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:
|     I | J                                   |   K |       L | M                     | N       |
|------:|:------------------------------------|----:|--------:|:----------------------|:--------|
| 21226 | Adna                                |   1 |   66.56 | 1.502403846153846E-2  | 2       |
| 29103 | Anacortes                           |  18 |  328.78 | 5.4747855708984723E-2 | 4       |
| 31016 | Arlington                           |   5 |  845.23 | 5.9155496137146104E-3 | 2       |
|  2420 | Asotin-Anatone                      |   1 |   91.44 | 1.0936132983377079E-2 | 2       |
| 17408 | Auburn                              | 103 | 2025.22 | 5.0858672144260868E-2 | 4       |
| 18303 | Bainbridge Island                   |  33 |  462.78 | 7.1308180993128495E-2 | 4       |
|  6119 | Battle Ground                       |  63 | 1936    | 3.2541322314049582E-2 | 4       |
| 17405 | Bellevue                            | 161 | 1841    | 8.7452471482889732E-2 | 4       |
| 37501 | Bellingham                          |  58 | 1702.44 | 3.4068748384671409E-2 | 4       |
| 27403 | Bethel                              |  72 | 2888.78 | 2.4924016366770746E-2 | 2       |
| 37503 | Blaine                              |  14 |  372.11 | 3.7623283437693153E-2 | 4       |
| 18100 | Bremerton                           |  18 |  748.66 | 2.4042956749392243E-2 | 2       |
| 29100 | Burlington-Edison                   |   6 |  542.33 | 1.1063374698062064E-2 | 2       |
|  6117 | Camas                               |  42 |  827.21 | 5.0773080596221022E-2 | 4       |
| 27019 | Carbonado                           |   2 |   26.89 | 7.4377091855708441E-2 | 4       |
|  8401 | Castle Rock                         |   4 |  284.34 | 1.40676654709151E-2   | 2       |
| 18401 | Central Kitsap                      |  67 | 1864.22 | 3.5939964167319309E-2 | 4       |
| 32356 | Central Valley                      |  48 | 2227.55 | 2.1548337859980699E-2 | 2       |
| 21401 | Centralia                           |  16 |  566.23 | 2.8257068682337565E-2 | 2       |
| 21302 | Chehalis                            |   4 |  424.22 | 9.4290698222620328E-3 | 2       |
| 32360 | Cheney                              |   2 |  896.11 | 2.2318688553860577E-3 | 2       |
| 16049 | Chimacum                            |  10 |  151.78 | 6.5884833311371738E-2 | 4       |
| 27400 | Clover Park                         |  96 | 2079.77 | 4.6158950268539313E-2 | 4       |
| 36250 | College Place                       |   6 |  210.34 | 2.852524484168489E-2  | 2       |
| 33115 | Colville                            |   5 |  285.22 | 1.7530327466517077E-2 | 2       |
| 29011 | Concrete                            |   8 |   96.11 | 8.3237956508167718E-2 | 4       |
| 29317 | Conway                              |   4 |   50.55 | 7.912957467853611E-2  | 4       |
| 14099 | Cosmopolis                          |   1 |   37    | 2.7027027027027029E-2 | 2       |
| 15204 | Coupeville                          |   5 |  166.33 | 3.0060722659772745E-2 | 4       |
| 31330 | Darrington                          |   2 |   80.89 | 2.4724935097045372E-2 | 2       |
| 27343 | Dieringer                           |   2 |  201.44 | 9.9285146942017476E-3 | 2       |
| 32361 | East Valley No. 361 (Spokane)       |   4 |  623.89 | 6.4113866226418121E-3 | 2       |
| 27404 | Eatonville                          |   6 |  245.11 | 2.4478805434294808E-2 | 2       |
| 31015 | Edmonds                             |  43 | 3154.78 | 1.3630110498988837E-2 | 2       |
| 19401 | Ellensburg                          |   7 |  453.89 | 1.5422238868448302E-2 | 2       |
| 14068 | Elma                                |   1 |  305    | 3.2786885245901639E-3 | 2       |
| 17216 | Enumclaw                            |  19 |  688.22 | 2.7607451105751066E-2 | 2       |
|  6701 | ESA 112                             |  95 | 1606.65 | 5.9129244079295422E-2 | 4       |
| 31002 | Everett                             | 100 | 2783.11 | 3.5931026800952892E-2 | 4       |
|  6114 | Evergreen No. 114 (Clark)           | 158 | 3519.67 | 4.489057212750059E-2  | 4       |
| 17210 | Federal Way                         | 158 | 3217.11 | 4.9112402124888488E-2 | 4       |
| 37502 | Ferndale                            |  32 |  751    | 4.2609853528628498E-2 | 4       |
| 27417 | Fife                                |   9 |  468.21 | 1.9222143909784068E-2 | 2       |
| 27402 | Franklin Pierce                     |  30 | 1170.23 | 2.5635986088204884E-2 | 2       |
| 13301 | Grand Coulee Dam                    |   6 |  113.66 | 5.2789019883864155E-2 | 4       |
| 39200 | Grandview                           |   4 |  541.55 | 7.3862062598098058E-3 | 2       |
| 31332 | Granite Falls                       |  28 |  392.22 | 7.1388506450461464E-2 | 4       |
| 17401 | Highline                            |  88 | 2880.56 | 3.0549615352570333E-2 | 4       |
|  6098 | Hockinson                           |  15 |  191.22 | 7.8443677439598361E-2 | 4       |
| 17411 | Issaquah                            |  58 | 1715    | 3.3819241982507291E-2 | 4       |
|  8458 | Kelso                               |  21 |  738.56 | 2.8433708838821493E-2 | 2       |
|  3017 | Kennewick                           |  16 | 2424.78 | 6.5985367744702617E-3 | 2       |
| 17415 | Kent                                | 138 | 3145.23 | 4.3875964555851243E-2 | 4       |
| 29311 | La Conner                           |   5 |  110.11 | 4.5409136318227225E-2 | 4       |
|  6101 | LaCenter                            |   4 |  225.66 | 1.7725782150137374E-2 | 2       |
| 31004 | Lake Stevens                        |  40 | 1507.33 | 2.6536989245885108E-2 | 2       |
| 17414 | Lake Washington                     | 215 | 3308.67 | 6.4980792886567718E-2 | 4       |
| 31306 | Lakewood                            |  10 |  419.78 | 2.3822002001048167E-2 | 2       |
|  8122 | Longview                            |  48 | 1191.67 | 4.0279607609489204E-2 | 4       |
| 28144 | Lopez Island                        |   1 |   46.56 | 2.147766323024055E-2  | 2       |
| 37504 | Lynden                              |   6 |  553    | 1.0849909584086799E-2 | 2       |
| 39120 | Mabton                              |   4 |   88.22 | 4.5341192473362053E-2 | 4       |
| 31025 | Marysville                          |  75 | 1825.55 | 4.1083509079455509E-2 | 4       |
| 17400 | Mercer Island                       |  18 |  445.45 | 4.0408575597710175E-2 | 4       |
| 37505 | Meridian                            |   4 |  212.67 | 1.8808482625664175E-2 | 2       |
| 31103 | Monroe                              |  21 |  869.44 | 2.4153478100846521E-2 | 2       |
| 21214 | Morton                              |   1 |   57.44 | 1.7409470752089137E-2 | 2       |
| 21206 | Mossyrock                           |   2 |  107.78 | 1.8556318426424197E-2 | 2       |
| 37507 | Mount Baker                         |   6 |  363.55 | 1.6503919680924219E-2 | 2       |
| 29320 | Mount Vernon                        |  58 |  998.66 | 5.807782428454128E-2  | 4       |
| 31006 | Mukilteo                            |  56 | 2247.66 | 2.4914800281181319E-2 | 2       |
| 21014 | Napavine                            |   6 |  108.23 | 5.5437494225261015E-2 | 4       |
| 14064 | North Beach                         |   3 |  128.11 | 2.3417375692764027E-2 | 2       |
| 18400 | North Kitsap                        |  67 |  867.66 | 7.7219187239241163E-2 | 4       |
| 23403 | North Mason                         |   6 |  371.55 | 1.6148566814695196E-2 | 2       |
| 34003 | North Thurston                      |  62 | 2404.89 | 2.5780804943261435E-2 | 2       |
| 17417 | Northshore                          | 122 | 3012.89 | 4.049268310492584E-2  | 4       |
| 15201 | Oak Harbor                          |  16 | 1034.78 | 1.5462223854345852E-2 | 2       |
| 34111 | Olympia                             |  65 | 1549.56 | 4.1947391517592095E-2 | 4       |
| 21300 | Onalaska                            |   3 |  134.67 | 2.2276676319893069E-2 | 2       |
| 28137 | Orcas Island                        |   7 |   95.22 | 7.3513967653854234E-2 | 4       |
| 27344 | Orting                              |  15 |  436.33 | 3.4377649943849842E-2 | 4       |
| 11001 | Pasco                               |  11 | 2489    | 4.4194455604660505E-3 | 2       |
| 21301 | Pe Ell                              |   1 |   52.34 | 1.910584638899503E-2  | 2       |
| 27401 | Peninsula                           |  15 | 1323.78 | 1.133118796174591E-2  | 2       |
|  5121 | Port Angeles                        |  14 |  591.78 | 2.3657440264963331E-2 | 2       |
| 16050 | Port Townsend                       |  10 |  189.11 | 5.2879276611495954E-2 | 4       |
| 38267 | Pullman                             |   2 |  352.89 | 5.6674884524922781E-3 | 2       |
| 27003 | Puyallup                            |  85 | 2933.45 | 2.8976120267943887E-2 | 2       |
| 16048 | Quilcene                            |   5 |   50.22 | 9.9561927518916765E-2 | 6       |
| 17403 | Renton                              | 122 | 2374.89 | 5.1370800331804835E-2 | 4       |
|  6122 | Ridgefield                          |  19 |  393.34 | 4.8304266029389337E-2 | 4       |
| 17407 | Riverview                           |   3 |  360.22 | 8.3282438509799557E-3 | 2       |
| 34401 | Rochester                           |  11 |  341.33 | 3.2226877215597811E-2 | 4       |
| 28149 | San Juan Island                     |  12 |  137.55 | 8.7241003271537609E-2 | 4       |
| 17001 | Seattle                             | 124 | 8063.34 | 1.5378242762924545E-2 | 2       |
| 29101 | Sedro-Woolley                       |  33 |  824.22 | 4.0037853971027153E-2 | 4       |
|  5323 | Sequim                              |   1 |  426    | 2.3474178403755869E-3 | 2       |
| 23309 | Shelton                             |  21 |  705    | 2.9787234042553193E-2 | 4       |
| 17412 | Shoreline                           |  48 | 1195.01 | 4.0167027890979999E-2 | 4       |
| 31201 | Snohomish                           |  65 | 1269.89 | 5.1185535755065403E-2 | 4       |
| 17410 | Snoqualmie Valley                   |  18 |  820.67 | 2.1933298402524767E-2 | 2       |
| 18402 | South Kitsap                        |  42 | 1580.45 | 2.6574709734569268E-2 | 2       |
| 15206 | South Whidbey                       |   9 |  207.33 | 4.3409058023440895E-2 | 4       |
| 32081 | Spokane                             |  61 | 4889.33 | 1.2476147038551294E-2 | 2       |
| 31401 | Stanwood-Camano                     |  21 |  729.33 | 2.8793550244745177E-2 | 2       |
| 27001 | Steilacoom Historical               |   8 |  464    | 1.7241379310344827E-2 | 2       |
| 31311 | Sultan                              |   4 |  332.67 | 1.2023927615955752E-2 | 2       |
| 27320 | Sumner-Bonney Lake                  |  46 | 1232.44 | 3.7324332219012699E-2 | 4       |
| 27010 | Tacoma                              | 156 | 4457.77 | 3.4995076013343E-2    | 4       |
| 17409 | Tahoma                              |  70 | 1131.45 | 6.1867515135445666E-2 | 4       |
| 34402 | Tenino                              |   2 |  208.11 | 9.6103022440055738E-3 | 2       |
| 34033 | Tumwater                            |  10 |  895.01 | 1.1173059518888057E-2 | 2       |
| 27083 | University Place                    |  10 |  596.67 | 1.6759682906799401E-2 | 2       |
|  6037 | Vancouver                           | 120 | 3051.56 | 3.9324148959876258E-2 | 4       |
| 17402 | Vashon Island                       |   7 |  192.34 | 3.6393885827181033E-2 | 4       |
| 34974 | WA State School for the Blind       |   5 |    0    | #DIV/0!               | #DIV/0! |
| 34975 | WA State School for the Deaf (CDHY) |   2 |    0    | #DIV/0!               | #DIV/0! |
|  6112 | Washougal                           |  28 |  558.45 | 5.013877697197601E-2  | 4       |
|  4246 | Wenatchee                           |  23 |  990.66 | 2.3216845335432942E-2 | 2       |
| 39208 | West Valley No. 208 (Yakima)        |   9 |  757.22 | 1.188558146905787E-2  | 2       |
| 32363 | West Valley No. 363 (Spokane)       |   2 |  499.78 | 4.0017607747408861E-3 | 2       |
| 27416 | White River                         |   3 |  588.11 | 5.1010865314311954E-3 | 2       |
| 22200 | Wilbur                              |   1 |   39.78 | 2.513826043237808E-2  | 2       |
| 21232 | Winlock                             |   3 |  146.44 | 2.0486205954657197E-2 | 2       |
|  8404 | Woodland                            |  24 |  350    | 6.8571428571428575E-2 | 4       |
| 39007 | Yakima                              |  11 | 2236.89 | 4.9175417655763125E-3 | 2       |
| 34002 | Yelm                                |  15 |  857.67 | 1.7489244114869355E-2 | 2       |
| 39205 | Zillah                              |   1 |  155.56 | 6.428387760349704E-3  | 2       |



label: M=K/L
labeled_formulas: M=K/L
output: {"Arithmetic-Relationship": ["M=K/L"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_705271___xlsx_f16eba1f11c93d382cab19a5200caed6ea809c7b.xlsx___line_709