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 |   Q |   R |
|:----------------------------------------|----:|----:|----:|----:|---------:|----:|----:|----:|----:|----:|----:|----:|----:|----:|---------:|----:|----:|
| Africana Studies                        |  15 |   8 |   7 |   0 | 0.533333 |   0 |   1 |   8 |   2 |   1 |   0 |   1 |  13 |   0 | 1        |   0 |   2 |
| American Studies                        |  26 |  11 |  15 |   0 | 0.423077 |   0 |   0 |   6 |   1 |   0 |   0 |   3 |  10 |  14 | 0.416667 |   0 |   2 |
| Anthropology                            |  98 |  75 |  23 |   0 | 0.765306 |   0 |   3 |   6 |  24 |   1 |   0 |   0 |  34 |  57 | 0.373626 |   3 |   4 |
| Anthropology - History                  |   3 |   1 |   2 |   0 | 0.333333 |   0 |   0 |   0 |   1 |   0 |   0 |   1 |   2 |   0 | 1        |   0 |   1 |
| Archaeology & History                   |  26 |   8 |  18 |   0 | 0.307692 |   0 |   0 |   2 |   2 |   0 |   0 |   0 |   4 |  22 | 0.153846 |   0 |   0 |
| No Track/Concentration                  |  13 |   6 |   7 |   0 | 0.461538 |   0 |   5 |   3 |   0 |   0 |   0 |   1 |   9 |   1 | 0.9      |   2 |   1 |
| Classical Languages                     |  10 |   5 |   5 |   0 | 0.5      |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   2 |   8 | 0.2      |   0 |   0 |
| Classical Studies                       |  10 |   5 |   5 |   0 | 0.5      |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   2 |   7 | 0.222222 |   0 |   1 |
| Early Childhood Licensure               |   1 |   1 |   0 |   0 | 1        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 | 0        |   0 |   0 |
| Translation Studies                     |   3 |   2 |   1 |   0 | 0.666667 |   0 |   0 |   0 |   3 |   0 |   0 |   0 |   3 |   0 | 1        |   0 |   0 |
| Economics                               | 433 | 132 | 301 |   0 | 0.30485  |   0 |  42 |  35 |  26 |   2 |   0 |  10 | 115 |  96 | 0.545024 | 197 |  25 |
| Creative Writing                        |  34 |  19 |  15 |   0 | 0.558824 |   0 |   3 |   5 |   4 |   1 |   0 |   1 |  14 |  19 | 0.424242 |   0 |   1 |
| Literary History                        |   1 |   1 |   0 |   0 | 1        |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 |   0 | 1        |   0 |   0 |
| Professional Writing                    |  10 |   7 |   3 |   0 | 0.7      |   0 |   0 |   1 |   1 |   0 |   0 |   0 |   2 |   8 | 0.2      |   0 |   0 |
| Transnational&Multicultur Lit           |   1 |   1 |   0 |   0 | 1        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   1 | 0        |   0 |   0 |
| Ethical, Social, & Political Philosophy |  19 |  12 |   7 |   0 | 0.631579 |   0 |   1 |   3 |   1 |   0 |   0 |   1 |   6 |  11 | 0.352941 |   1 |   1 |
| French                                  |  26 |  15 |  11 |   0 | 0.576923 |   0 |   0 |   9 |   2 |   1 |   0 |   2 |  14 |  10 | 0.583333 |   2 |   0 |
| Italian                                 |   8 |   8 |   0 |   0 | 1        |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   6 | 0.142857 |   0 |   1 |
| Italian Studies                         |   4 |   4 |   0 |   0 | 1        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   3 | 0        |   0 |   1 |
| Language and Literature                 |   2 |   2 |   0 |   0 | 1        |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   0 |   2 | 0        |   0 |   0 |
| No Track/Concentration                  |   2 |   2 |   0 |   0 | 1        |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   1 | 0.5      |   0 |   0 |
| Latin American & Iberian Studies        |  57 |  43 |  14 |   0 | 0.754386 |   0 |   2 |   3 |  33 |   2 |   0 |   0 |  40 |  12 | 0.769231 |   0 |   5 |
| Language,Culture & Society              |  14 |   9 |   5 |   0 | 0.642857 |   0 |   0 |   0 |   7 |   1 |   0 |   0 |   8 |   4 | 0.666667 |   0 |   2 |
| Latin American Studies                  |   1 |   1 |   0 |   0 | 1        |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   0 | 1        |   0 |   0 |
| Spanish Language                        |   4 |   4 |   0 |   0 | 1        |   0 |   0 |   0 |   2 |   0 |   0 |   0 |   2 |   1 | 0.666667 |   0 |   1 |
| Spanish Literature                      |   2 |   1 |   1 |   0 | 0.5      |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   1 | 0.5      |   0 |   0 |
| Translation Studies                     |  11 |   9 |   2 |   0 | 0.818182 |   0 |   1 |   1 |   7 |   0 |   0 |   0 |   9 |   1 | 0.9      |   0 |   1 |
| No Track/Concentration                  |  25 |  19 |   6 |   0 | 0.76     |   0 |   1 |   2 |  15 |   1 |   0 |   0 |  19 |   5 | 0.791667 |   0 |   1 |
| Music                                   |  82 |  33 |  49 |   0 | 0.402439 |   0 |   3 |  13 |  11 |   0 |   0 |   2 |  29 |  36 | 0.446154 |  12 |   5 |
| Philosophy & Public Policy              |  20 |  11 |   9 |   0 | 0.55     |   0 |   0 |   3 |   3 |   1 |   0 |   1 |   8 |  10 | 0.444444 |   0 |   2 |
| Political Science                       | 289 | 123 | 166 |   0 | 0.425606 |   0 |  15 |  48 |  44 |   0 |   0 |  10 | 117 | 121 | 0.491597 |  25 |  26 |
| Early Childhood Licensure               |   2 |   2 |   0 |   0 | 1        |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 |   1 | 0.5      |   0 |   0 |
| Early Intervention                      |   1 |   1 |   0 |   0 | 1        |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   0 | 1        |   0 |   0 |
| Social Psychology                       | 173 | 135 |  38 |   0 | 0.780347 |   0 |   8 |  41 |  37 |   6 |   0 |   8 | 100 |  61 | 0.621118 |   3 |   9 |
| Translation Studies                     |   1 |   1 |   0 |   0 | 1        |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   0 | 1        |   0 |   0 |
| Women's  & Gender Studies               |  28 |  25 |   3 |   0 | 0.892857 |   0 |   1 |   5 |   8 |   0 |   0 |   0 |  14 |  12 | 0.538462 |   1 |   1 |
| Language,Culture & Society              |   1 |   1 |   0 |   0 | 1        |   0 |   0 |   0 |   1 |   0 |   0 |   0 |   1 |   0 | 1        |   0 |   0 |
| No Track/Concentration                  |  27 |  24 |   3 |   0 | 0.888889 |   0 |   1 |   5 |   7 |   0 |   0 |   0 |  13 |  12 | 0.52     |   1 |   1 |
| Individual Major                        |   1 |   0 |   1 |   0 | 0        |   0 |   1 |   0 |   0 |   0 |   0 |   0 |   1 |   0 | 1        |   0 |   0 |



label: F=C/B
B=C+D+E
labeled_formulas: F=C/B
L=B*G
L=C*G
L=D*G
L=E*G
L=E*K
L=F*G
L=G*H
L=G*I
L=G*J
L=G*K
L=G*M
L=G*N
L=G*O
L=G*P
L=G*Q
L=G*R
B=C+D+E
L=(B-C)-D
C=(B*F)+G
C=(B*F)+L
L=(B+C)*G
L=(B+D)*G
L=(B*E)*G
L=(B*E)*K
L=(B+F)*G
L=(B*G)*H
L=(B*G)*I
L=(B*G)*J
L=(B*G)*K
L=(B*G)*M
L=(B*G)*N
L=(B*G)*O
L=(B*G)*P
L=(B*G)*Q
L=(B*G)*R
L=(C+D)*G
L=(C*E)*G
L=(C*E)*K
L=(C+F)*G
L=(C*G)*H
L=(C*G)*I
L=(C*G)*J
L=(C*G)*K
L=(C*G)*M
L=(C*G)*N
L=(C*G)*O
L=(C*G)*P
L=(C*G)*Q
L=(C*G)*R
output: {"Arithmetic-Relationship": ["F=C/B", "B=C+D+E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_476838___xlsx_d1d32ef404dd946985bf0ce971a7f63ef92e8412.xlsx___line_763