43572 | 43576 |   4 | Single | Hilton   |
| Raye        | Alice     | Raye, Alice          | Southwest | 43572 | 43575 |   3 | Double | Hilton   |
| Richards    | Phillip   | Richards, Phillip    | Southwest | 43571 | 43576 |   5 | Double | Sheraton |
| Robbins     | Bob       | Robbins, Bob         | Southeast | 43572 | 43577 |   5 | Single | Hilton   |
| Roberts     | Charles   | Roberts, Charles     | Southwest | 43574 | 43576 |   2 | Single | Sheraton |
| Sammler     | Mark      | Sammler, Mark        | Southeast | 43573 | 43575 |   2 | Single | Hilton   |
| Sampson     | Carla     | Sampson, Carla       | West      | 43574 | 43575 |   1 | Single | Sheraton |
| Sargent     | Eileen    | Sargent, Eileen      | Midwest   | 43574 | 43576 |   2 | Single | Hilton   |
| Sargent     | Evelyn    | Sargent, Evelyn      | Midwest   | 43572 | 43577 |   5 | Single | Hilton   |
| Scote       | Gail      | Scote, Gail          | West      | 43570 | 43576 |   6 | Single | Hilton   |
| Scott       | Rhonda    | Scott, Rhonda        | Northeast | 43574 | 43576 |   2 | Single | Hilton   |
| Selznick    | Anna      | Selznick, Anna       | West      | 43571 | 43577 |   6 | Single | Hilton   |
| Simpson     | Sandrae   | Simpson, Sandrae     | Northeast | 43571 | 43576 |   5 | Single | Hilton   |
| Sindole     | Randy     | Sindole, Randy       | Southwest | 43571 | 43576 |   5 | Double | Sheraton |
| Smith       | Barbara   | Smith, Barbara       | Southwest | 43573 | 43577 |   4 | Single | Hilton   |
| Smith       | Ellen     | Smith, Ellen         | Midwest   | 43571 | 43577 |   6 | Single | Marriott |
| Smith       | Howard    | Smith, Howard        | West      | 43569 | 43577 |   8 | Single | Hilton   |
| Smith       | Nelson    | Smith, Nelson        | Southeast | 43575 | 43576 |   1 | Single | Hilton   |
| Smith       | Rich      | Smith, Rich          | Midwest   | 43574 | 43575 |   1 | Double | Hilton   |
| Smith       | Sam       | Smith, Sam           | Southwest | 43575 | 43576 |   1 | Single | Sheraton |
| Smythe      | Leslie    | Smythe, Leslie       | Southwest | 43572 | 43576 |   4 | Double | Marriott |
| Sofer       | Ariel     | Sofer, Ariel         | West      | 43571 | 43576 |   5 | Single | Hilton   |
| Solomon     | Ari       | Solomon, Ari         | West      | 43570 | 43577 |   7 | Single | Sheraton |
| Stewart     | Iain      | Stewart, Iain        | Southwest | 43572 | 43576 |   4 | Single | Hilton   |
| Stone       | Cindy     | Stone, Cindy         | Southeast | 43572 | 43575 |   3 | Single | Sheraton |
| Stryker     | Carlos    | Stryker, Carlos      | West      | 43575 | 43576 |   1 | Single | Sheraton |
| Szcznyck    | Tadeuz    | Szcznyck, Tadeuz     | West      | 43571 | 43577 |   6 | Single | Sheraton |
| Taylor      | Ralph     | Taylor, Ralph        | West      | 43571 | 43575 |   4 | Double | Sheraton |
| Tercan      | Robert    | Tercan, Robert       | Southwest | 43569 | 43577 |   8 | Single | Hilton   |
| Townes      | Everett   | Townes, Everett      | Northeast | 43572 | 43576 |   4 | Single | Marriott |
| Tuppman     | Lise-Anne | Tuppman, Lise-Anne   | Northeast | 43572 | 43577 |   5 | Double | Sheraton |
| Ugarte      | Lisa      | Ugarte, Lisa         | Midwest   | 43572 | 43573 |   1 | Single | Sheraton |
| Vuanuo      | Tuome     | Vuanuo, Tuome        | Southwest | 43571 | 43577 |   6 | Single | Sheraton |
| Wang        | Matt      | Wang, Matt           | West      | 43571 | 43576 |   5 | Single | Hilton   |
| Wells       | Jason     | Wells, Jason         | Northeast | 43573 | 43574 |   1 | Single | Hilton   |
| Wells       | Rose      | Wells, Rose          | West      | 43572 | 43578 |   6 | Double | Hilton   |
| Weston      | Sam       | Weston, Sam          | West      | 43572 | 43577 |   5 | Single | Sheraton |
| White       | Jessica   | White, Jessica       | West      | 43572 | 43576 |   4 | Single | Hilton   |
| Wu          | Tammy     | Wu, Tammy            | West      | 43572 | 43575 |   3 | Double | Hilton   |
| Zaremba     | Howard    | Zaremba, Howard      | West      | 43574 | 43576 |   2 | Single | Hilton   |
| Zostoc      | Melissa   | Zostoc, Melissa      | Northeast | 43573 | 43576 |   3 | Double | Hilton   |



label: G=F-E
labeled_formulas: G=F-E
output: {"Arithmetic-Relationship": ["G=F-E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_8190___xlsx_7385dcccd12f0081382324a6f9994804be37e616.xlsx___line_299