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:
|   B |    C | D                                                              |         E |          F |          G |
|----:|-----:|:---------------------------------------------------------------|----------:|-----------:|-----------:|
|   1 | 2009 | Avatar                                                         | 760507625 | 2023411357 | 2783918982 |
|   2 | 1997 | Titanic                                                        | 658672302 | 1548943366 | 2207615668 |
|   3 | 2015 | Jurassic World                                                 | 652270625 | 1017739569 | 1670010194 |
|   4 | 2012 | The Avengers                                                   | 623279547 |  896200000 | 1519479547 |
|   5 | 2008 | The Dark Knight                                                | 533345358 |  469546000 | 1002891358 |
|   6 | 1999 | Star Wars Ep. I: The Phantom Menace                            | 474544677 |  552500000 | 1027044677 |
|   7 | 1977 | Star Wars Ep. IV: A New Hope                                   | 460935665 |  325600000 |  786535665 |
|   8 | 2015 | The Avengers: Age of Ultron                                    | 459005868 |  945700000 | 1404705868 |
|   9 | 2012 | The Dark Knight Rises                                          | 448139099 |  636300000 | 1084439099 |
|  10 | 2004 | Shrek 2                                                        | 436471036 |  495781885 |  932252921 |
|  11 | 1982 | ET: The Extra-Terrestrial                                      | 434949459 |  357854772 |  792804231 |
|  12 | 2013 | The Hunger Games: Catching Fire                                | 424668047 |  440200000 |  864868047 |
|  13 | 2006 | Pirates of the Caribbean: Dead Man's Chest                     | 423315812 |  642900000 | 1066215812 |
|  14 | 1994 | The Lion King                                                  | 422780140 |  564700000 |  987480140 |
|  15 | 2010 | Toy Story 3                                                    | 415004880 |  654813349 | 1069818229 |
|  16 | 2013 | Iron Man 3                                                     | 408992272 |  806400000 | 1215392272 |
|  17 | 2012 | The Hunger Games                                               | 408010692 |  269912687 |  677923379 |
|  18 | 2002 | Spider-Man                                                     | 403706375 |  418000000 |  821706375 |
|  19 | 2009 | Transformers: Revenge of the Fallen                            | 402111870 |  434407829 |  836519699 |
|  20 | 2013 | Frozen                                                         | 400738009 |  873496971 | 1274234980 |
|  21 | 1993 | Jurassic Park                                                  | 395708305 |  643104279 | 1038812584 |
|  22 | 2011 | Harry Potter and the Deathly Hallows: Part II                  | 381011219 |  960500000 | 1341511219 |
|  23 | 2003 | Finding Nemo                                                   | 380529370 |  555900000 |  936429370 |
|  24 | 2005 | Star Wars Ep. III: Revenge of the Sith                         | 380270577 |  468728300 |  848998877 |
|  25 | 2003 | The Lord of the Rings: The Return of the King                  | 377845905 |  763562762 | 1141408667 |
|  26 | 2004 | Spider-Man 2                                                   | 373524485 |  410180516 |  783705001 |
|  27 | 2004 | The Passion of the Christ                                      | 370782930 |  251637737 |  622420667 |
|  28 | 2013 | Despicable Me 2                                                | 368065385 |  606808379 |  974873764 |
|  29 | 2015 | Inside Out                                                     | 356461711 |  496569504 |  853031215 |
|  30 | 2015 | Furious 7                                                      | 353007020 | 1165213799 | 1518220819 |
|  31 | 2011 | Transformers: Dark of the Moon                                 | 352390543 |  771400000 | 1123790543 |
|  32 | 2014 | American Sniper                                                | 350126372 |  197200000 |  547326372 |
|  33 | 2002 | The Lord of the Rings: The Two Towers                          | 342548984 |  592154195 |  934703179 |
|  34 | 2014 | The Hunger Games: Mockingjay - Part 1                          | 337135885 |  372500000 |  709635885 |
|  35 | 2007 | Spider-Man 3                                                   | 336530303 |  554345000 |  890875303 |
|  36 | 2015 | Minions                                                        | 336037315 |  827489131 | 1163526446 |
|  37 | 2010 | Alice in Wonderland                                            | 334191110 |  691300000 | 1025491110 |
|  38 | 2014 | Guardians of the Galaxy                                        | 333172112 |  438000000 |  771172112 |
|  39 | 1994 | Forrest Gump                                                   | 330151138 |  349706026 |  679857164 |
|  40 | 2007 | Shrek the Third                                                | 321012359 |  484610992 |  805623351 |
|  41 | 2007 | Transformers                                                   | 319071806 |  389026399 |  708098205 |
|  42 | 2008 | Iron Man                                                       | 318604126 |  263839000 |  582443126 |
|  43 | 2001 | Harry Potter and the Sorcerer’s Stone                          | 317575550 |  657179821 |  974755371 |
|  44 | 2008 | Indiana Jones and the Kingdom of the Crystal Skull             | 317023851 |  469534294 |  786558145 |
|  45 | 2001 | The Lord of the Rings: The Fellowship of the Ring              | 315544750 |  571672938 |  887217688 |
|  46 | 2010 | Iron Man 2                                                     | 312128345 |  311128000 |  623256345 |
|  47 | 2007 | Pirates of the Caribbean: At World's End                       | 309420425 |  654000000 |  963420425 |
|  48 | 1983 | Star Wars Ep. VI: Return of the Jedi                           | 309125409 |  263500000 |  572625409 |
|  49 | 1996 | Independence Day                                               | 306124059 |  511231623 |  817355682 |
|  50 | 2003 | Pirates of the Caribbean: The Curse of the Black Pearl         | 305411224 |  329542879 |  634954103 |
|  51 | 2012 | Skyfall                                                        | 304360277 |  806166704 | 1110526981 |
|  52 | 2012 | The Hobbit: An Unexpected Journey                              | 303003568 |  714000000 | 1017003568 |
|  53 | 2002 | Star Wars Ep. II: Attack of the Clones                         | 302181125 |  346018875 |  648200000 |
|  54 | 2009 | Harry Potter and the Half-Blood Prince                         | 301959197 |  633124489 |  935083686 |
|  55 | 2010 | The Twilight Saga: Eclipse                                     | 300531751 |  405571077 |  706102828 |
|  56 | 2009 | The Twilight Saga: New Moon                                    | 296623634 |  390934093 |  687557727 |
|  57 | 2010 | Harry Potter and the Deathly Hallows: Part I                   | 295001070 |  664300000 |  959301070 |
|  58 | 1999 | The Sixth Sense                                                | 293506292 |  379300000 |  672806292 |
|  59 | 2009 | Up                                                             | 293004164 |  438538457 |  731542621 |
|  60 | 2010 | Inception                                                      | 292576195 |  540008221 |  832584416 |
|  61 | 2012 | The Twilight Saga: Breaking Dawn, Part 2                       | 292324737 |  537400000 |  829724737 |
|  62 | 2007 | Harry Potter and the Order of the Phoenix                      | 292004738 |  650939197 |  942943935 |
|  63 | 2005 | The Chronicles of Narnia: The Lion, the Witch and the Wardrobe | 291710957 |  428828615 |  720539572 |
|  64 | 2013 | Man of Steel                                                   | 291045518 |  376954000 |  667999518 |
|  65 | 1980 | Star Wars Ep. V: The Empire Strikes Back                       | 290158751 |  243900000 |  534058751 |
|  66 | 2005 | Harry Potter and the Goblet of Fire                            | 290013036 |  606898042 |  896911078 |
|  67 | 2001 | Monsters, Inc.                                                 | 289423425 |  270334294 |  559757719 |
|  68 | 2003 | The Matrix Reloaded                                            | 281553689 |  457023240 |  738576929 |
|  69 | 2011 | The Twilight Saga: Breaking Dawn, Part 1                       | 281287133 |  408132918 |  689420051 |
|  70 | 2004 | Meet the Fockers                                               | 279167575 |  237400000 |  516567575 |
|  71 | 1990 | Home Alone                                                     | 277504018 |  190923432 |  468427450 |
|  72 | 2009 | The Hangover                                                   | 277322503 |  188441583 |  465764086 |
|  73 | 2013 | Gravity                                                        | 274092705 |  442300000 |  716392705 |
|  74 | 2013 | Monsters University                                            | 268488329 |  475100000 |  743588329 |
|  75 | 2001 | Shrek                                                          | 267655011 |  224157783 |  491812794 |
|  76 | 2012 | The Amazing Spider-Man                                         | 262030663 |  495859604 |  757890267 |
|  77 | 2002 | Harry Potter and the Chamber of Secrets                        | 261987880 |  616991754 |  878979634 |
|  78 | 2004 | The Incredibles                                                | 261441092 |  353285660 |  614726752 |
|  79 | 2000 | How the Grinch Stole Christmas                                 | 260044825 |   85096578 |  345141403 |
|  80 | 1975 | Jaws                                                           | 260000000 |  210700000 |  470700000 |
|  81 | 2014 | Captain America: The Winter Soldier                            | 259746958 |  454100000 |  713846958 |
|  82 | 2013 | The Hobbit: The Desolation of Smaug                            | 258366855 |  702000000 |  960366855 |
|  83 | 2014 | The Lego Movie                                                 | 257784718 |  199944670 |  457729388 |
|  84 | 2009 | Star Trek                                                      | 257730019 |  127950427 |  385680446 |
|  85 | 2007 | I am Legend                                                    | 256393010 |  329139674 |  585532684 |
|  86 | 2009 | The Blind Side                                                 | 255959475 |   49746319 |  305705794 |
|  87 | 2014 | The Hobbit: The Battle of the Five Armies                      | 255119788 |  700000000 |  955119788 |
|  88 | 2011 | The Hangover Part II                                           | 254464305 |  332000000 |  586464305 |
|  89 | 2010 | Despicable Me                                                  | 251513985 |  291981048 |  543495033 |
|  90 | 2006 | Night at the Museum                                            | 250863268 |  328583139 |  579446407 |
|  91 | 1997 | Men in Black                                                   | 250147615 |  337100000 |  587247615 |
|  92 | 2004 | Harry Potter and the Prisoner of Azkaban                       | 249538952 |  547149597 |  796688549 |
|  93 | 1989 | Batman                                                         | 248972777 |  160160000 |  409132777 |
|  94 | 1981 | Raiders of the Lost Ark                                        | 248159971 |  141766000 |  389925971 |
|  95 | 2015 | The Hunger Games: Mockingjay - Part 2                          | 246883184 |  320100000 |  566983184 |
|  96 | 1999 | Toy Story 2                                                    | 245823397 |  265506097 |  511329494 |
|  97 | 2014 | Transformers: Age of Extinction                                | 245439076 |  858600000 | 1104039076 |
|  98 | 2006 | Cars                                                           | 244082982 |  217568264 |  461651246 |
|  99 | 2003 | Bruce Almighty                                                 | 242704995 |  240768967 |  483473962 |
| 100 | 1984 | Ghostbusters                                                   | 242212467 |   53000000 |  295212467 |



label: G=E+F
labeled_formulas: G=E+F
output: {"Arithmetic-Relationship": ["G=E+F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_100539___xlsx_50a9a8fd49d315dbffeb13ce3b285af54184e2d4.xlsx___line_218