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:
| DD       |   DE | DF                                       | DG   |   DH |   DI |   DJ |   DK |   DL |
|:---------|-----:|:-----------------------------------------|:-----|-----:|-----:|-----:|-----:|-----:|
| Academic |   55 | Accountancy                              | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  808 | Agriculture                              | skl  |   70 |    0 |   30 |    0 |  100 |
| Skill    |  827 | Air-Conditioning & Refrigeration         | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  839 | Applied Chemistry                        | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  840 | Applied Mathematics                      | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  838 | Applied Physics                          | prct |   70 |    0 |   30 |    0 |  100 |
| Academic |   52 | Applied/ Commercial Art                  | sppr |   30 |    0 |   70 |    0 |  100 |
| Language |  116 | Arabic                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Language |  114 | Assamese                                 | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  804 | Automotive                               | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  199 | Bahasa Melayu                            | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  811 | Banking                                  | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  807 | Beauty & Wellness                        | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  105 | Bengali                                  | prj  |   80 |    0 |    0 |   20 |  100 |
| Academic |   57 | Bharatnatyam – Dance                     | sppr |   30 |    0 |   70 |    0 |  100 |
| Language |  195 | Bhutia                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Academic |   44 | Biology                                  | prct |   70 |    0 |   30 |    0 |  100 |
| Academic |   45 | Biotechnology                            | prct |   70 |    0 |   30 |    0 |  100 |
| Language |  192 | Bodo                                     | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  833 | Business Administration                  | prct |   70 |    0 |   30 |    0 |  100 |
| Academic |   54 | Business Studies                         | prct |   70 |    0 |   30 |    0 |  100 |
| Academic |   43 | Chemistry                                | prct |   70 |    0 |   30 |    0 |  100 |
| Academic |   83 | Computer Science                         | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  823 | Cost Accounting                          | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  830 | Design                                   | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  842 | Early Childhood Education                | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  819 | Electrical   Technology                  | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  820 | Electronic Technology                    | skl  |   60 |    0 |   40 |    0 |  100 |
| Academic |   46 | Engineering Graphics                     | prct |   70 |    0 |   30 |    0 |  100 |
| Language |  301 | English Core                             | int  |   80 |    0 |    0 |   20 |  100 |
| Language |    1 | English Elective                         | int  |  100 |    0 |    0 |    0 |  100 |
| Academic |   66 | Entrepreneurship                         | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  837 | Fashion Studies                          | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  805 | Financial Markets Management             | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  834 | Food Nutrition & Dietetics               | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  809 | Food Production                          | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  118 | French                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  810 | Front Office Operations                  | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  818 | Geospatial Technology                    | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  120 | German                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Academic |   50 | Graphics                                 | sppr |   30 |    0 |   70 |    0 |  100 |
| Language |  110 | Gujarati                                 | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  813 | Health Care                              | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  302 | Hindi Core                               | int  |   80 |    0 |    0 |   20 |  100 |
| Language |    2 | Hindi Elective                           | int  |   80 |    0 |    0 |   20 |  100 |
| Academic |   64 | Home Science                             | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  816 | Horticulture                             | skl  |   60 |    0 |   40 |    0 |  100 |
| Academic |   65 | Informatics Practices (New)              | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  802 | Information  Technology                  | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  814 | Insurance                                | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  194 | Japanese                                 | prj  |   80 |    0 |    0 |   20 |  100 |
| Language |  115 | Kannada                                  | prj  |   80 |    0 |    0 |   20 |  100 |
| Language |  197 | Kashmiri                                 | prj  |   80 |    0 |    0 |   20 |  100 |
| Academic |   56 | Kathak – Dance                           | sppr |   30 |    0 |   70 |    0 |  100 |
| Academic |   61 | Kathakali – Dance                        | sppr |   30 |    0 |   70 |    0 |  100 |
| Academic |   73 | Knowledge Tradition & Practices Of India | prct |   70 |    0 |   30 |    0 |  100 |
| Academic |   58 | Kuchipudi – Dance                        | sppr |   30 |    0 |   70 |    0 |  100 |
| Academic |   74 | Legal Studies                            | prct |   70 |    0 |   30 |    0 |  100 |
| Language |  126 | Lepcha                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  836 | Library & Information Science            | prct |   70 |    0 |   30 |    0 |  100 |
| Language |  125 | Limboo                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Language |  112 | Malayalam                                | prj  |   80 |    0 |    0 |   20 |  100 |
| Language |  111 | Manipuri                                 | prj  |   80 |    0 |    0 |   20 |  100 |
| Academic |   60 | Manipuri – Dance                         | sppr |   30 |    0 |   70 |    0 |  100 |
| Language |  109 | Marathi                                  | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  812 | Marketing                                | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  835 | Mass Media Studies                       | prct |   70 |    0 |   30 |    0 |  100 |
| Skill    |  821 | Media                                    | skl  |   60 |    0 |   40 |    0 |  100 |
| Skill    |  828 | Medical Diagnostics                      | skl  |   60 |    0 |   40 |    0 |  100 |
| Language |  198 | Mizo                                     | prj  |   80 |    0 |    0 |   20 |  100 |
| Skill    |  832 | Music Production                         | skl  |   60 |    0 |   40 |    0 |  100 |
| Academic |   76 | National Cadet Corps (Ncc)               | prct |   70 |    0 |   30 |    0 |  100 |
| Language |  124 | Nepali                                   | prj  |   80 |    0 |    0 |   20 |  100 |
| Language |  113 | Odia                                     | prj  |   80 |    0 |    0 |   20 |  100 |
| Academic |   59 | Odissi – Dance                           | sppr |   30 |    0 |   70 |    0 |  100 |
| Skill    |  824 | Office Procedures & Practices            | skl  |   60 |    0 |   40 |    0 |  100 |



labeled_formulas: DI=DJ*DK
DI=(DE*DJ)*DK
DI=(DH*DJ)*DK
DL=(DH+DJ)+DK
DI=(DJ*DK)*DL
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_628082___xlsx_2c5ac40b2112c9f70fbe9c3402019957cbf56d1b.xlsx___line_129