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   | F   |   G |   H |   I |   J |   K |   L |   M |   N |   O |   P |   Q |   R |   S |   T |   U |   V |    W |   X |
|----:|----:|:-----------|:-----------|:----|:----|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|----:|-----:|----:|
|   1 | 393 | Lauren     | PHILLIPS   | WA  | J1  |  99 |  95 |  99 |  98 |  95 |  95 | 581 |  26 |  97 |  96 |  99 |  98 |  94 |  95 | 579 |  28 | 1160 |  54 |
|   2 | 460 | Lorelie    | STANFIELD  | AK  | J1  |  96 |  97 |  96 |  98 |  95 |  89 | 571 |  23 |  98 |  97 |  99 |  98 |  93 |  94 | 579 |  24 | 1150 |  47 |
|   3 | 484 | Virginia   | THRASHER   | VA  | J2  |  96 |  98 |  98 |  98 |  89 |  96 | 575 |  25 |  97 |  96 |  98 | 100 |  92 |  93 | 576 |  23 | 1151 |  48 |
|   4 | 224 | Deanna     | BINNIE     | PA  | J1  |  96 |  96 |  99 |  98 |  95 |  90 | 574 |  22 |  94 |  95 |  98 |  98 |  95 |  95 | 575 |  18 | 1149 |  40 |
|   5 | 208 | Amy        | FISTER     | PA  | J1  |  93 |  97 |  95 |  97 |  94 |  91 | 567 |  15 |  97 |  96 | 100 |  99 |  96 |  92 | 580 |  21 | 1147 |  36 |
|   6 | 376 | Sarah      | OSBORN     | VA  | J2  |  94 |  98 |  97 |  99 |  94 |  98 | 580 |  27 |  93 |  93 |  98 |  97 |  97 |  93 | 571 |  20 | 1151 |  47 |
|   7 | 350 | Minden     | MILES      | TX  | J1  |  96 |  99 |  98 |  98 |  94 |  98 | 583 |  24 |  94 |  97 |  99 |  95 |  94 |  89 | 568 |  16 | 1151 |  40 |
|   8 | 235 | Elizabeth  | GRATZ      | ILL | J1  |  96 |  93 |  99 |  97 |  94 |  94 | 573 |  23 |  97 |  99 |  99 |  98 |  94 |  92 | 579 |  23 | 1152 |  46 |
|   9 | 341 | Sonya      | MAY        | MA  | J1  |  96 |  96 |  96 |  99 |  96 |  93 | 576 |  17 |  90 |  95 |  99 |  99 |  93 |  93 | 569 |  27 | 1145 |  44 |
|  10 | 432 | Rachael    | SCHOENROCK | TX  | J1  |  96 |  98 |  98 |  97 |  91 |  92 | 572 |  25 |  95 |  97 |  96 |  97 |  92 |  94 | 571 |  20 | 1143 |  45 |
|  11 | 372 | Greta      | OCHSNER    | NV  | J1  |  96 |  97 |  98 |  97 |  89 |  96 | 573 |  22 |  96 |  94 |  97 |  98 |  92 |  93 | 570 |  14 | 1143 |  36 |
|  12 | 125 | Hannah     | BLACK      | VA  | J1  |  97 |  92 |  98 |  98 |  91 |  97 | 573 |  20 |  90 |  92 |  98 |  99 |  95 |  95 | 569 |  19 | 1142 |  39 |
|  13 | 334 | Denise     | MARTIN     | WA  | J1  |  95 |  95 |  98 |  97 |  94 |  88 | 567 |  17 |  99 |  94 |  96 |  97 |  96 |  93 | 575 |  21 | 1142 |  38 |
|  14 | 331 | Elizabeth  | MARSH      | AR  | J2  |  94 |  94 |  95 |  98 |  95 |  91 | 567 |  13 |  97 |  97 |  98 |  98 |  94 |  91 | 575 |  22 | 1142 |  35 |
|  15 | 333 | Rachel     | MARTIN     | NM  | J1  |  92 |  95 |  97 |  97 |  94 |  94 | 569 |  17 |  95 |  94 |  98 |  98 |  93 |  94 | 572 |  21 | 1141 |  38 |
|  16 | 203 | Dacotah    | FAUGHT     | ND  | J1  |  96 |  95 |  98 |  98 |  89 |  94 | 570 |  20 |  93 |  95 |  97 |  98 |  93 |  94 | 570 |  19 | 1140 |  39 |
|  17 | 332 | Mackenzie  | MARTIN     | MA  | J2  |  97 |  94 |  98 |  97 |  94 |  93 | 573 |  14 |  95 |  97 |  98 | 100 |  89 |  88 | 567 |  23 | 1140 |  37 |
|  18 | 135 | Haylea     | BROUGHTON  | OK  | J1  |  95 |  95 | 100 |  99 |  92 |  91 | 572 |  17 |  95 |  96 |  97 |  98 |  93 |  89 | 568 |  16 | 1140 |  33 |
|  19 | 227 | Alyssa     | GESTL      | PA  | J1  |  94 |  95 |  96 |  96 |  96 |  88 | 565 |  17 |  97 |  96 |  96 |  95 |  97 |  93 | 574 |  24 | 1139 |  41 |
|  20 | 133 | Katie      | BRIDGES    | TX  | J1  |  95 |  96 |  99 |  99 |  89 |  89 | 567 |  20 |  97 |  94 | 100 | 100 |  88 |  92 | 571 |  25 | 1138 |  45 |
|  21 | 146 | Hanna      | CARR       | KY  | J2  |  96 |  94 |  95 |  98 |  92 |  91 | 566 |  14 |  94 |  95 | 100 |  95 |  93 |  94 | 571 |  19 | 1137 |  33 |
|  22 | 234 | Ariana     | GRABOWSKI  | PA  | J1  |  92 |  95 |  99 |  98 |  94 |  91 | 569 |  19 |  97 |  95 |  99 |  98 |  87 |  91 | 567 |  20 | 1136 |  39 |
|  23 | 505 | Anna       | WEILBACHER | CA  | J2  |  93 |  87 |  97 |  97 |  91 |  97 | 562 |  15 |  96 |  95 |  97 |  99 |  95 |  91 | 573 |  18 | 1135 |  33 |
|  24 | 302 | Alexandra  | KISSELL    | PA  | J2  |  99 |  94 |  97 |  96 |  87 |  88 | 561 |  18 |  95 |  93 | 100 |  99 |  94 |  91 | 572 |  24 | 1133 |  42 |
|  25 | 220 | Rachel     | GARNER     | TX  | J2  |  95 |  96 |  97 |  96 |  86 |  92 | 562 |  17 |  94 |  97 |  97 |  98 |  92 |  93 | 571 |  25 | 1133 |  42 |
|  26 | 391 | Samantha   | PETERSON   | MN  | J2  |  96 |  97 |  93 |  98 |  93 |  93 | 570 |  13 |  95 |  96 |  94 |  96 |  90 |  92 | 563 |  16 | 1133 |  29 |
|  27 | 215 | Carmen     | FRY        | MN  | J2  |  97 |  92 |  97 |  96 |  93 |  93 | 568 |  15 |  92 |  94 |  97 |  96 |  93 |  93 | 565 |  11 | 1133 |  26 |
|  28 | 129 | Kelly      | BOGART     | NY  | J1  |  93 |  93 |  96 |  96 |  97 |  89 | 564 |  14 |  95 |  93 |  97 |  96 |  94 |  93 | 568 |  20 | 1132 |  34 |
|  29 | 446 | Sydney     | SMITH      | WV  | J1  |  95 |  96 |  94 |  93 |  94 |  93 | 565 |  10 |  93 |  94 |  97 |  98 |  91 |  93 | 566 |  17 | 1131 |  27 |
|  30 | 326 | Casey      | LUTZ       | ID  | J2  |  93 |  93 |  99 |  89 |  95 |  95 | 564 |  19 |  89 |  93 |  93 |  98 |  94 |  94 | 561 |  10 | 1125 |  29 |
|  31 | 101 | Reagan     | ABERNATHY  | TN  | J2  |  95 |  94 |  97 |  97 |  89 |  90 | 562 |  16 |  91 |  95 |  98 |  97 |  92 |  89 | 562 |  24 | 1124 |  40 |
|  32 | 201 | Cassidy    | FAIRMAN    | PA  | J2  |  93 |  93 |  97 |  99 |  90 |  90 | 562 |  16 |  97 |  92 |  96 |  98 |  91 |  88 | 562 |  13 | 1124 |  29 |
|  33 | 300 | Heather    | KIRBY      | KY  | J1  |  90 |  93 |  91 |  97 |  92 |  89 | 552 |   8 |  95 |  94 |  98 |  97 |  92 |  95 | 571 |  25 | 1123 |  33 |
|  34 | 253 | Julia      | HATCH      | VT  | J1  |  95 |  95 |  95 |  96 |  90 |  88 | 559 |  12 |  96 |  95 |  95 |  95 |  88 |  90 | 559 |  15 | 1118 |  27 |
|  35 | 516 | Rachel     | YAGER *    | MT  | J2  |  98 |  90 |  96 |  97 |  93 |  91 | 565 |  12 |  87 |  95 |  98 |  95 |  86 |  92 | 553 |   9 | 1118 |  21 |
|  36 | 256 | Nicole     | HANKEY     | TX  | J1  |  93 |  91 |  97 |  97 |  92 |  79 | 549 |  14 |  95 |  96 |  96 |  96 |  93 |  92 | 568 |  18 | 1117 |  32 |
|  37 | 219 | Harley     | GARDNER    | TX  | J2  |  89 |  90 |  96 |  97 |  91 |  89 | 552 |  14 |  91 |  94 |  99 |  94 |  92 |  94 | 564 |  11 | 1116 |  25 |
|  38 | 410 | Mekenna    | RICHARDSON | MD  | J2  |  95 |  95 |  98 |  96 |  91 |  89 | 564 |  14 |  93 |  92 |  96 |  94 |  85 |  91 | 551 |   9 | 1115 |  23 |
|  39 | 409 | Hannah     | RICHARDSON | MI  | J1  |  95 |  94 |  99 |  98 |  83 |  91 | 560 |  18 |  94 |  94 |  96 |  96 |  86 |  87 | 553 |  12 | 1113 |  30 |
|  40 | 471 | Sarah      | SUTTON     | OH  | J2  |  97 |  96 |  96 |  97 |  80 |  91 | 557 |  17 |  92 |  96 |  96 |  94 |  91 |  86 | 555 |  19 | 1112 |  36 |
|  41 | 466 | Megan      | STULKEN    | SD  | J1  |  93 |  94 |  96 |  98 |  90 |  88 | 559 |  20 |  90 |  94 |  98 |  97 |  85 |  86 | 550 |  21 | 1109 |  41 |
|  42 | 204 | Alexandra  | FEDORKO    | PA  | J1  |  93 |  93 |  94 |  98 |  87 |  87 | 552 |   8 |  94 |  93 |  99 |  95 |  90 |  85 | 556 |  13 | 1108 |  21 |
|  43 | 214 | Emma       | FRENCHU    | NJ  | J1  |  90 |  90 |  98 |  99 |  89 |  91 | 557 |  18 |  87 |  87 |  98 |  97 |  88 |  92 | 549 |  10 | 1106 |  28 |
|  44 | 457 | Sarah      | SROKA      | PA  | J1  |  94 |  98 |  94 |  96 |  84 |  89 | 555 |  14 |  90 |  93 |  93 |  96 |  91 |  88 | 551 |  11 | 1106 |  25 |
|  45 | 114 | Kathryn    | BACON      | CO  | J1  |  92 |  92 |  96 |  95 |  90 |  80 | 545 |  11 |  95 |  92 |  99 |  98 |  88 |  86 | 558 |  20 | 1103 |  31 |
|  46 | 394 | Morgan     | PHILLIPS   | MD  | J2  |  92 |  93 |  95 |  98 |  89 |  90 | 557 |  12 |  85 |  90 |  96 |  97 |  88 |  89 | 545 |  10 | 1102 |  22 |
|  47 | 492 | Bailey     | URBACH     | NH  | J1  |  94 |  87 |  96 |  96 |  91 |  91 | 555 |  15 |  93 |  91 |  97 |  95 |  83 |  87 | 546 |  16 | 1101 |  31 |
|  48 | 246 | Amy        | HAMMER     | PA  | J2  |  90 |  92 |  98 |  95 |  91 |  92 | 558 |  13 |  94 |  81 |  97 |  94 |  88 |  89 | 543 |  16 | 1101 |  29 |
|  49 | 119 | Jaimie     | BARNES     | AK  | J1  |  93 |  86 |  96 |  96 |  88 |  87 | 546 |  16 |  91 |  95 |  95 |  96 |  92 |  86 | 555 |   9 | 1101 |  25 |
|  50 | 226 | Amy        | GENTRY     | AK  | J2  |  93 |  89 |  98 |  94 |  89 |  88 | 551 |  12 |  91 |  91 |  91 |  94 |  90 |  90 | 547 |   9 | 1098 |  21 |
|  51 | 507 | Abby       | WEST       | MN  | J1  |  92 |  95 |  94 |  93 |  89 |  87 | 550 |  13 |  89 |  92 |  92 |  95 |  89 |  90 | 547 |  13 | 1097 |  26 |
|  52 | 127 | Corinne    | BLAIR      | WA  | J2  |  90 |  90 |  94 |  97 |  83 |  90 | 544 |  12 |  89 |  94 |  96 |  98 |  89 |  87 | 553 |  13 | 1097 |  25 |
|  53 | 349 | Malgorzada | MICAL      | FL  | J2  |  94 |  95 |  97 |  96 |  85 |  90 | 557 |  15 |  91 |  96 |  96 |  95 |  86 |  75 | 539 |  14 | 1096 |  29 |
|  54 | 477 | Sara       | TASHIMA    | HI  | J1  |  86 |  86 |  98 |  94 |  86 |  91 | 541 |  12 |  91 |  88 |  94 |  94 |  91 |  93 | 551 |   9 | 1092 |  21 |
|  55 | 459 | Annabelle  | STANEC     | OH  | J3  |  90 |  90 |  93 |  96 |  86 |  83 | 538 |   6 |  95 |  90 |  97 |  94 |  88 |  83 | 547 |  12 | 1085 |  18 |
|  56 | 196 | Amity      | ERMARTH    | VA  | J3  |  95 |  95 |  97 |  88 |  90 |  91 | 556 |  12 |  88 |  90 |  93 |  85 |  87 |  84 | 527 |  15 | 1083 |  27 |
|  57 | 216 | Kayla      | GADEKEN    | NE  | J2  |  89 |  89 |  94 |  94 |  83 |  87 | 536 |  12 |  86 |  89 |  96 |  95 |  87 |  94 | 547 |   8 | 1083 |  20 |
|  58 | 193 | Ashley     | ELLIOT     | ME  | J1  |  89 |  89 |  96 |  97 |  90 |  90 | 551 |  12 |  87 |  89 |  95 |  88 |  86 |  86 | 531 |  11 | 1082 |  23 |
|  59 | 513 | Sonora     | WIRTJES    | AZ  | J2  |  86 |  93 |  96 |  96 |  83 |  79 | 533 |  10 |  90 |  93 |  96 |  97 |  86 |  83 | 545 |  15 | 1078 |  25 |
|  60 | 290 | Jessica    | KATSUYAMA  | CA  | J1  |  89 |  86 |  93 |  95 |  87 |  91 | 541 |  10 |  89 |  92 |  92 |  86 |  83 |  89 | 531 |   4 | 1072 |  14 |
|  61 | 177 | Bailey     | DETTLE     | TX  | J3  |  91 |  96 |  93 |  91 |  79 |  75 | 525 |   9 |  90 |  91 |  94 |  94 |  83 |  83 | 535 |   8 | 1060 |  17 |
|  62 | 136 | Kaitlyn    | BROWN      | KS  | J2  |  88 |  91 |  95 |  93 |  75 |  77 | 519 |  11 |  92 |  93 |  96 |  90 |  77 |  78 | 526 |   8 | 1045 |  19 |
|  63 | 268 | Stori      | HOPPER     | UT  | J2  |  85 |  89 |  90 |  90 |  85 |  85 | 524 |   7 |  88 |  91 |  89 |  95 |  74 |  84 | 521 |  12 | 1045 |  19 |
|  64 | 512 | Cassidy    | WILSON     | WA  | J3  |  93 |  87 |  91 |  91 |  74 |  77 | 513 |   6 |  93 |  81 |  93 |  91 |  66 |  74 | 498 |   6 | 1011 |  12 |
|  65 | 249 | Kendall    | HANKEY     | TX  | J3  |  90 |  83 |  94 |  95 |  82 |  87 | 531 |  11 |  84 |  82 |  82 |  78 |  68 |  78 | 472 |   3 | 1003 |  14 |
|  66 | 186 | Simmons    | DUNCAN     | NC  | J3  |  88 |  88 |  83 |  89 |  84 |  80 | 512 |   4 |  87 |  86 |  87 |  92 |  67 |  64 | 483 |   5 |  995 |   9 |



label: W=U+M
X=V+N
labeled_formulas: W=U+M
X=V+N
output: {"Arithmetic-Relationship": ["W=U+M", "X=V+N"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_559429___xlsx_08e390b9812a6f830ff3f80a3d274f54bfcb0ba5.xlsx___line_79