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 |
|:--------------------------|:------------|----:|----:|----:|-------:|----:|-------:|----:|--------:|
| SIVBC 16 Thunder          | fj6sudni1ps |   1 | 715 |   2 | 875    |   1 | 1072.5 |   1 | 2662.5  |
| Lake Tapps 16 Orange      | fj6ltapp1ps |   3 | 695 |   1 | 893.75 |   3 | 1042.5 |   2 | 2631.25 |
| DaKine Warriors 15 Surf   | fj5dakwa1ps |   3 | 695 |   3 | 868.75 |   4 | 1035   |   3 | 2598.75 |
| ITVC 16 Baden             | fj6islan1ps |   7 | 675 |   5 | 856.25 |   2 | 1050   |   4 | 2581.25 |
| SIVBC Typhoon 15-1        | fj5sudni1ps |   2 | 700 |   4 | 862.5  |   8 | 1005   |   5 | 2567.5  |
| 253 Elite 16              | fj6253vc1ps |   5 | 685 |   7 | 843.75 |   5 | 1027.5 |   6 | 2556.25 |
| Kent Juniors 16           | fj6kjvbc1ps |   9 | 665 |   6 | 850    |   7 | 1012.5 |   7 | 2527.5  |
| PSVBA 16-1                | fj6psvba1ps |   8 | 670 |   9 | 831.25 |   6 | 1020   |   8 | 2521.25 |
| SIVA 16 Blue              | fj6skais1ps |   5 | 685 |   8 | 837.5  |  11 |  982.5 |   9 | 2505    |
| NW Jrs. 16 UA Black       | fj6nwest1ps |  10 | 660 |  11 | 818.75 |  13 |  967.5 |  10 | 2446.25 |
| All Out U16               | fj6allot1ps |  11 | 655 |  10 | 825    |  14 |  960   |  11 | 2440    |
| Oly Reign 16 Gold         | fj6olyrn1ps |  17 | 625 |  13 | 806.25 |   9 |  997.5 |  12 | 2428.75 |
| Boost U15 Black           | fj5bovbc1ps |  11 | 655 |  12 | 812.5  |  15 |  952.5 |  13 | 2420    |
| REACH 16 GREEN DELANEY    | fj6rchps1ps |  15 | 635 |  14 | 800    |  12 |  975   |  14 | 2410    |
| OPVBC 16 Elite            | fj6olypr1ps |  18 | 620 |  15 | 793.75 |  10 |  990   |  15 | 2403.75 |
| LYNCS 16                  | fj6lyncs1ps |  13 | 645 |  17 | 781.25 |  18 |  930   |  16 | 2356.25 |
| DaKine Warriors 16 Surf   | fj6dakwa1ps |  13 | 645 |  16 | 787.5  |  19 |  922.5 |  17 | 2355    |
| SIVBC 16 Tornado          | fj6sudni2ps |  23 | 595 |  21 | 756.25 |  17 |  937.5 |  18 | 2288.75 |
| Blue Royals 16-A          | fj6brvbaaps |  19 | 615 |  19 | 768.75 |  23 |  892.5 |  19 | 2276.25 |
| LAKE U16 Drew             | fj6lakev2ps |  16 | 630 |  18 | 775    |  26 |  870   |  20 | 2275    |
| Apex NW U16 Summit        | fj6apexn1ps |  25 | 585 |  23 | 743.75 |  16 |  945   |  21 | 2273.75 |
| SEATTLE JRS 16            | fj6stljr1ps |  27 | 575 |  22 | 750    |  20 |  915   |  22 | 2240    |
| Cascade U-16-1            | fj6casca1ps |  19 | 615 |  20 | 762.5  |  27 |  862.5 |  22 | 2240    |
| SEVC U16 National         | fj6soejr1ps |  21 | 605 |  24 | 737.5  |  24 |  885   |  24 | 2227.5  |
| NW Jrs. 16 UA Blue        | fj6nwest2ps |  26 | 580 |  25 | 731.25 |  21 |  907.5 |  25 | 2218.75 |
| Puyallup Jrs U16 National | fj6puyal1ps |  21 | 605 |  28 | 712.5  |  29 |  847.5 |  26 | 2165    |
| Kitsap Select U16 Black   | fj6kitvc1ps |  31 | 555 |  30 | 700    |  22 |  900   |  27 | 2155    |
| PSVBA 16-2                | fj6psvba2ps |  33 | 545 |  29 | 706.25 |  25 |  877.5 |  28 | 2128.75 |
| Kraken VC - 16 Reef       | fj6krakn1ps |  24 | 590 |  26 | 725    |  34 |  810   |  29 | 2125    |
| Rainier VBC U16 Summit    | fj6rrvbc1ps |  29 | 565 |  31 | 693.75 |  28 |  855   |  30 | 2113.75 |
| Boost U16 Black           | fj6bovbc1ps |  27 | 575 |  27 | 718.75 |  33 |  817.5 |  31 | 2111.25 |
| Cascade U-15-1            | fj5casca1ps |  34 | 540 |  32 | 687.5  |  30 |  840   |  32 | 2067.5  |
| REACH 16 BLUE DANNIE      | fj6rchps2ps |  32 | 550 |  33 | 681.25 |  35 |  802.5 |  33 | 2033.75 |
| SIVA 16 White             | fj6skais2ps |  37 | 525 |  37 | 656.25 |  31 |  832.5 |  34 | 2013.75 |
| Kahiau U16 Navy           | fj6kahiu1ev |  29 | 565 |  35 | 668.75 |  41 |  757.5 |  35 | 1991.25 |
| Moxie 16s Panther         | fj6moxie1ps |  35 | 535 |  34 | 675    |  38 |  780   |  36 | 1990    |
| SNVF 16-1 Reign           | fj6spacn1ps |  35 | 535 |  36 | 662.5  |  37 |  787.5 |  37 | 1985    |
| Ignite 16-1               | fj6ignit1ps |  40 | 510 |  39 | 643.75 |  32 |  825   |  38 | 1978.75 |
| Capital Ice 16's          | fj6capit1ps |  37 | 525 |  38 | 650    |  36 |  795   |  39 | 1970    |
| Cyborg U16 Storm          | fj6cybor1ps |  42 | 500 |  41 | 631.25 |  39 |  772.5 |  40 | 1903.75 |
| Falcon U16                | fj6falco1ps |  43 | 495 |  40 | 637.5  |  42 |  750   |  41 | 1882.5  |
| NW Jrs. 16 UA White       | fj6nwest4ps |  49 | 465 |  45 | 606.25 |  40 |  765   |  42 | 1836.25 |
| SEVC U16 Regional         | fj6soejr2ps |  43 | 495 |  42 | 625    |  47 |  712.5 |  43 | 1832.5  |
| Foothills Select U16      | fj5foots1ps |  45 | 485 |  47 | 593.75 |  43 |  742.5 |  44 | 1821.25 |
| Skagit U16 Red            | fj6skagt2ps |  41 | 505 |  43 | 618.75 |  49 |  697.5 |  44 | 1821.25 |
| Kraken VC - 16 Surf       | fj6krakn2ps |  39 | 515 |  44 | 612.5  |  51 |  682.5 |  46 | 1810    |
| NW Jrs. 16 UA Grey        | fj6nwest3ps |  45 | 485 |  49 | 581.25 |  45 |  727.5 |  47 | 1793.75 |
| 206vb16Maddie             | fj6206vb3ps |  51 | 455 |  46 | 600    |  44 |  735   |  48 | 1790    |
| Apex NW U16 Elevate       | fj6apexn2ps |  51 | 455 |  48 | 587.5  |  50 |  690   |  49 | 1732.5  |
| Northshore Jrs 16         | fj6north1ps |  53 | 445 |  53 | 556.25 |  46 |  720   |  50 | 1721.25 |
| Whidbey VBC U16           | fj6whidb1ps |  54 | 440 |  54 | 550    |  48 |  705   |  51 | 1695    |
| Puyallup Jrs U16 Regional | fj6puyal2ps |  50 | 460 |  50 | 575    |  54 |  660   |  51 | 1695    |
| Grays Harbor 16           | fj6grayh1ps |  47 | 475 |  51 | 568.75 |  56 |  645   |  53 | 1688.75 |
| EJVBC U16 Katie/Rachel    | fj6everg1ps |  48 | 470 |  52 | 562.5  |  55 |  652.5 |  54 | 1685    |
| School of Volleyball 16-1 | fj6schvb1ps |  57 | 425 |  55 | 543.75 |  52 |  675   |  55 | 1643.75 |
| DaKine Warriors 16 Tiki   | fj6dakwa2ps |  55 | 435 |  58 | 525    |  53 |  667.5 |  56 | 1627.5  |
| OPVBC 16 Wave             | fj6olypr2ps |  56 | 430 |  59 | 518.75 |  57 |  637.5 |  57 | 1586.25 |
| Valley View U16 Black     | fj6valyv1ps |  59 | 415 |  56 | 537.5  |  58 |  630   |  58 | 1582.5  |
| SSVBC 16-3                | fj6ssvbc3ps |  58 | 420 |  57 | 531.25 |  60 |  615   |  59 | 1566.25 |
| NW Jrs. 16 Baden Blue     | fj6nwest5ps |  62 | 400 |  60 | 512.5  |  59 |  622.5 |  60 | 1535    |
| ETown Everett Junior U16  | fj6evrtj1ps |  60 | 410 |  62 | 500    |  61 |  607.5 |  61 | 1517.5  |
| EJVBC U16 Tasha           | fj6everg2ps |  61 | 405 |  61 | 506.25 |  62 |  600   |  62 | 1511.25 |



label: J=D+F+H
labeled_formulas: J=D+F+H
output: {"Arithmetic-Relationship": ["J=D+F+H"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_683493___xlsx_566370356773a95547a764cd30249bdcfa807712.xlsx___line_324