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 |
|----:|--------:|:---------------------|:----|------:|------:|-------:|
|   1 | 1031397 | William Shaner       | J1  | 627.6 | 624.9 | 1252.5 |
|   2 |  100930 | Rylan Kissell        | J1  | 623.1 | 627.1 | 1250.2 |
|   3 |  102740 | Gavin Perkowski      | J1  | 620.4 | 620.3 | 1240.7 |
|   4 | 1033931 | Scott Rockett        | J1  | 619.1 | 621   | 1240.1 |
|   5 |  104371 | John Blanton III     | J1  | 618.4 | 621.1 | 1239.5 |
|   6 |  104424 | Gavin Barnick        | J1  | 618.3 | 618.3 | 1236.6 |
|   7 |  103123 | Andrew Duryea        | J1  | 616.2 | 620.3 | 1236.5 |
|   8 |  102393 | Derek Keiser         | J1  | 616.7 | 615.7 | 1232.4 |
|   9 | 1042822 | Parker Haydin        | J1  | 615.8 | 615.6 | 1231.4 |
|  10 |  137890 | Scott Patterson      | J1  | 616.2 | 613.1 | 1229.3 |
|  11 |  104456 | John Kersey          | J1  | 616.5 | 611.9 | 1228.4 |
|  12 |  102896 | Andrew Duross        | J1  | 615.3 | 613   | 1228.3 |
|  13 |  101389 | Matt Sanchez         | J1  | 613.2 | 614.7 | 1227.9 |
|  14 | 1042155 | Dylan Gregory        | J2  | 609.4 | 611.2 | 1220.6 |
|  15 | 1041814 | Cory Stroupe         | J1  | 611.5 | 607.4 | 1218.9 |
|  16 | 1042165 | Jacob Day            | J2  | 605.5 | 613   | 1218.5 |
|  17 | 1042142 | Nathan Wehrlen       | J1  | 610.1 | 607.1 | 1217.2 |
|  18 | 1039165 | Theodore Clark       | J2  | 608.8 | 608.4 | 1217.2 |
|  19 | 1039071 | Nick VanRyswyk       | J1  | 606.5 | 609.3 | 1215.8 |
|  20 | 1038990 | Griffin Lake         | J2  | 603.7 | 611.8 | 1215.5 |
|  21 | 1040745 | Maximus DUNCAN       | J1  | 612.5 | 602.8 | 1215.3 |
|  22 |  101695 | Philip Becker        | J1  | 606.1 | 609   | 1215.1 |
|  23 | 1042594 | Joseph Kovach        | J2  | 607.2 | 607   | 1214.2 |
|  24 |  104265 | Braden Peiser        | J2  | 608.1 | 605.6 | 1213.7 |
|  25 | 1037849 | Bryce Ward           | J1  | 603.9 | 609.6 | 1213.5 |
|  26 | 1039225 | Logan Michael        | J2  | 606.4 | 605.9 | 1212.3 |
|  27 | 1042669 | Saxon Weaver         | J1  | 605.6 | 605.5 | 1211.1 |
|  28 |  102899 | Hayden Bell          | J2  | 603.3 | 607.1 | 1210.4 |
|  29 | 1042786 | Aaron Hoversten      | J1  | 605   | 605.1 | 1210.1 |
|  30 |  103130 | Andrew Fedora        | J1  | 604.4 | 605.3 | 1209.7 |
|  31 | 1041053 | Eli Guise            | J2  | 604.6 | 604.3 | 1208.9 |
|  32 | 1041178 | Marcus Klemp         | J2  | 608.3 | 599.5 | 1207.8 |
|  33 | 1038836 | Alok Joarder         | J2  | 603.1 | 603.2 | 1206.3 |
|  34 | 1040758 | Grayson Ellis        | J2  | 603.3 | 601.9 | 1205.2 |
|  35 | 1038060 | Joshua Potts         | J1  | 605.7 | 598.8 | 1204.5 |
|  36 | 1040707 | Grant Kimberling     | J2  | 606.8 | 597.1 | 1203.9 |
|  37 | 1038811 | CHRISTIAN CONRAD     | J1  | 606.4 | 596   | 1202.4 |
|  38 |  104346 | Jacob Bzdafka        | J1  | 599.6 | 602.2 | 1201.8 |
|  39 |  100853 | Mason Hamilton       | J1  | 600.7 | 600.9 | 1201.6 |
|  40 | 1042506 | Andrew SCHMIDT       | J1  | 599.7 | 601.3 | 1201   |
|  41 | 1039218 | Tanner Barth         | J2  | 599.8 | 600.6 | 1200.4 |
|  42 |  104064 | Anthony Buatti       | J1  | 603.9 | 595.9 | 1199.8 |
|  43 | 1040933 | Ryan Wee             | J2  | 599.7 | 599.4 | 1199.1 |
|  44 | 1040932 | Tyler Wee            | J3  | 594.6 | 603.8 | 1198.4 |
|  45 | 1042280 | Anthony James Hotko  | J2  | 599.1 | 599   | 1198.1 |
|  46 |  104473 | Briggs Moore         | J1  | 600.6 | 597.4 | 1198   |
|  47 | 1038971 | Zachary Lee Jackson  | J1  | 603.2 | 593.9 | 1197.1 |
|  48 |  102609 | SAWYER WILLIAMS      | J1  | 600.4 | 596.4 | 1196.8 |
|  49 |  104305 | Justin Casteel       | J1  | 606   | 590.5 | 1196.5 |
|  50 | 1039195 | Elias Hunt           | J1  | 594.7 | 601.3 | 1196   |
|  51 | 1041301 | Thomas Mikolashek    | J2  | 594.3 | 600.9 | 1195.2 |
|  52 | 1041224 | Ben Roche            | J2  | 593.2 | 600.7 | 1193.9 |
|  53 |  100897 | Antone SELLERS       | J1  | 600   | 593.3 | 1193.3 |
|  54 |  335808 | Matthew Stout        | J2  | 593   | 600   | 1193   |
|  55 |  103145 | Anthony Kissik       | J1  | 597.8 | 595   | 1192.8 |
|  56 | 1035100 | Sam Burrow           | J1  | 589.9 | 602.4 | 1192.3 |
|  57 | 1043406 | Trey Myers           | J2  | 590.2 | 601.8 | 1192   |
|  58 | 1042247 | Logan McClimans      | J2  | 593.8 | 598.2 | 1192   |
|  59 | 1040714 | Joshua PLUMMER       | J1  | 589.2 | 602.4 | 1191.6 |
|  60 | 1041465 | Logan HASSSELL       | J2  | 600   | 590   | 1190   |
|  61 |  101092 | Grant Benson         | J1  | 597.9 | 591   | 1188.9 |
|  62 |  101518 | JOSEPH HAHN          | J1  | 591.8 | 596.6 | 1188.4 |
|  63 | 1041377 | Carson Wood          | J1  | 592   | 595.1 | 1187.1 |
|  64 | 1043362 | Brandon Evans        | J2  | 592   | 594.7 | 1186.7 |
|  65 | 1040774 | Andrew Zhao          | J2  | 599.6 | 586.8 | 1186.4 |
|  66 | 1040953 | Ryan Kim             | J2  | 598.1 | 587.7 | 1185.8 |
|  67 | 1040570 | Cooper GRAY          | J2  | 590.8 | 593.9 | 1184.7 |
|  68 |  100780 | Garrett Boggan       | J1  | 589.4 | 594.7 | 1184.1 |
|  69 | 1043346 | Pruitt Bain          | J2  | 588.7 | 595.2 | 1183.9 |
|  70 | 1039234 | Ryan Sponauer        | J1  | 595.6 | 587.8 | 1183.4 |
|  71 |  104552 | Wrangle Kruckenberg  | J1  | 591.6 | 591.3 | 1182.9 |
|  72 | 1043561 | WYATT BELANGER       | J1  | 585.3 | 597.5 | 1182.8 |
|  73 | 1039103 | Ben Rogers           | J1  | 590.2 | 590.8 | 1181   |
|  74 | 1042282 | Everett Smith        | J3  | 587.8 | 592.9 | 1180.7 |
|  75 | 1040401 | William Steen        | J2  | 589.7 | 590   | 1179.7 |
|  76 |   89503 | SPENCER GILLIS       | J1  | 586.3 | 592.8 | 1179.1 |
|  77 | 1038813 | David Antonenko      | J1  | 594   | 584.8 | 1178.8 |
|  78 | 1042454 | Joe Neireiter        | J2  | 586.6 | 592   | 1178.6 |
|  79 | 1040713 | Deitrich Bergman     | J3  | 580.9 | 596.7 | 1177.6 |
|  80 |  103926 | Jacob Wisman         | J2  | 584.4 | 591.2 | 1175.6 |
|  81 | 1039464 | Leo VEATCH           | J2  | 577.9 | 597.7 | 1175.6 |
|  82 | 1042592 | Charles MOOTS        | J2  | 583.2 | 590.3 | 1173.5 |
|  83 | 1042712 | Liam Tegeler         | J2  | 585.4 | 586.5 | 1171.9 |
|  84 | 1042593 | MARSHALL SCHMIDT     | J3  | 585.2 | 586   | 1171.2 |
|  85 | 1038592 | Dante Aletto         | J1  | 581.2 | 589.8 | 1171   |
|  86 | 1042553 | Mateo MORENO         | J2  | 582.5 | 587.6 | 1170.1 |
|  87 | 1042533 | Jack Ogoreuc         | J3  | 584.6 | 583   | 1167.6 |
|  88 |  102272 | Nathan Engman        | J2  | 583.8 | 582.6 | 1166.4 |
|  89 | 1042025 | Samuel Sparrow       | J1  | 587.2 | 578.6 | 1165.8 |
|  90 | 1040543 | Dylan Zaun           | J2  | 578.7 | 586.4 | 1165.1 |
|  91 | 1038863 | STEPHEN MCAFEE       | J2  | 579   | 584.5 | 1163.5 |
|  92 | 1039171 | Elijah Butler        | J2  | 579   | 581.8 | 1160.8 |
|  93 | 1037699 | Kemper Pearson       | J2  | 578.6 | 580.9 | 1159.5 |
|  94 | 1039473 | Brock BILLINGS       | J2  | 575   | 581.6 | 1156.6 |
|  95 | 1041056 | Jacob Shaw           | J2  | 572   | 582.4 | 1154.4 |
|  96 | 1043897 | Michael Lumetta      | J2  | 575.6 | 578.6 | 1154.2 |
|  97 | 1042693 | Hunter Root          | J3  | 578.1 | 575.4 | 1153.5 |
|  98 | 1039364 | Elias Haddad         | J1  | 575   | 577.1 | 1152.1 |
|  99 | 1042378 | Gatlin JAMES         | J2  | 566.1 | 584.6 | 1150.7 |
| 100 |  104129 | Braden Michalak      | J2  | 575.6 | 574.5 | 1150.1 |
| 101 | 1042252 | Jackson Wall         | J3  | 571.9 | 573.5 | 1145.4 |
| 102 | 1042264 | Matteo Yoon          | J2  | 573.7 | 570.2 | 1143.9 |
| 103 | 1042770 | Parker Sullivan      | J3  | 577.9 | 564.9 | 1142.8 |
| 104 | 1043899 | Cameron Young        | J2  | 568.4 | 574   | 1142.4 |
| 105 | 1042405 | Kyle Barron          | J2  | 562   | 577.7 | 1139.7 |
| 106 | 1041016 | Zachary Osvald       | J1  | 568.8 | 565.3 | 1134.1 |
| 107 | 1043642 | Dylan Payne          | J1  | 560.4 | 568.7 | 1129.1 |
| 108 | 1043580 | Chris Jennings       | J2  | 559.8 | 567.7 | 1127.5 |
| 109 | 1043731 | Thaddeus Edwards     | J2  | 565.7 | 558   | 1123.7 |
| 110 | 1042482 | Christopher Forrest  | J2  | 553.6 | 566.2 | 1119.8 |
| 111 | 1042709 | Nate Steinhaus       | J3  | 546.9 | 570.7 | 1117.6 |
| 112 | 1042179 | Zach Tan             | J3  | 556.1 | 551.6 | 1107.7 |
| 113 | 1043724 | Augustine Courtright | J3  | 546.5 | 554.1 | 1100.6 |



label: F=G-E
labeled_formulas: F=G-E
output: {"Arithmetic-Relationship": ["F=G-E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_429466___xlsx_bffca8f162ff2e44970650d25032d038a0bdd5e6.xlsx___line_1051