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:
| F       | G                                                                                                              |   H |     I |     J |   K |   L |    M |
|:--------|:---------------------------------------------------------------------------------------------------------------|----:|------:|------:|----:|----:|-----:|
| FTJP065 | Hilary Jones: Behind the Squires, Devon                                                                        |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP068 | Angela Harding: The Salt Path                                                                                  |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP070 | Pietr van der Keere: World Map, 1607                                                                           |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP071 | Abu'l-Qasim Manur Firdawsi: 'First Meeting of Rostam and his Grandfather, Sam' from 'Shahnama' (Book of Kings) |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP066 | Robert Gillmor: Ducks, Falcons and Lapwings                                                                    |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP067 | Pierre Auguste Renoir: Luncheon of the Boating Party                                                           |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP064 | Kew: Marianne North: Amatungula and Blue Ipomoea, South Africa                                                 |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP063 | Bex Parkin: Birds & Flowers                                                                                    |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP061 | Angela Harding: Rose Cottage                                                                                   |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP058 | Beryl Cook: Date Night                                                                                         |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP062 | Sandro Botticelli: The Birth of Venus                                                                          |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP060 | Alice and the Cheshire Cat                                                                                     |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP059 | Utagawa Hiroshige: Plum Garden                                                                                 |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP057 | NGS: Mabel Royds - Water Lilies                                                                                |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP056 | Tamara de Lempicka: Tamara in the Green Bugatti, 1929                                                          |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP055 | Nel Whatmore: Star of the Garden                                                                               |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP054 | Anne Stokes: Wheel of the Year                                                                                 |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP053 | L.S. Lowry: Market Scene, Northern Town, 1939                                                                  |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP052 | William Morris Gallery: Golden Lily                                                                            |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP051 | Ashmolean Museum: Embroidered Hanging with Peacock                                                             |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP050 | Angela Harding: Look Out!                                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP049 | Annie Soudain: Foxgloves and Finches                                                                           |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP048 | Anne Stokes: Moonstone                                                                                         |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP047 | National Galleries Scotland - Samuel Peploe: Pink Roses, Chinese Vase                                          |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP046 | National Gallery Bosschaert the Elder: A Still Life of Flowers                                                 |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP045 | Moomins on the Riviera                                                                                         |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP044 | Vincent van Gogh: Wheatfield with Cypress                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP043 | Louis Comfort Tiffany: Displaying Peacock                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP042 | Nel Whatmore: Love For My Garden                                                                               |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP041 | Annie Soudain: Midsummer Morning                                                                               |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP040 | Vincent van Gogh: Bedroom at Arles                                                                             |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP039 | Angela Harding: The Common                                                                                     |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP038 | Gustav Klimt: Poppy Field                                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP037 | Kew Gardens' Marianne North: Honeyflowers and Honeysuckers                                                     |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP034 | National Gallery: Monet The Museum at Le Havre                                                                 |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP033 | Frida Kahlo Pink                                                                                               |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP032 | Beryl Cook: Good Times                                                                                         |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP031 | Angela Harding: Marsh Owl                                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP030 | Gustav Klimt: Adele Bloch Bauer                                                                                |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP029 | Wilhelm List: Magnolia Tree                                                                                    |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP028 | Nel Whatmore: Up, Up and Away                                                                                  |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP027 | National Gallery: Vincent Van Gogh, Sunflowers                                                                 |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP025 | Hieronymus Bosch: Garden of Earthly Delights                                                                   |   0 | 14.99 | 12.49 |   8 |   0 | 6.37 |
| FTJP024 | Hokusai: The Great Wave                                                                                        |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP023 | Aimee Stewart: Fantastic Voyage                                                                                |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP022 | Vincent van Gogh: Almond Blossom                                                                               |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP021 | National Galleries Scotland: Robert Burns, The Hunt                                                            |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP020 | Nel Whatmore: A Million Shades                                                                                 |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP019 | Arthur Rackham: Alice in Wonderland Tea Party                                                                  |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP018 | National Gallery Monet: Bridge over Lily Pond                                                                  |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP017 | National Gallery Turner: Fighting Temeraire                                                                    |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP016 | Alphonse Mucha: Reverie                                                                                        |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP015 | Tenniel: Alice in Wonderland Jigsaw                                                                            |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP014 | Gustav Klimt: The Kiss                                                                                         |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP013 | Gustav Klimt: Three Ages of Woman                                                                              |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP012 | Moomin: A Dangerous Journey                                                                                    |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP011 | L.S. Lowry: Going to Work                                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP010 | Bodleian Library: High Jinks Bookshelves                                                                       |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP009 | Vincent Van Gogh: Wheat Field with a Lark                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP007 | Lesley Anne Ivory: Blossom                                                                                     |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP006 | J Howard Miller: Rosie the Riveter Poster                                                                      |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP005 | Grant Wood: American Gothic                                                                                    |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |
| FTJP004 | Van Gogh: Starry Night                                                                                         |   0 | 12.99 | 10.83 |   8 |   0 | 5.52 |



label: L=H*M
labeled_formulas: L=H*M
output: {"Arithmetic-Relationship": ["L=H*M"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_194299___xlsx_d59008bd0e431e04e1f5a5b59474ed86a5e47bcf.xlsx___line_633