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 |
|:--------|:------------------------------------------------------|----:|------:|------:|----:|----:|-----:|
| FTSB068 | William Morris: Seaweed                               |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB067 | Catrin Weltz-Stein: Chasing the Moon                  |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB066 | Vincent van Gogh: Bedroom at Arles                    |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB065 | Leonardo da Vinci: Detail of the Head of the Virgin   |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB064 | Annie Soudain: Midsummer Morning                      |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB063 | Kew Gardens: Foliage and Flowers by Marianne North    |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB062 | Rudyard Kipling: The Cat that Walked by Himself       |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB061 | Claude Monet: Bridge over a Pond for Water Lilies     |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB060 | National Gallery: Bosschaert: A Still Life of Flowers |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB059 | Johannes Vermeer: Girl With a Pearl Earring           |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB058 | Anne Stokes: Once Upon a Time                         |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB057 | Frida Kahlo Pink                                      |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB056 | Gustav Klimt: The Virgin                              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB055 | Vincent van Gogh: Wheat Field with a Lark             |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB053 | Aimee Stewart: Treasure Hunt Bookshelves              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB052 | Kerem Beyit: Black Dragon                             |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB051 | Aimee Stewart: A Stitch in Time Bookshelf             |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB050 | Vincent van Gogh: Wheat Field with Cypresses          |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB049 | Gustav Klimt: Adele Bloch Bauer I                     |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB048 | British Library Tenniel: Alice                        |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB047 | Paul Klee: Landscape with Yellow Birds                |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB046 | Alhambra Tile                                         |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB045 | Octavio Ocampo: Colomba                               |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB044 | Gustav Klimt: Water Serpents I                        |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB043 | Van Gogh: Café Terrace                                |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB041 | British Library: Rubaiyat of Omar Khayyam             |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB040 | Tiffany: Trellised Rambler Roses                      |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB039 | Rackham: Alice In Wonderland Tea Party                |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB038 | Turkish Wall Tiles                                    |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB037 | Bodleian Libraries: Hobbies and Pastimes Bookshelves  |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB036 | Josephine Wall: Daughter of the Deep                  |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB033 | Moomin: Dangerous Journey                             |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB030 | Gustav Klimt: Fulfilment                              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB028 | Van Gogh: Sunflowers                                  |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB027 | Edvard Munch: The Scream                              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB025 | Josephine Wall: Virgo                                 |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB024 | L.S Lowry: Coming from the Mill                       |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB023 | Van Gogh: Almond Blossom                              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB022 | Klimt: Detail from the Kiss                           |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB021 | Bodleian Library: High Jinks Bookshelves              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB020 | Da Vinci: Vitruvian Man                               |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB019 | Hiroshige: Plum Garden                                |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB018 | Beyit: Red Dragon                                     |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB015 | Mucha: Monaco Monte Carlo                             |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB013 | Gustav Klimt: The Kiss                                |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB012 | Jean & Ron Henry: Moon Maiden                         |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB010 | Gibson Les Paul Black Guitar                          |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB009 | Hiroshige: Sea at Satta                               |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB007 | William Morris: Acanthus                              |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB003 | Gustav Klimt: Tree of Life                            |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB002 | Van Gogh: Starry Night Over the Rhone                 |   0 | 12.99 | 10.83 |  16 |   0 | 5.52 |
| FTSB001 | Hokusai: The Great Wave                               |   0 | 12.99 | 10.83 |  16 |   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_194304___xlsx_d59008bd0e431e04e1f5a5b59474ed86a5e47bcf.xlsx___line_633