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 |
|--------:|:-----------------------------------------------|-----:|----:|----------:|
| 1210014 | Ashfield Girls' High School                    |  697 | 241 | 0.345768  |
| 1210015 | Ashfield Boys' High School                     |  737 | 270 | 0.36635   |
| 1210021 | Belfast Model School For Girls                 |  884 | 452 | 0.511312  |
| 1210022 | Belfast Boys' Model School                     |  969 | 522 | 0.5387    |
| 1230026 | St Patrick's College, Belfast                  |  679 | 375 | 0.552283  |
| 1230053 | St Louise's Comprehensive College              | 1518 | 821 | 0.540843  |
| 1230089 | Little Flower Girls' School                    |  644 | 311 | 0.482919  |
| 1230104 | Mercy College                                  |  433 | 337 | 0.778291  |
| 1230130 | St Rose’s Dominican College                    |  316 | 217 | 0.686709  |
| 1230146 | Christian Brothers School, Belfast             |  490 | 270 | 0.55102   |
| 1230155 | St Genevieve's High School                     | 1061 | 539 | 0.508011  |
| 1230182 | De La Salle College                            | 1116 | 535 | 0.479391  |
| 1230262 | Corpus Christi College                         |  344 | 247 | 0.718023  |
| 1230275 | St Joseph's College, Belfast                   |  634 | 280 | 0.44164   |
| 1240291 | Colaiste Feirste                               |  581 | 352 | 0.605852  |
| 1260269 | Hazelwood College                              |  916 | 501 | 0.546943  |
| 1260294 | Malone Integrated College                      |  617 | 354 | 0.573744  |
| 1410079 | Grosvenor Grammar School                       | 1090 |  70 | 0.0642202 |
| 1410270 | Wellington College                             |  815 | 122 | 0.149693  |
| 1410315 | Bloomfield Collegiate                          |  695 |  83 | 0.119424  |
| 1420020 | Campbell College                               |  899 |  15 | 0.0166852 |
| 1420021 | St Mary's Christian Brothers' Grammar, Belfast | 1200 | 429 | 0.3575    |
| 1420022 | Methodist College                              | 1788 | 104 | 0.0581655 |
| 1420027 | The Royal Belfast Academical Institution       | 1009 |  69 | 0.0683845 |
| 1420028 | Belfast Royal Academy                          | 1396 | 173 | 0.123926  |
| 1420029 | St Dominic's High School, Belfast              | 1021 | 273 | 0.267385  |
| 1420030 | St Malachy's College, Belfast                  | 1071 | 175 | 0.163399  |
| 1420082 | Dominican College, Belfast                     | 1023 | 174 | 0.170088  |
| 1420089 | Strathearn School, Belfast                     |  781 |  34 | 0.0435339 |
| 1420095 | Rathmore Grammar School                        | 1274 |  81 | 0.0635793 |
| 1420264 | Victoria College                               |  897 |  90 | 0.100334  |
| 1420265 | Hunterhouse College                            |  697 |  80 | 0.114778  |
| 1420277 | Aquinas Diocesan Grammar School                |  807 |  45 | 0.0557621 |
| 2210065 | Castlederg High School                         |  459 | 188 | 0.409586  |
| 2210125 | Omagh High School                              |  396 | 106 | 0.267677  |
| 2210302 | Limavady High School                           |  729 | 305 | 0.418381  |
| 2210306 | Lisneal College                                |  664 | 287 | 0.432229  |
| 2210312 | Devenish College                               |  519 | 138 | 0.265896  |
| 2230077 | St Mary's High School, Limavady                |  624 | 291 | 0.466346  |
| 2230081 | St Mary's College, Londonderry                 |  880 | 509 | 0.578409  |
| 2230085 | St Mary's High School, Brollagh                |  109 |  50 | 0.458716  |
| 2230099 | St Fanchea's College                           |  328 | 107 | 0.32622   |
| 2230100 | St Joseph's College, Enniskillen               |  266 | 113 | 0.424812  |
| 2230109 | St Mary's Secondary School, Irvinestown        |  150 |  75 | 0.5       |
| 2230122 | St Patricks & St Brigids High School           |  524 | 244 | 0.465649  |
| 2230131 | St Joseph's Secondary School, Londonderry      |  900 | 575 | 0.638889  |
| 2230138 | Dean Maguirc College                           |  489 | 206 | 0.421268  |
| 2230144 | St Patrick's College, Dungiven                 |  262 | 132 | 0.503817  |
| 2230148 | St John's College                              |  177 |  89 | 0.502825  |
| 2230166 | St Aidan's High School                         |  176 |  42 | 0.238636  |
| 2230180 | St Eugene's College, Roslea                    |   78 |  25 | 0.320513  |
| 2230188 | St Cecilia's College                           |  837 | 499 | 0.596177  |
| 2230190 | St Comhghall's College                         |  470 | 225 | 0.478723  |
| 2230225 | St Brigid's College, Carnhill                  |  514 | 368 | 0.715953  |
| 2230254 | Immaculate Conception College                  |   42 |  28 | 0.666667  |
| 2230298 | Sacred Heart College, Omagh                    |  882 | 401 | 0.454649  |
| 2230301 | Holy Cross College                             | 1615 | 707 | 0.437771  |
| 2260276 | Oakgrove Integrated College                    |  855 | 417 | 0.487719  |
| 2260280 | Erne Integrated College                        |  411 | 122 | 0.296837  |
| 2260283 | Drumragh Integrated College                    |  663 | 264 | 0.39819   |
| 2410040 | Collegiate Grammar School                      |  505 |  52 | 0.10297   |
| 2410048 | Limavady Grammar School                        |  884 | 154 | 0.174208  |
| 2410066 | Omagh Academy                                  |  664 |  73 | 0.10994   |
| 2410311 | Strabane Academy                               |  605 | 229 | 0.378512  |
| 2420041 | Mount Lourdes Grammar School                   |  747 | 101 | 0.135207  |
| 2420042 | Portora Royal School                           |  495 |  73 | 0.147475  |
| 2420043 | St Michael's College, Enniskillen              |  714 | 101 | 0.141457  |
| 2420052 | Thornhill College                              | 1398 | 334 | 0.238913  |
| 2420054 | St Columb's College, Londonderry               | 1534 | 400 | 0.260756  |
| 2420064 | Christian Brothers' Grammar School, Omagh      |  968 | 205 | 0.211777  |
| 2420065 | Loreto Grammar School                          |  882 | 185 | 0.209751  |
| 2420229 | Foyle College                                  |  834 | 131 | 0.157074  |
| 2420287 | Lumen Christi College                          |  851 | 103 | 0.121034  |
| 3210035 | Magherafelt High School                        |  579 | 159 | 0.274611  |
| 3210038 | Larne High School                              |  483 | 173 | 0.358178  |
| 3210091 | Carrickfergus College                          |  670 | 211 | 0.314925  |
| 3210124 | Ballycastle High School                        |  417 | 108 | 0.258993  |
| 3210133 | Ballymoney High School                         |  655 | 236 | 0.360305  |
| 3210134 | Ballyclare Secondary School                    | 1027 | 173 | 0.168452  |
| 3210172 | Cullybackey High School                        |  654 | 183 | 0.279817  |
| 3210200 | Monkstown Community School                     |  478 | 168 | 0.351464  |
| 3210202 | Glengormley High School                        |  838 | 291 | 0.347255  |
| 3210208 | Dunclug College                                |  839 | 266 | 0.317044  |
| 3210222 | Dunluce High School                            |  387 | 143 | 0.369509  |
| 3210232 | Downshire School                               |  630 | 145 | 0.230159  |
| 3210279 | Newtownabbey Community High School             |  188 | 108 | 0.574468  |
| 3210300 | Coleraine College                              |  232 | 111 | 0.478448  |
| 3230075 | Our Lady of Lourdes High School                |  227 |  96 | 0.422907  |
| 3230084 | St Patrick's College Ballymena                 |  532 | 205 | 0.385338  |
| 3230110 | St Joseph's College, Coleraine                 |  292 | 102 | 0.349315  |
| 3230132 | St Colm's High School, Magherafelt             |  446 |  87 | 0.195067  |
| 3230142 | St Mary's College, Ballymena                   |  315 |  76 | 0.24127   |
| 3230151 | St Paul's College                              |  292 |  78 | 0.267123  |
| 3230168 | St Pius X College                              |  941 | 220 | 0.233794  |
| 3230203 | Edmund Rice College                            |  605 | 283 | 0.467769  |
| 3230227 | Cross and Passion College                      |  753 | 167 | 0.22178   |
| 3230234 | St Patrick's College Maghera                   | 1313 | 255 | 0.194212  |
| 3230308 | St Benedict's College                          |  387 | 138 | 0.356589  |
| 3230310 | St Killian's College                           |  846 | 171 | 0.202128  |
| 3250149 | Crumlin Integrated College                     |  107 |  29 | 0.271028  |
| 3250207 | Parkhall Integrated College                    |  667 | 216 | 0.323838  |
| 3260289 | Slemish College                                |  772 | 173 | 0.224093  |
| 3260290 | North Coast Integrated College                 |  448 | 219 | 0.488839  |
| 3260299 | Ulidia Integrated College                      |  568 | 144 | 0.253521  |
| 3260303 | Sperrin Integrated College                     |  501 | 133 | 0.265469  |
| 3410008 | Ballyclare High School                         | 1233 |  44 | 0.0356853 |
| 3410033 | Coleraine High School                          |  802 | 102 | 0.127182  |
| 3410098 | Carrickfergus Grammar School                   |  799 |  67 | 0.0838548 |
| 3410209 | Antrim Grammar School                          |  743 |  54 | 0.0726783 |
| 3410297 | Cambridge House Grammar School                 |  923 |  94 | 0.101842  |
| 3420010 | St Louis Grammar School, Ballymena             | 1036 | 105 | 0.101351  |
| 3420011 | Ballymena Academy                              | 1238 |  61 | 0.049273  |
| 3420012 | Dalriada School                                |  880 |  53 | 0.0602273 |
| 3420032 | Coleraine Academical Institution               |  763 |  63 | 0.0825688 |
| 3420034 | Loreto College                                 |  818 |  82 | 0.100244  |
| 3420046 | Larne Grammar School                           |  739 |  78 | 0.105548  |
| 3420058 | Rainey Endowed School                          |  711 |  66 | 0.092827  |
| 3420068 | Dominican College, Portstewart                 |  502 |  75 | 0.149402  |
| 3420077 | Belfast High School                            |  928 |  60 | 0.0646552 |
| 3420080 | St Mary's Grammar School, Magherafelt          | 1080 |  92 | 0.0851852 |
| 4210012 | Movilla High School                            |  286 | 129 | 0.451049  |
| 4210029 | The High School Ballynahinch                   |  202 |  45 | 0.222772  |
| 4210045 | Nendrum College                                |  413 | 129 | 0.312349  |
| 4210046 | Glastry College                                |  643 | 179 | 0.278383  |
| 4210051 | Lisnagarvey High School                        |  509 | 181 | 0.355599  |
| 4210063 | Saintfield High School                         |  367 |  47 | 0.128065  |
| 4210086 | Knockbreda High School                         |  266 | 133 | 0.5       |
| 4210183 | Newtownbreda High School                       |  666 | 313 | 0.46997   |
| 4210201 | Laurelhill Community College                   |  718 | 177 | 0.246518  |
| 4210262 | Dundonald High School                          |  241 | 113 | 0.46888   |
| 4210296 | Bangor Academy and 6th Form College            | 1448 | 375 | 0.258978  |
| 4230023 | St Mary's High School, Downpatrick             |  437 | 169 | 0.386728  |
| 4230067 | St Columba's College                           |  183 |  50 | 0.273224  |
| 4230102 | St Colmcille's High School, Crossgar           |  311 | 101 | 0.324759  |
| 4230107 | St Columbanus' College                         |  593 | 147 | 0.247892  |
| 4230161 | St Colman's High School, Ballynahinch          |  409 | 160 | 0.391198  |
| 4230165 | St Patrick's Academy, Lisburn                  |  475 | 145 | 0.305263  |
| 4230211 | St Malachy's High School, Castlewellan         |  996 | 356 | 0.35743   |
| 4230223 | St Colm's High School, Belfast                 |  478 | 310 | 0.648536  |
| 4230224 | De La Salle High School                        |  360 | 144 | 0.4       |
| 4250024 | Priory College                                 |  549 | 183 | 0.333333  |
| 4250072 | Fort Hill College                              |  867 | 239 | 0.275663  |
| 4260255 | Lagan College                                  | 1270 | 278 | 0.218898  |
| 4260281 | Shimna Integrated College                      |  577 | 150 | 0.259965  |
| 4260295 | Strangford Integrated College                  |  554 | 168 | 0.303249  |
| 4260309 | Blackwater Integrated College                  |  213 |  81 | 0.380282  |
| 4410063 | Regent House Grammar School                    | 1422 | 131 | 0.0921238 |
| 4410085 | Down High School                               |  979 |  67 | 0.0684372 |
| 4410097 | Glenlola Collegiate                            | 1060 | 107 | 0.100943  |
| 4420015 | Bangor Grammar School                          |  875 |  95 | 0.108571  |
| 4420044 | Sullivan Upper School                          | 1077 |  43 | 0.0399257 |
| 4420050 | Friends' School                                |  982 |  37 | 0.0376782 |
| 4420051 | Wallace High School                            | 1164 |  55 | 0.0472509 |
| 4420086 | Assumption Grammar School                      |  843 |  88 | 0.104389  |
| 4420088 | St Patrick's Grammar School, Downpatrick       |  686 |  78 | 0.113703  |
| 4420259 | Our Lady and St Patrick's College              | 1279 |  44 | 0.0344019 |
| 5210016 | Kilkeel High School                            |  681 | 126 | 0.185022  |
| 5210025 | Newtownhamilton High School                    |  167 |  31 | 0.185629  |
| 5210043 | Clounagh Junior High School                    |  611 | 171 | 0.279869  |
| 5210047 | Banbridge High School                          |  553 | 154 | 0.278481  |
| 5210054 | Killicomaine Junior High School                |  449 |  79 | 0.175947  |
| 5210064 | Dromore High School                            |  926 | 141 | 0.152268  |
| 5210083 | Markethill High School                         |  496 |  99 | 0.199597  |
| 5210097 | Fivemiletown College                           |  414 |  80 | 0.193237  |
| 5210121 | City Armagh High School                        |  248 |  95 | 0.383065  |
| 5210127 | Rathfriland High School                        |  306 |  69 | 0.22549   |
| 5210143 | Tandragee Junior High School                   |  282 |  71 | 0.251773  |
| 5210153 | Aughnacloy College                             |  153 |  35 | 0.228758  |
| 5210186 | Newry High School                              |  422 | 122 | 0.2891    |
| 5210230 | Cookstown High School                          |  808 | 159 | 0.196782  |
| 5210231 | Drumglass High School                          |  300 |  91 | 0.303333  |
| 5210271 | Lurgan Junior High                             |  602 | 134 | 0.222591  |
| 5210282 | Craigavon Senior High School                   |  610 | 177 | 0.290164  |
| 5230056 | St Joseph's Boys' High School, Newry           |  381 | 186 | 0.488189  |
| 5230059 | St Columban's College                          |  154 |  72 | 0.467532  |
| 5230070 | St Mary's Girls' High, Lurgan                  |  457 | 137 | 0.299781  |
| 5230076 | St Patrick's College, Banbridge                |  291 | 104 | 0.357388  |
| 5230088 | St Paul's Junior High School, Lurgan           |  320 |  93 | 0.290625  |
| 5230108 | St Mary's High School, Newry                   |  554 | 254 | 0.458484  |
| 5230135 | St Mark's High School                          |  851 | 325 | 0.381904  |
| 5230152 | St Ciaran's High School                        |  800 | 208 | 0.26      |
| 5230157 | St Paul's High School, Bessbrook               | 1583 | 582 | 0.367656  |
| 5230160 | St Brigid's Boys' High                         |  106 |  57 | 0.537736  |
| 5230167 | St Joseph's High School, Crossmaglen           |  610 | 293 | 0.480328  |
| 5230187 | St Patrick's High School, Keady                | 1045 | 348 | 0.333014  |
| 5230192 | St Joseph's College, Coalisland                |  311 | 175 | 0.562701  |
| 5230213 | Lismore Comprehensive School                   | 1157 | 423 | 0.365601  |
| 5230218 | St Catherine's College                         | 1164 | 329 | 0.282646  |
| 5230256 | Drumcree College                               |  181 | 110 | 0.607735  |
| 5230278 | Holy Trinity College                           | 1002 | 467 | 0.466068  |
| 5230293 | St Patrick's College, Dungannon                |  631 | 239 | 0.378764  |
| 5250216 | Brownlow Int College                           |  312 | 158 | 0.50641   |
| 5260285 | New-Bridge Integrated College                  |  584 | 139 | 0.238014  |
| 5260286 | Integrated College Dungannon                   |  543 | 187 | 0.344383  |
| 5410013 | Banbridge Academy                              | 1324 |  67 | 0.0506042 |
| 5410057 | Lurgan College                                 |  453 |  37 | 0.0816777 |
| 5410067 | Portadown College                              |  791 |  46 | 0.0581542 |
| 5420045 | St Louis Grammar School, Kilkeel               |  591 | 135 | 0.228426  |
| 5420056 | St Michael's Grammar School, Lurgan            |  612 |  92 | 0.150327  |
| 5420059 | Abbey Christian Brothers Grammar School        |  911 | 141 | 0.154775  |
| 5420060 | Our Lady's Grammar School                      |  845 | 129 | 0.152663  |
| 5420062 | St Colman's College, Newry                     |  904 | 135 | 0.149336  |
| 5420073 | St Joseph's Convent Grammar School, Donaghmore |  678 | 155 | 0.228614  |
| 5420076 | Sacred Heart Grammar School, Newry             |  853 | 122 | 0.143025  |
| 5420260 | The Royal School, Dungannon                    |  660 |  58 | 0.0878788 |
| 5420263 | The Royal School, Armagh                       |  722 |  49 | 0.067867  |
| 5420268 | St Patrick's Grammar School, Armagh            |  872 | 204 | 0.233945  |
| 5420304 | St Patrick's Academy, Dungannon                | 1391 | 241 | 0.173257  |



label: E=D/C
labeled_formulas: E=D/C
output: {"Arithmetic-Relationship": ["E=D/C"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_575296___xlsx_f11c0abc2e1531d3b568bb2ee50cc7e5887bf49d.xlsx___line_821