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:
|     A | B                                          |   C |        D |         E |
|------:|:-------------------------------------------|----:|---------:|----------:|
|  1109 | Washtucna School District                  |   0 |    56    |    -56    |
|  1122 | Benge School District                      |   0 |    11.65 |    -11.65 |
|  1158 | Lind School District                       |   0 |   180.95 |   -180.95 |
|  1160 | Ritzville School District                  |   0 |   314.32 |   -314.32 |
|  2250 | Clarkston School District                  |   0 |  2600.97 |  -2600.97 |
|  3017 | Kennewick School District                  |   0 | 16753.1  | -16753.1  |
|  3050 | Paterson School District                   |   0 |   112.1  |   -112.1  |
|  3400 | Richland School District                   |   0 | 11352.7  | -11352.7  |
|  4019 | Manson School District                     |   0 |   656.87 |   -656.87 |
|  4069 | Stehekin School District                   |   0 |     7.2  |     -7.2  |
|  4127 | Entiat School District                     |   0 |   363.04 |   -363.04 |
|  4129 | Lake Chelan School District                |   0 |  1379.3  |  -1379.3  |
|  4222 | Cashmere School District                   |   0 |  1441.05 |  -1441.05 |
|  5313 | Crescent School District                   |   0 |   302.47 |   -302.47 |
|  5323 | Sequim School District                     |   0 |  2689.13 |  -2689.13 |
|  5401 | Cape Flattery School District              |   0 |   446.17 |   -446.17 |
|  5402 | Quillayute Valley School District          |   0 |  3167.8  |  -3167.8  |
|  6037 | Vancouver School District                  |   0 | 22259    | -22259    |
|  6101 | La Center School District                  |   0 |  1542.33 |  -1542.33 |
|  6103 | Green Mountain School District             |   0 |   137.5  |   -137.5  |
|  6112 | Washougal School District                  |   0 |  3044    |  -3044    |
|  6119 | Battle Ground School District              |   0 | 12617.9  | -12617.9  |
|  6122 | Ridgefield School District                 |   0 |  2071.01 |  -2071.01 |
|  7002 | Dayton School District                     |   0 |   427.3  |   -427.3  |
|  7035 | Starbuck School District                   |   0 |    28.9  |    -28.9  |
|  8130 | Toutle Lake School District                |   0 |   579.69 |   -579.69 |
|  8402 | Kalama School District                     |   0 |   894.02 |   -894.02 |
|  8404 | Woodland School District                   |   0 |  2232.48 |  -2232.48 |
|  9013 | Orondo School District                     |   0 |   158.2  |   -158.2  |
|  9075 | Bridgeport School District                 |   0 |   812.5  |   -812.5  |
|  9102 | Palisades School District                  |   0 |    24.8  |    -24.8  |
|  9207 | Mansfield School District                  |   0 |    79    |    -79    |
|  9209 | Waterville School District                 |   0 |   270.44 |   -270.44 |
| 10003 | Keller School District                     |   0 |    38.3  |    -38.3  |
| 10050 | Curlew School District                     |   0 |   208.7  |   -208.7  |
| 10065 | Orient School District                     |   0 |   102.74 |   -102.74 |
| 10070 | Inchelium School District                  |   0 |   208.45 |   -208.45 |
| 10309 | Republic School District                   |   0 |   335.75 |   -335.75 |
| 11054 | Star School District No. 054               |   0 |     4    |     -4    |
| 11056 | Kahlotus School District                   |   0 |    50.5  |    -50.5  |
| 12110 | Pomeroy School District                    |   0 |   315.05 |   -315.05 |
| 13073 | Wahluke School District                    |   0 |  2183.67 |  -2183.67 |
| 13146 | Warden School District                     |   0 |   950.53 |   -950.53 |
| 13151 | Coulee-Hartline School District            |   0 |   187.94 |   -187.94 |
| 13165 | Ephrata School District                    |   0 |  2314.47 |  -2314.47 |
| 13167 | Wilson Creek School District               |   0 |   140.47 |   -140.47 |
| 13301 | Grand Coulee Dam School District           |   0 |   674.88 |   -674.88 |
| 14005 | Aberdeen School District                   |   0 |  3213.85 |  -3213.85 |
| 14064 | North Beach School District                |   0 |   628.31 |   -628.31 |
| 14065 | McCleary School District                   |   0 |   264.64 |   -264.64 |
| 14068 | Elma School District                       |   0 |  1507.15 |  -1507.15 |
| 14077 | Taholah School District                    |   0 |   178.28 |   -178.28 |
| 14097 | Lake Quinault School District              |   0 |   163.58 |   -163.58 |
| 14099 | Cosmopolis School District                 |   0 |   121.71 |   -121.71 |
| 14104 | Satsop School District                     |   0 |    57.2  |    -57.2  |
| 14117 | Wishkah Valley School District             |   0 |   142.51 |   -142.51 |
| 14172 | Ocosta School District                     |   0 |   647.6  |   -647.6  |
| 14400 | Oakville School District                   |   0 |   248.14 |   -248.14 |
| 15204 | Coupeville School District                 |   0 |   899.29 |   -899.29 |
| 15206 | South Whidbey School District              |   0 |  1407.95 |  -1407.95 |
| 16020 | Queets-Clearwater School District          |   0 |    20.9  |    -20.9  |
| 16046 | Brinnon School District                    |   0 |    35.8  |    -35.8  |
| 16048 | Quilcene School District                   |   0 |   555.62 |   -555.62 |
| 16049 | Chimacum School District                   |   0 |  1070.53 |  -1070.53 |
| 16050 | Port Townsend School District              |   0 |  1194.24 |  -1194.24 |
| 17001 | Seattle Public Schools                     |   0 | 49017.4  | -49017.4  |
| 17210 | Federal Way School District                |   0 | 21515.3  | -21515.3  |
| 17216 | Enumclaw School District                   |   0 |  4197.22 |  -4197.22 |
| 17400 | Mercer Island School District              |   0 |  4136.22 |  -4136.22 |
| 17402 | Vashon Island School District              |   0 |  1487.54 |  -1487.54 |
| 17404 | Skykomish School District                  |   0 |    39.13 |    -39.13 |
| 17405 | Bellevue School District                   |   0 | 18234    | -18234    |
| 17407 | Riverview School District                  |   0 |  3142.93 |  -3142.93 |
| 17408 | Auburn School District                     |   0 | 14711.9  | -14711.9  |
| 17409 | Tahoma School District                     |   0 |  7437.65 |  -7437.65 |
| 17410 | Snoqualmie Valley School District          |   0 |  6077.55 |  -6077.55 |
| 17411 | Issaquah School District                   |   0 | 17770.2  | -17770.2  |
| 17415 | Kent School District                       |   0 | 26661.8  | -26661.8  |
| 17417 | Northshore School District                 |   0 | 19471.5  | -19471.5  |
| 18303 | Bainbridge Island School District          |   0 |  3740.22 |  -3740.22 |
| 18401 | Central Kitsap School District             |   0 | 10535.7  | -10535.7  |
| 18402 | South Kitsap School District               |   0 |  9027.65 |  -9027.65 |
| 19007 | Damman School District                     |   0 |    43    |    -43    |
| 19028 | Easton School District                     |   0 |   105.13 |   -105.13 |
| 19400 | Thorp School District                      |   0 |   108.61 |   -108.61 |
| 19401 | Ellensburg School District                 |   0 |  2935.96 |  -2935.96 |
| 19404 | Cle Elum-Roslyn School District            |   0 |   875.71 |   -875.71 |
| 20094 | Wishram School District                    |   0 |    77.38 |    -77.38 |
| 20203 | Bickleton School District                  |   0 |    87.21 |    -87.21 |
| 20215 | Centerville School District                |   0 |    73.1  |    -73.1  |
| 20400 | Trout Lake School District                 |   0 |   198.74 |   -198.74 |
| 20401 | Glenwood School District                   |   0 |    65.88 |    -65.88 |
| 20402 | Klickitat School District                  |   0 |    90.42 |    -90.42 |
| 20403 | Roosevelt School District                  |   0 |    26.9  |    -26.9  |
| 20404 | Goldendale School District                 |   0 |   931.13 |   -931.13 |
| 20405 | White Salmon Valley School District        |   0 |  1243.33 |  -1243.33 |
| 20406 | Lyle School District                       |   0 |   218.71 |   -218.71 |
| 21014 | Napavine School District                   |   0 |   735.98 |   -735.98 |
| 21036 | Evaline School District                    |   0 |    42.5  |    -42.5  |
| 21206 | Mossyrock School District                  |   0 |   526.7  |   -526.7  |
| 21214 | Morton School District                     |   0 |   293.55 |   -293.55 |
| 21234 | Boistfort School District                  |   0 |    84.45 |    -84.45 |
| 21237 | Toledo School District                     |   0 |   750.32 |   -750.32 |
| 21300 | Onalaska School District                   |   0 |   731.65 |   -731.65 |
| 21301 | Pe Ell School District                     |   0 |   280.16 |   -280.16 |
| 21302 | Chehalis School District                   |   0 |  2721.07 |  -2721.07 |
| 21401 | Centralia School District                  |   0 |  3521.86 |  -3521.86 |
| 22008 | Sprague School District                    |   0 |    65.69 |    -65.69 |
| 22009 | Reardan-Edwall School District             |   0 |   564.1  |   -564.1  |
| 22017 | Almira School District                     |   0 |    75.34 |    -75.34 |
| 22073 | Creston School District                    |   0 |    98.05 |    -98.05 |
| 22105 | Odessa School District                     |   0 |   204.82 |   -204.82 |
| 22200 | Wilbur School District                     |   0 |   268.06 |   -268.06 |
| 22204 | Harrington School District                 |   0 |    97.4  |    -97.4  |
| 22207 | Davenport School District                  |   0 |   550.75 |   -550.75 |
| 23042 | Southside School District                  |   0 |   191.52 |   -191.52 |
| 23054 | Grapeview School District                  |   0 |   200.55 |   -200.55 |
| 23311 | Mary M Knight School District              |   0 |   189.96 |   -189.96 |
| 23402 | Pioneer School District                    |   0 |   654.57 |   -654.57 |
| 23403 | North Mason School District                |   0 |  2026.54 |  -2026.54 |
| 23404 | Hood Canal School District                 |   0 |   281.6  |   -281.6  |
| 24014 | Nespelem School District                   |   0 |   132.9  |   -132.9  |
| 24019 | Omak School District                       |   0 |  4941.35 |  -4941.35 |
| 24111 | Brewster School District                   |   0 |   903.53 |   -903.53 |
| 24122 | Pateros School District                    |   0 |   293.68 |   -293.68 |
| 24350 | Methow Valley School District              |   0 |   584.75 |   -584.75 |
| 24404 | Tonasket School District                   |   0 |  1074.36 |  -1074.36 |
| 24410 | Oroville School District                   |   0 |   576.32 |   -576.32 |
| 25101 | Ocean Beach School District                |   0 |   941.29 |   -941.29 |
| 25116 | Raymond School District                    |   0 |   654.57 |   -654.57 |
| 25118 | South Bend School District                 |   0 |   533.05 |   -533.05 |
| 25155 | Naselle-Grays River Valley School District |   0 |   503.72 |   -503.72 |
| 25160 | Willapa Valley School District             |   0 |   319.84 |   -319.84 |
| 25200 | North River School District                |   0 |    50.39 |    -50.39 |
| 26056 | Newport School District                    |   0 |  1021.85 |  -1021.85 |
| 26059 | Cusick School District                     |   0 |   268.18 |   -268.18 |
| 26070 | Selkirk School District                    |   0 |   244.31 |   -244.31 |
| 27010 | Tacoma School District                     |   0 | 28011.5  | -28011.5  |
| 27019 | Carbonado School District                  |   0 |   176.8  |   -176.8  |
| 27083 | University Place School District           |   0 |  5377.61 |  -5377.61 |
| 27320 | Sumner School District                     |   0 |  8318.75 |  -8318.75 |
| 27343 | Dieringer School District                  |   0 |  1419.23 |  -1419.23 |
| 27344 | Orting School District                     |   0 |  2236.92 |  -2236.92 |
| 27401 | Peninsula School District                  |   0 |  8575.01 |  -8575.01 |
| 27402 | Franklin Pierce School District            |   0 |  7392.11 |  -7392.11 |
| 27404 | Eatonville School District                 |   0 |  1803.28 |  -1803.28 |
| 28010 | Shaw Island School District                |   0 |    14    |    -14    |
| 28137 | Orcas Island School District               |   0 |   806.67 |   -806.67 |
| 28144 | Lopez School District                      |   0 |   218.82 |   -218.82 |
| 29011 | Concrete School District                   |   0 |   523.37 |   -523.37 |
| 29100 | Burlington-Edison School District          |   0 |  3647.03 |  -3647.03 |
| 29101 | Sedro-Woolley School District              |   0 |  4132.6  |  -4132.6  |
| 29103 | Anacortes School District                  |   0 |  2609.01 |  -2609.01 |
| 29311 | La Conner School District                  |   0 |   607.18 |   -607.18 |
| 29317 | Conway School District                     |   0 |   414.85 |   -414.85 |
| 30002 | Skamania School District                   |   0 |    77.1  |    -77.1  |
| 30029 | Mount Pleasant School District             |   0 |    58.9  |    -58.9  |
| 30031 | Mill A School District                     |   0 |    22.85 |    -22.85 |
| 30303 | Stevenson-Carson School District           |   0 |   899.92 |   -899.92 |
| 31002 | Everett School District                    |   0 | 18250    | -18250    |
| 31004 | Lake Stevens School District               |   0 |  7805.01 |  -7805.01 |
| 31006 | Mukilteo School District                   |   0 | 14692.8  | -14692.8  |
| 31015 | Edmonds School District                    |   0 | 19558.9  | -19558.9  |
| 31016 | Arlington School District                  |   0 |  5171.57 |  -5171.57 |
| 31025 | Marysville School District                 |   0 | 10895.1  | -10895.1  |
| 31063 | Index School District                      |   0 |    31.45 |    -31.45 |
| 31103 | Monroe School District                     |   0 |  6818.54 |  -6818.54 |
| 31306 | Lakewood School District                   |   0 |  2215.74 |  -2215.74 |
| 31311 | Sultan School District                     |   0 |  1890.31 |  -1890.31 |
| 31330 | Darrington School District                 |   0 |   432.46 |   -432.46 |
| 31332 | Granite Falls School District              |   0 |  1976.28 |  -1976.28 |
| 31401 | Stanwood-Camano School District            |   0 |  4314.42 |  -4314.42 |
| 32081 | Spokane School District                    |   0 | 28994.8  | -28994.8  |
| 32123 | Orchard Prairie School District            |   0 |    73.1  |    -73.1  |
| 32312 | Great Northern School District             |   0 |    43.8  |    -43.8  |
| 32325 | Nine Mile Falls School District            |   0 |  1458.81 |  -1458.81 |
| 32326 | Medical Lake School District               |   0 |  1773.44 |  -1773.44 |
| 32354 | Mead School District                       |   0 |  9287.24 |  -9287.24 |
| 32356 | Central Valley School District             |   0 | 12474.4  | -12474.4  |
| 32358 | Freeman School District                    |   0 |   865.37 |   -865.37 |
| 32361 | East Valley School District (Spokane)      |   0 |  4354.42 |  -4354.42 |
| 32362 | Liberty School District                    |   0 |   398.84 |   -398.84 |
| 32363 | West Valley School District (Spokane)      |   0 |  3690.6  |  -3690.6  |
| 32414 | Deer Park School District                  |   0 |  2491.89 |  -2491.89 |
| 32416 | Riverside School District                  |   0 |  1483.11 |  -1483.11 |
| 33030 | Onion Creek School District                |   0 |    37.7  |    -37.7  |
| 33049 | Wellpinit School District                  |   0 |   504.8  |   -504.8  |
| 33070 | Valley School District                     |   0 |   862.7  |   -862.7  |
| 33115 | Colville School District                   |   0 |  1801.42 |  -1801.42 |
| 33183 | Loon Lake School District                  |   0 |   211.97 |   -211.97 |
| 33202 | Summit Valley School District              |   0 |    79.27 |    -79.27 |
| 33205 | Evergreen School District (Stevens)        |   0 |    27.7  |    -27.7  |
| 33206 | Columbia (Stevens) School District         |   0 |   156.95 |   -156.95 |
| 33207 | Mary Walker School District                |   0 |   492.54 |   -492.54 |
| 33211 | Northport School District                  |   0 |   227.9  |   -227.9  |
| 33212 | Kettle Falls School District               |   0 |   861.92 |   -861.92 |
| 34003 | North Thurston Public Schools              |   0 | 14091.2  | -14091.2  |
| 34033 | Tumwater School District                   |   0 |  6478.4  |  -6478.4  |
| 34324 | Griffin School District                    |   0 |   616.34 |   -616.34 |
| 34402 | Tenino School District                     |   0 |  1155.61 |  -1155.61 |
| 35200 | Wahkiakum School District                  |   0 |   404.68 |   -404.68 |
| 36101 | Dixie School District                      |   0 |    27.6  |    -27.6  |
| 36140 | Walla Walla Public Schools                 |   0 |  6074.14 |  -6074.14 |
| 36250 | College Place School District              |   0 |   827.84 |   -827.84 |
| 36300 | Touchet School District                    |   0 |   234.07 |   -234.07 |
| 36401 | Waitsburg School District                  |   0 |   280.66 |   -280.66 |
| 36402 | Prescott School District                   |   0 |   360.61 |   -360.61 |
| 37501 | Bellingham School District                 |   0 | 10656.2  | -10656.2  |
| 37503 | Blaine School District                     |   0 |  2030.1  |  -2030.1  |
| 37505 | Meridian School District                   |   0 |  1683.96 |  -1683.96 |
| 37506 | Nooksack Valley School District            |   0 |  1517.62 |  -1517.62 |
| 37507 | Mount Baker School District                |   0 |  1782.73 |  -1782.73 |
| 38126 | LaCrosse School District                   |   0 |    69.42 |    -69.42 |
| 38264 | Lamont School District                     |   0 |    31.1  |    -31.1  |
| 38265 | Tekoa School District                      |   0 |   184.55 |   -184.55 |
| 38267 | Pullman School District                    |   0 |  2403.68 |  -2403.68 |
| 38300 | Colfax School District                     |   0 |   607.73 |   -607.73 |
| 38301 | Palouse School District                    |   0 |   187.25 |   -187.25 |
| 38302 | Garfield School District                   |   0 |    92.65 |    -92.65 |
| 38304 | Steptoe School District                    |   0 |    28.8  |    -28.8  |
| 38306 | Colton School District                     |   0 |   158.59 |   -158.59 |
| 38308 | Endicott School District                   |   0 |    72.39 |    -72.39 |
| 38320 | Rosalia School District                    |   0 |   198.92 |   -198.92 |
| 38322 | St. John School District                   |   0 |   173.33 |   -173.33 |
| 38324 | Oakesdale School District                  |   0 |   109.45 |   -109.45 |
| 39002 | Union Gap School District                  |   0 |   610    |   -610    |
| 39003 | Naches Valley School District              |   0 |  1306.29 |  -1306.29 |
| 39007 | Yakima School District                     |   0 | 15617.1  | -15617.1  |
| 39090 | East Valley School District (Yakima)       |   0 |  2974.76 |  -2974.76 |
| 39119 | Selah School District                      |   0 |  3378.02 |  -3378.02 |
| 39120 | Mabton School District                     |   0 |   911.14 |   -911.14 |
| 39200 | Grandview School District                  |   0 |  3532.45 |  -3532.45 |
| 39202 | Toppenish School District                  |   0 |  3969.18 |  -3969.18 |
| 39203 | Highland School District                   |   0 |  1189.81 |  -1189.81 |
| 39205 | Zillah School District                     |   0 |  1295.35 |  -1295.35 |
| 39209 | Mount Adams School District                |   0 |   974.13 |   -974.13 |



label: E=C-D
labeled_formulas: E=C-D
E=(A*C)-D
output: {"Arithmetic-Relationship": ["E=C-D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_7299___xlsx_ca01a9597b8c579c13c0f345d0ea66156dc93a4b.xlsx___line_728