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 |
|:--------------------|:----------------------------------------------------------------------------------|---------:|--------:|----:|----:|----:|----:|----:|--------:|----:|--------:|---------:|
| David Alexander     | Co-Leader of Administration                                                       | 30499.1  |    0    |   0 |   0 |   0 |   0 |   0 |  808.27 |   0 |  808.27 | 31307.4  |
| David Barratt       | Councillor                                                                        | 17426.5  |  635.85 |   0 |   0 |   0 |   0 |   0 |   54.01 |   0 |  689.86 | 18116.4  |
| James Calder        | Councillor                                                                        | 17426.5  |  273.6  |   0 |   0 |   0 |   0 |   0 |    0    |   0 |  273.6  | 17700.1  |
| Ken Caldwell        | Convener - Levenmouth Area Committee                                              | 22225.5  |  611.1  |   0 |   0 |   0 |   0 |   0 |   77.91 |   0 |  689.01 | 22914.5  |
| Alex Campbell       | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  152.91 |   0 |  152.91 | 17579.4  |
| Robert Clelland     | Councillor                                                                        | 17426.5  |  234    |   0 |   0 |   0 |   0 |   0 | 1060.81 |   0 | 1294.81 | 18721.3  |
| Dave Coleman        | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  131.92 |   0 |  131.92 | 17558.4  |
| Alan Craig          | Councillor until 4/9/19                                                           |  7236.86 |    0    |   0 |   0 |   0 |   0 |   0 |    0    |   0 |    0    |  7236.86 |
| Neil Crooks         | Convener - Kirkcaldy Area Committee                                               | 22225.5  | 1065.6  |   0 |   0 |   0 |   0 |   0 |   54.01 |   0 | 1119.61 | 23345.1  |
| John Docherty       | Councillor                                                                        | 17426.5  | 2094.3  |   0 |   0 |   0 |   0 |   0 |  106.21 |   0 | 2200.51 | 19627    |
| Gavin Ellis         | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  131.91 |   0 |  131.91 | 17558.4  |
| Linda Erskine       | Convener Cowdenbeath Area Committee & HR Spokesperson                             | 22225.5  |    0    |   0 |   0 |   0 |   0 |   0 |  189.49 |   0 |  189.49 | 22415    |
| Ian Ferguson        | Councillor                                                                        | 17426.5  |  648.05 |   0 |   0 |   0 |   0 |   0 |   78    |   0 |  726.05 | 18152.5  |
| Julie Ford          | Depute Provost                                                                    | 22225.5  |    0    |   0 |   0 |   0 |   0 |   0 |   69.91 |   0 |   69.91 | 22295.4  |
| Derek Glen          | Councillor from 4/11/19                                                           |  6839.24 |  189.45 |   0 |   0 |   0 |   0 |   0 |    0    |   0 |  189.45 |  7028.69 |
| David Graham        | Councillor                                                                        | 17426.5  | 1851.75 |   0 |   0 |   0 |   0 |   0 |  335.77 |   0 | 2187.52 | 19614    |
| Fiona Grant         | Convener Glenrothes Area Committee                                                | 22225.5  |    0    |   0 |   0 |   0 |   0 |   0 |  610.8  |   0 |  610.8  | 22836.3  |
| Mick Green          | Councillor                                                                        | 17426.5  |   27    |   0 |   0 |   0 |   0 |   0 |  155.82 |   0 |  182.82 | 17609.3  |
| Sharon Green-Wilson | Councillor from 15/11/19                                                          |  6772.23 |    0    |   0 |   0 |   0 |   0 |   0 |  108.5  |   0 |  108.5  |  6880.73 |
| Gary Guichan        | Councillor                                                                        | 17426.5  |  454.05 |   0 |   0 |   0 |   0 |   0 |    0    |   0 |  454.05 | 17880.5  |
| Garry Haldane       | Councillor                                                                        | 17426.5  |  850.95 |   0 |   0 |   0 |   0 |   0 |   54    |   0 |  904.95 | 18331.5  |
| Jean Hall Muir      | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  123.83 |   0 |  123.83 | 17550.3  |
| Andy Heer           | Councillor                                                                        | 17426.5  |  981    |   0 |   0 |   0 |   0 |   0 |   97.6  |   0 | 1078.6  | 18505.1  |
| Zoe Hisbent         | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |   54.01 |   0 |   54.01 | 17480.5  |
| Linda Holt          | Councillor                                                                        | 17426.5  | 2103.3  |   0 |   0 |   0 |   0 |   0 |    0    |   0 | 2103.3  | 19529.8  |
| Margaret Kennedy    | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |    0    |   0 |    0    | 17426.5  |
| Gordon Langlands    | Councillor                                                                        | 17426.5  |  549.9  |   0 |   0 |   0 |   0 |   0 |   80.41 |   0 |  630.31 | 18056.8  |
| Helen Law           | Convener City of Dunfermline Area Committee                                       | 22225.5  |    0    |   0 |   0 |   0 |   0 |   0 |  131.92 |   0 |  131.92 | 22357.4  |
| James Leishman      | Provost                                                                           | 30499.1  |    0    |   0 |   0 |   0 |   0 |   0 |  293.95 |   0 |  293.95 | 30793.1  |
| Rosemary Liewald    | Councillor                                                                        | 22622.9  |    0    |   0 |   0 |   0 |   0 |   0 |  138.3  |   0 |  138.3  | 22761.2  |
| Carol Lindsay       | Convener Regulation & Licensing Committee and Fife Licensing Board                | 22225.5  |   99    |   0 |   0 |   0 |   0 |   0 |  816.37 |   0 |  915.37 | 23140.9  |
| Mary Lockhart       | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  108.6  |   0 |  108.6  | 17535.1  |
| Donald Lothian      | Convener North East Fife Area Committee                                           | 22225.5  | 1303.2  |   0 |   0 |   0 |   0 |   0 |  762.36 |   0 | 2065.56 | 24291.1  |
| David Macdiarmid    | Councillor                                                                        | 17426.5  |  301.5  |   0 |   0 |   0 |   0 |   0 | 1067.17 |   0 | 1368.67 | 18795.2  |
| Karen Marjoram      | Councillor                                                                        | 17426.5  |  625.05 |   0 |   0 |   0 |   0 |   0 |  267.4  |   0 |  892.45 | 18319    |
| Alice Mcgarry       | Convener South West Fife Area Committee / Central & West Planning Committee       | 22225.5  |  647.55 |   0 |   0 |   0 |   0 |   0 |   78.01 |   0 |  725.56 | 22951.1  |
| Lea Mclelland       | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |    0    |   0 |    0    | 17426.5  |
| Tony Miklinski      | Convener Education & Children's Services and H&SC Scrutiny Committee w/e 27/09/19 | 19937.3  |  819.9  |   0 |   0 |   0 |   0 |   0 |   54    |   0 |  873.9  | 20811.2  |
| Derek Noble         | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |   54.01 |   0 |   54.01 | 17480.5  |
| John O Brien        | Councillor                                                                        | 17426.5  |  273.6  |   0 |   0 |   0 |   0 |   0 |  131.91 |   0 |  405.51 | 17832    |
| Tony Orton          | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |   77.91 |   0 |   77.91 | 17504.4  |
| Ross Paterson       | Councillor                                                                        | 17426.5  |  234.9  |   0 |   0 |   0 |   0 |   0 |  143.92 |   0 |  378.82 | 17805.3  |
| Bill Porteous       | Councillor                                                                        | 17426.5  |  633.6  |   0 |   0 |   0 |   0 |   0 |  128.09 |   0 |  761.69 | 18188.2  |
| Graham Ritchie      | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |    0    |   0 |    0    | 17426.5  |
| David J Ross        | Councillor                                                                        | 17426.5  | 1630.35 |   0 |   0 |   0 |   0 |   0 |  127.82 |   0 | 1758.17 | 19184.7  |
| Ryan Smart          | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  280.87 |   0 |  280.87 | 17707.4  |
| Sam Steele          | Councillor until 16/9/19                                                          |  7772.93 |    0    |   0 |   0 |   0 |   0 |   0 |   55.18 |   0 |   55.18 |  7828.11 |
| Catherine Stewart   | Councillor                                                                        | 17426.5  | 1366.65 |   0 |   0 |   0 |   0 |   0 |  132.65 |   0 | 1499.3  | 18925.8  |
| Alistair Suttie     | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  131.91 |   0 |  131.91 | 17558.4  |
| Brian Thomson       | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |  131.91 |   0 |  131.91 | 17558.4  |
| Ann Verner          | Councillor                                                                        | 17426.5  | 1368.45 |   0 |   0 |   0 |   0 |   0 |  132.1  |   0 | 1500.55 | 18927    |
| Andrew Verrecchia   | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |   78.01 |   0 |   78.01 | 17504.5  |
| Ross Vettriano      | Convener Environment & Protective Services Committee                              | 22225.5  |    0    |   0 |   0 |   0 |   0 |   0 |  132.45 |   0 |  132.45 | 22358    |
| Craig Walker        | Convener Assets, Property & Facilities Committee                                  | 22225.5  |    0    |   0 |   0 |   0 |   0 |   0 |  654    |   0 |  654    | 22879.5  |
| Darren Watt         | Councillor                                                                        | 17426.5  |   54.9  |   0 |   0 |   0 |   0 |   0 |   77.91 |   0 |  132.81 | 17559.3  |
| Richard Watt        | Councillor                                                                        | 17426.5  |  213.3  |   0 |   0 |   0 |   0 |   0 |   24    |   0 |  237.3  | 17663.8  |
| Vikki Wilton        | Councillor                                                                        | 17426.5  |    0    |   0 |   0 |   0 |   0 |   0 |    0    |   0 |    0    | 17426.5  |



labeled_formulas: F=C*E
G=C*E
K=C*E
H=C*F
I=C*F
H=C*G
I=C*G
I=C*H
K=C*H
K=C*I
F=D*E
G=D*E
I=D*E
K=D*E
F=D*H
I=D*F
G=D*H
I=D*G
I=D*H
K=D*H
K=D*I
F=E*H
F=E*J
F=E*L
F=E*M
G=E*H
G=E*J
G=E*L
G=E*M
I=E*H
E=H*J
K=E*H
I=E*J
K=E*J
K=E*L
K=E*M
F=H*J
H=F*L
H=F*M
I=F*J
I=F*L
I=F*M
G=H*J
H=G*L
H=G*M
I=G*J
I=G*L
I=G*M
I=H*J
I=H*L
F=(C*D)*E
G=(C*D)*E
I=(C*D)*E
K=(C*D)*E
F=(C*D)*H
I=(C+D)*F
G=(C*D)*H
I=(C+D)*G
I=(C*D)*H
K=(C*D)*H
K=(C+D)*I
F=(C*E)*H
F=(C*E)*J
F=(C*E)*L
F=(C*E)*M
G=(C*E)*H
G=(C*E)*J
G=(C*E)*L
G=(C*E)*M
I=(C*E)*H
E=(C*H)*J
K=(C*E)*H
I=(C*E)*J
K=(C*E)*J
K=(C*E)*L
K=(C*E)*M
M=(C+E)+L
F=(C*H)*J
H=(C*F)*L
H=(C*F)*M
I=(C*F)*J
I=(C*F)*L
I=(C*F)*M
G=(C*H)*J
H=(C*G)*L
H=(C*G)*M
I=(C*G)*J
I=(C*G)*L
I=(C*G)*M
I=(C*H)*J
I=(C*H)*L
I=(C*H)*M
K=(C*H)*J
K=(C*H)*L
K=(C*H)*M
M=(C+H)+L
K=(C*I)*J
K=(C*I)*L
K=(C*I)*M
M=(C+I)+L
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_614100___xlsx_021647af922b3faff57687eea302597a323048ac.xlsx___line_1