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 |
|:-------------------------------|:------------|----:|----:|----:|-------:|----:|-------:|----:|--------:|
| PSVBA 18-Bobby (PS)            | fj8psvba1ps |   1 | 715 |   2 | 875    |   1 | 1072.5 |   1 | 2662.5  |
| Kent Juniors 17 (PS)           | fj7kjvbc1ps |   3 | 695 |   1 | 893.75 |   2 | 1050   |   2 | 2638.75 |
| SSVBC U18 BLACK (PS)           | fj8ssvbc1ps |   3 | 695 |   3 | 868.75 |   4 | 1035   |   3 | 2598.75 |
| SEATTLE JRS 18 (PS)            | fj8stljr1ps |   2 | 700 |   4 | 862.5  |   6 | 1020   |   4 | 2582.5  |
| Lake Tapps 17 Orange  (PS)     | fj7ltapp1ps |   5 | 685 |   6 | 850    |   5 | 1027.5 |   5 | 2562.5  |
| SIVBC 18 Tsunami (PS)          | fj8sudni1ps |  11 | 655 |   5 | 856.25 |   3 | 1042.5 |   6 | 2553.75 |
| Kent Juniors 18 (PS)           | fj8kjvbc1ps |   7 | 675 |   8 | 837.5  |   7 | 1012.5 |   7 | 2525    |
| BOOST Black 18-1 (PS)          | fj8bovbc1ps |   5 | 685 |   9 | 831.25 |   9 |  997.5 |   8 | 2513.75 |
| SIVBC 17 Storm (PS)            | fj7sudni1ps |   9 | 665 |   7 | 843.75 |  10 |  990   |   9 | 2498.75 |
| OPVBC 18 Legend (PS)           | fj8olypr1ps |  13 | 645 |  13 | 806.25 |   8 | 1005   |  10 | 2456.25 |
| Oly Reign 17 Gold (PS)         | fj7olyrn1ps |   8 | 670 |  12 | 812.5  |  13 |  967.5 |  11 | 2450    |
| All Out U17 (PS)               | fj7allot1ps |  11 | 655 |  10 | 825    |  14 |  960   |  12 | 2440    |
| SIVA 17 BLUE (PS)              | fj7skais1ps |  10 | 660 |  11 | 818.75 |  15 |  952.5 |  13 | 2431.25 |
| Power Surge 18 Black (PS)      | fj8spana1ps |  17 | 625 |  14 | 800    |  11 |  982.5 |  14 | 2407.5  |
| Apex NW U18 Summit (PS)        | fj8apexn1ps |  19 | 615 |  15 | 793.75 |  12 |  975   |  15 | 2383.75 |
| ITVC 17 Baden (PS)             | fj7islan1ps |  18 | 620 |  17 | 781.25 |  16 |  945   |  16 | 2346.25 |
| Ignite 18-1 (PS)               | fj8ignit1ps |  19 | 615 |  16 | 787.5  |  18 |  930   |  17 | 2332.5  |
| SEATTLE JRS 17 (PS)            | fj7stljr1ps |  13 | 645 |  18 | 775    |  21 |  907.5 |  18 | 2327.5  |
| Kahiau U18 Navy (EV)           | fj8kahiu1ev |  15 | 635 |  20 | 762.5  |  22 |  900   |  19 | 2297.5  |
| Capital Ice 18's (PS)          | fj8capit1ps |  16 | 630 |  19 | 768.75 |  23 |  892.5 |  20 | 2291.25 |
| Blue Royals  18-A (PS)         | fj8brvbaaps |  23 | 595 |  21 | 756.25 |  17 |  937.5 |  21 | 2288.75 |
| PSVBA 17-Kim (PS)              | fj7psvba1ps |  21 | 605 |  22 | 750    |  20 |  915   |  22 | 2270    |
| DaKine Warriors 17 Surf (PS)   | fj7dakwa1ps |  24 | 590 |  23 | 743.75 |  19 |  922.5 |  23 | 2256.25 |
| Lake Tapps 18 Orange (PS)      | fj8ltapp1ps |  25 | 585 |  25 | 731.25 |  24 |  885   |  24 | 2201.25 |
| SCVBC 17 Red (PS)              | fj7scvbc2ps |  26 | 580 |  24 | 737.5  |  27 |  862.5 |  25 | 2180    |
| 253 Elite 18 (PS)              | fj8253vc1ps |  29 | 565 |  30 | 700    |  25 |  877.5 |  26 | 2142.5  |
| Skagit U18 South (PS)          | fj8skagt1ps |  27 | 575 |  27 | 718.75 |  30 |  840   |  27 | 2133.75 |
| SIVA 18 BLUE (PS)              | fj8skais1ps |  21 | 605 |  28 | 712.5  |  36 |  795   |  28 | 2112.5  |
| FSPVB 18-1 ROYAL (PS)          | fj8fspvb1ps |  33 | 545 |  29 | 706.25 |  28 |  855   |  29 | 2106.25 |
| Whidbey VBC 18 National (PS)   | fj8whidb1ps |  27 | 575 |  26 | 725    |  35 |  802.5 |  30 | 2102.5  |
| DaKine Warriors 18 Surf (PS)   | fj8dakwa1ps |  35 | 535 |  31 | 693.75 |  26 |  870   |  31 | 2098.75 |
| SEVC 18-1 (PS)                 | fj8soejr1ps |  29 | 565 |  33 | 681.25 |  33 |  817.5 |  32 | 2063.75 |
| Puyallup Jrs U17 National (PS) | fj7puyal1ps |  35 | 535 |  32 | 687.5  |  31 |  832.5 |  33 | 2055    |
| Kitsap Select U18 Black (PS)   | fj8ksvbc1ps |  31 | 555 |  34 | 675    |  37 |  787.5 |  34 | 2017.5  |
| Apex NW U18 Elevate (PS)       | fj8apexn2ps |  37 | 525 |  39 | 643.75 |  29 |  847.5 |  35 | 2016.25 |
| DaKine Warriors 18 Lokahi (PS) | fj8dakwa2ps |  37 | 525 |  38 | 650    |  32 |  825   |  36 | 2000    |
| Ignite 17-1 (PS)               | fj7ignit1ps |  32 | 550 |  36 | 662.5  |  41 |  757.5 |  37 | 1970    |
| SEVC 18-2 (PS)                 | fj8soejr2ps |  43 | 495 |  37 | 656.25 |  34 |  810   |  38 | 1961.25 |
| SNVF 18-1 Waves (PS)           | fj8spacn1ps |  34 | 540 |  35 | 668.75 |  43 |  742.5 |  39 | 1951.25 |
| REACH 18 GREEN (PS)            | fj8rchps1ps |  39 | 515 |  40 | 637.5  |  39 |  772.5 |  40 | 1925    |
| NW Jrs. 17 UA Blue (PS)        | fj7nwest2ps |  42 | 500 |  41 | 631.25 |  44 |  735   |  41 | 1866.25 |
| Rainier VBC U17 Gariann (PS)   | fj7rrvbc2ps |  41 | 505 |  42 | 625    |  45 |  727.5 |  42 | 1857.5  |
| Kraken VC - 18 Reef (PS)       | fj8krakn2ps |  49 | 465 |  45 | 606.25 |  38 |  780   |  43 | 1851.25 |
| Washington Elite U18 (PS)      | fj8washe1ps |  40 | 510 |  43 | 618.75 |  46 |  720   |  44 | 1848.75 |
| Capital Ice 17's (PS)          | fj7capit1ps |  49 | 465 |  46 | 600    |  40 |  765   |  45 | 1830    |
| EJVBC 18-2 Black (PS)          | fj8everg2ps |  45 | 485 |  47 | 593.75 |  42 |  750   |  46 | 1828.75 |
| SNVF 17-1 Eclipse (PS)         | fj7spacn1ps |  43 | 495 |  44 | 612.5  |  47 |  712.5 |  47 | 1820    |
| Rain City Eclipse (PS)         | fj8raincaps |  45 | 485 |  48 | 587.5  |  51 |  682.5 |  48 | 1755    |
| 206vb17 (PS)                   | fj7206vbaps |  47 | 475 |  51 | 568.75 |  50 |  690   |  49 | 1733.75 |
| Kitsap Select U17 Black (PS)   | fj7ksvbc1ps |  48 | 470 |  53 | 556.25 |  48 |  705   |  50 | 1731.25 |
| Grays Harbor 18 (PS)           | fj8grayh1ps |  53 | 445 |  52 | 562.5  |  49 |  697.5 |  51 | 1705    |
| FSPVB 18-2 GOLD (PS)           | fj8fspvb2ps |  51 | 455 |  49 | 581.25 |  53 |  667.5 |  52 | 1703.75 |
| Northshore Jrs 18 (PS)         | fj8north1ps |  51 | 455 |  50 | 575    |  54 |  660   |  53 | 1690    |
| EJVBC 18-1 Green (PS)          | fj8everg1ps |  55 | 435 |  54 | 550    |  52 |  675   |  54 | 1660    |
| EJVBC 17-1 Green (PS)          | fj7everg1ps |  54 | 440 |  55 | 543.75 |  55 |  652.5 |  55 | 1636.25 |



label: J=H+F+D
labeled_formulas: J=H+F+D
output: {"Arithmetic-Relationship": ["J=H+F+D"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_788345___xlsx_54be7c042ec3363795a73d8c790ece1aa6918709.xlsx___line_212