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 |
|:------------------------------------------------|-----------------:|---------:|-------:|:----------|---------:|----------:|---------:|----------:|----------:|----------:|--------:|----:|---------:|---------:|----------:|-----------------:|----:|:----------------------------------|-------:|-----------:|
| Adventist Medical Center                        |      5.11139e+06 | 0.434766 | 0.1816 | Note 1, 3 |  6836280 |  37838264 |   957496 |  45632040 |  55840804 |  10208764 | 1502499 |   0 |  7322816 |  5820317 |  16029081 | 611662           |   0 | 158253, 500603902                 | 380060 |  196516776 |
| Ashland Community Hospital                      | 420180           | 0.294083 | 0.1665 | Note 3    |  1157821 |   5044400 |        0 |   6202221 |   8970849 |   2768628 |  302570 |   0 |  1173245 |   870675 |   3639303 |  42967.9         |   0 | 136114                            | 380005 |   43334103 |
| Bay Area Hospital                               |      3.95394e+06 | 0.427979 | 0.1963 | Note 3    |  2593834 |  21975313 |   342942 |  24912089 |  41332378 |  16420289 |  714972 |   0 |  3604089 |  2889117 |  19309406 | 377969           |   0 | 015214                            | 380090 |  119105567 |
| Blue Mountain Hospital (Note 10)                | 346097           | 0.41507  | 0.2859 | Note 3    |   159478 |   2526676 |        0 |   2686154 |   2769918 |     83764 |  155939 |   0 |   250687 |    94748 |    178512 |  32426.2         |   0 | 018507                            | 381305 |    8597154 |
| Columbia Memorial Hospital                      |      1.12358e+06 | 0.321634 | 0.1595 | Note 3    |  1923242 |   6902085 |        0 |   8825327 |   9923298 |   1097971 |  336695 |   0 |  2106370 |  1769675 |   2867646 | 105151           |   0 | 170989                            | 381320 |   53458769 |
| Coquille Valley Hospital                        | 210618           | 0.163972 | 0.1001 | Note 3    |   300014 |   1617219 |        0 |   1917233 |   2697027 |    779794 |       0 |   0 |        0 |        0 |    779794 |  20792           |   0 | 000013                            | 381312 |   18208740 |
| Cottage Grove Community Hospital                |      1.46327e+06 | 0.274725 | 0.1875 | Note 3    |   883337 |   3057693 |        0 |   3941030 |   5445678 |   1504648 |   46644 |   0 |  1131037 |  1084393 |   2589041 | 153269           |   0 | 237519                            | 381301 |   21676021 |
| Curry General Hospital (Note 8)                 | 379716           | 0.282909 | 0.2021 | Note 3    |   931187 |   3138113 |        0 |   4069300 |   6376397 |   2307097 |       0 |   0 |        0 |        0 |   2307097 |  33915.7         |   0 | 119263                            | 381322 |   21710690 |
| Good Shepherd Medical Center                    |      4.09173e+06 | 0.420516 | 0.2634 | Note 1, 3 |  2500384 |   9480428 |        0 |  11980812 |  15625575 |   3644763 |  331593 |   0 |  3151477 |  2819884 |   6464647 | 465425           |   0 | 008776                            | 381325 |   54267632 |
| Grande Ronde Hospital                           |      2.62808e+06 | 0.338924 | 0.2021 | Note 3    |  2558465 |   6895770 |        0 |   9454235 |  12192939 |   2738704 |  359645 |   0 |  1915227 |  1555582 |   4294286 | 251779           |   0 | 067801                            | 381321 |   51928593 |
| Harney District Hospital (Note 8)               | 252767           | 0.303932 | 0.2566 | Note 3    |   377367 |   2070781 |        0 |   2448148 |   3293001 |    844853 |       0 |   0 |        0 |        0 |    844853 |  24402.2         |   0 | 092502                            | 381307 |   12150309 |
| Kaiser Sunnyside Medical Center                 |      2.78284e+06 | 0.102616 | 0.049  | Note 3    | 20808151 |   2829089 |   177994 |  23815234 |  28978559 |   5163325 |  134111 |   0 |  6148389 |  6014278 |  11177603 | 271123           |   0 | 182311                            | 380091 |  408513766 |
| Lake District Hospital                          | 558729           | 0.20374  | 0.1237 | Note 3    |   687655 |    997292 |        0 |   1684947 |   2444809 |    759862 |  129390 |   0 |   437691 |   308301 |   1068163 |  49228.6         |   0 | 107532                            | 381309 |   13357941 |
| Lower Umpqua Hospital                           | 199027           | 0.197946 | 0.1626 | Note 3    |   419896 |    954739 |        0 |   1374635 |   2543635 |   1169000 |   96607 |   0 |   393305 |   296698 |   1465698 |  19340.9         |   0 | 000054                            | 381311 |   12703330 |
| Mercy Medical Center (Note 10)                  |      3.40153e+06 | 0.361694 | 0.2252 | Note 3    |  3192232 |  26854907 |   553605 |  30600744 |  45975991 |  15375247 |  408352 |   0 |  4725416 |  4317064 |  19692311 | 327760           |   0 | 123109                            | 380027 |  137107998 |
| Mid-Columbia Medical Center (Note 8)            |      2.00352e+06 | 0.340752 | 0.1612 | Note 3    |  2348695 |   6288019 |        0 |   8636714 |  15021796 |   6385082 |       0 |   0 |        0 |        0 |   6385082 | 199070           |   0 | 000070                            | 380001 |   61232723 |
| St Charles Madras (Mountain View Hospital)      | 489927           | 0.576192 | 0.3346 | Note 1, 3 |  3077460 |   3895829 |        0 |   6973289 |   9907014 |   2933725 |   93721 |   0 |   725074 |   631353 |   3565078 |  80305.9         |   0 | 000088                            | 381324 |   21095486 |
| Oregon Health Sciences University (Note 7)      |      3.35544e+07 | 0.444683 | 0.2468 | Note 1, 2 | 38508096 | 207568224 | 35964283 | 282040603 | 399787600 | 117746997 | 2331549 |   0 | 35179361 | 32847812 | 150594809 |      3.35544e+07 |   0 | 041178                            | 380009 | 1162507679 |
| Peace Harbor Hospital                           |      3.12827e+06 | 0.222291 | 0.1682 | Note 3    |  2009364 |   4559183 |        0 |   6568547 |   8688441 |   2119894 |   93041 |   0 |  1562436 |  1469395 |   3589289 | 320016           |   0 | 000195                            | 381316 |   54132837 |
| Pioneer Memorial Hospital (Heppner)             | 130511           | 0.796748 | 0.0962 | Note 3    |    70998 |    168765 |        0 |    239763 |   1732510 |   1492747 |       0 |   0 |        0 |        0 |   1492747 |  12889.2         |   0 | 134697                            | 381310 |    2913656 |
| Pioneer Memorial Hospital (Prineville)          | 695110           | 0.455814 | 0.2415 | Note 3    |   552638 |   4296484 |        0 |   4849122 |   6466971 |   1617849 |  199378 |   0 |   721013 |   521635 |   2139484 |  65713.8         |   0 | 213312                            | 381313 |   17672410 |
| Hood River Memorial Hospital                    |      3.87961e+06 | 0.452153 | 0.1955 | Note 3    |  2684553 |   6390088 |        0 |   9074641 |  14162523 |   5087882 |  510124 |   0 |  2057867 |  1547743 |   6635625 | 378278           |   0 | 210241, 500603889                 | 381318 |   53705575 |
| Providence Medford Medical Center               |      8.71178e+06 | 0.328636 | 0.2254 | Note 3    |  3537958 |  23481790 |   492654 |  27512402 |  39807422 |  12295020 |  692557 |   0 |  5008367 |  4315810 |  16610830 | 817932           |   0 | 153023, 286211                    | 380075 |  144216517 |
| Providence Milwaukie Hospital                   |      6.13211e+06 | 0.262769 | 0.2287 | Note 3    |  1426839 |  12955838 |   252968 |  14635645 |  18273816 |   3638171 |  525119 |   0 |  3714534 |  3189415 |   6827586 | 584404           |   0 | 175620                            | 380082 |   73969894 |
| Providence Newberg Medical Center               |      3.93683e+06 | 0.288134 | 0.185  | Note 3    |  2349839 |   9030881 |        0 |  11380720 |  13896369 |   2515649 |  585293 |   0 |  2862570 |  2277277 |   4792926 | 394129           |   0 | 129028                            | 380037 |   64499744 |
| Providence Portland Medical Center              |      2.67924e+07 | 0.336609 | 0.195  | Note 3    | 11616243 |  74939786 |  2300796 |  88856825 | 135591161 |  46734336 | 2671877 |   0 | 17426267 | 14754390 |  61488726 |      2.58013e+06 |   0 | 150300, 053210, 023981, 500400190 | 380061 |  499930342 |
| Providence Seaside Hospital                     |      2.74926e+06 | 0.341801 | 0.2268 | Note 3    |  2029748 |   5454962 |        0 |   7484710 |   8413299 |    928589 |  248407 |   0 |  1507885 |  1259478 |   2188067 | 274857           |   0 | 000138                            | 381303 |   30952655 |
| St Vincent Medical Center                       |      2.88744e+07 | 0.281808 | 0.1443 | Note 3    | 15817257 |  61304026 |  3170818 |  80292101 | 124386820 |  44094719 | 2821790 |   0 | 15995834 | 13174044 |  57268763 |      2.71399e+06 |   0 | 193805                            | 380004 |  601142832 |
| Providence Willamette Falls Medical Center      |      3.56125e+06 | 0.382678 | 0.2251 | Note 3    |  2147151 |  16231748 |   515502 |  18894401 |  26656934 |   7762533 |  424851 |   0 |  3400291 |  2975440 |  10737973 | 353632           |   0 | 500646328                         | 380038 |   92499606 |
| Rogue Regional Medical Center                   |      1.80523e+07 | 0.304478 | 0.221  | Note 3    | 11860384 |  60359729 |  1242705 |  73462818 |  96329162 |  22866344 | 1304289 |   0 |  8726462 |  7422173 |  30288517 |      1.76103e+06 |   0 | 162008, 276205, 500604342         | 380018 |  358989003 |
| Sacred Heart Medical Center at Riverbend        |      2.05234e+07 | 0.340296 | 0.2065 | Note 3    | 17661503 |  76077252 |  2072991 |  95811746 | 122753565 |  26941819 | 1555430 |   0 | 13892386 | 12336956 |  39278775 |      1.82412e+06 |   0 | 276221                            | 380102 |  450300649 |
| Sacred Heart Medical Center University District |      7.47239e+06 | 0.428985 | 0.1985 | Note 3    |  2448811 |  13843288 |    69861 |  16361960 |  25221883 |   8859923 |  234463 |   0 |  4348224 |  4113761 |  12973684 | 786727           |   0 | 192500, 118497, 500604635         | 380033 |   74895438 |
| Salem Hospital                                  |      2.20944e+07 | 0.377307 | 0.4086 | Note 3    | 15723980 |  72149471 |  2287796 |  90161247 | 148129427 |  57968180 |  285763 |   0 |  6206427 |  5920664 |  63888844 |      2.16096e+06 |   0 | 194001, 053251                    | 380051 |  494028725 |
| Samaritan Albany General Hospital               |      3.83246e+06 | 0.389368 | 0.1728 | Note 1, 3 |  2063322 |  14820894 |   396742 |  17280958 |  27485088 |  10204130 |  547879 |   0 |  4110728 |  3562849 |  13766979 | 397647           |   0 | 000292                            | 380022 |  105285035 |
| Samaritan Lebanon Community Hospital            |      2.85042e+06 | 0.451434 | 0.1835 | Note 1, 3 |  1784553 |   8367788 |        0 |  10152341 |  20961811 |  10809470 |  319795 |   0 |  2172687 |  1852892 |  12662362 | 287032           |   0 | 026638                            | 381323 |   63966940 |
| Samaritan North Lincoln Hospital                |      1.12466e+06 | 0.375287 | 0.2341 | Note 3    |  1665432 |   4389060 |        0 |   6054492 |   9812944 |   3758452 |  258193 |   0 |  1581868 |  1323675 |   5082127 | 111567           |   0 | 226659                            | 381302 |   32098386 |
| Samaritan Pacific Communities Hospital          |      2.01744e+06 | 0.363784 | 0.1955 | Note 3    |  2759931 |   5668977 |        0 |   8428908 |  13365030 |   4936122 |  320200 |   0 |  1724193 |  1403993 |   6340115 | 192457           |   0 | 268916                            | 381314 |   48839959 |
| Santiam Memorial Hospital                       | 796213           | 0.236978 | 0.1253 | Note 3    |   606174 |   2657262 |        0 |   3263436 |   5769365 |   2505929 |   27348 |   0 |  1180549 |  1153201 |   3659130 |  75936.2         |   0 | 000120                            | 380056 |   26784946 |
| Shiners Childrens (Note 9)                      |  97627.1         | 0.418233 | 0.8962 | Note 3    |   841209 |  11831438 |        0 |  12672647 |  10991467 |  -1681180 |       0 |   0 |  4660082 |  4660082 |   2978902 |   9946.41        |   0 | 271154                            | 383300 |   28898441 |
| Silverton Hospital                              |      4.01955e+06 | 0.398184 | 0.2238 | Note 1, 3 |  3342467 |  13361726 |        0 |  16704193 |  17566120 |    861927 | 1064841 |   0 |  2248345 |  1183504 |   2045431 | 545458           |   0 | 000146                            | 380029 |   65155603 |
| Sky Lakes Medical Center                        |      4.23526e+06 | 0.365145 | 0.1708 | Note 3    |  9067762 |  13363536 |  1352927 |  23784225 |  38671470 |  14887245 |  866486 |   0 |  4750734 |  3884248 |  18771493 | 403345           |   0 | 152371                            | 380050 |  142481002 |
| Southern Coos General Hospital                  | 323563           | 0.226174 | 0.0578 | Note 3    |   222008 |    337836 |        0 |    559844 |   1349343 |    789499 |       0 |   0 |        0 |        0 |    789499 |  32192.6         |   0 | 000153                            | 381304 |   11528436 |
| St Charles Medical Center - Bend                |      1.19382e+07 | 0.322917 | 0.1781 | Note 3    |  9150811 |  49590996 |  1017485 |  59759292 |  91026687 |  31267395 | 1686530 |   0 |  8849657 |  7163127 |  38430522 |      1.13775e+06 |   0 | 179069, 053228, 500400231         | 380047 |  347867551 |
| St Charles Medical Center - Redmond             |      2.64797e+06 | 0.357042 | 0.2658 | Note 3    |  2160354 |  12585771 |        0 |  14746125 |  17593951 |   2847826 |  367104 |   0 |  2376180 |  2009076 |   4856902 | 256683           |   0 | 292848                            | 380040 |   54828859 |
| St Alphonsus Medical Center-Baker               | 721821           | 0.403007 | 0.1733 | Note 3    |  1047401 |   2637936 |        0 |   3685337 |   6767946 |   3082609 |  142149 |   0 |   778291 |   636142 |   3718751 |  64774.1         |   0 | 500619115                         | 381315 |   22565252 |
| Three Rivers Medical Center                     |      9.11462e+06 | 0.342005 | 0.2852 | Note 3    |  3008653 |  26296990 |   500192 |  29805835 |  35147156 |   5341321 |  693369 |   0 |  4472058 |  3778689 |   9120010 | 896682           |   0 | 022560                            | 380002 |  118147954 |
| Tillamook County General Hospital               |      3.75461e+06 | 0.281567 | 0.2435 | Note 3    |  1597692 |   5711321 |        0 |   7309013 |   7549623 |    240610 |  181116 |   0 |  1505660 |  1324544 |   1565154 | 360601           |   0 | 005533                            | 381317 |   34492326 |
| Wallowa County Health Care District (Note 8)    | 359818           | 0.309476 | 0.1298 | Note 3    |   438908 |   1074441 |        0 |   1513349 |   2747480 |   1234131 |       0 |   0 |        0 |        0 |   1234131 |  33664.5         |   0 | 214205                            | 381306 |   12340372 |
| West Valley Hospital                            |      1.16254e+06 | 0.324873 | 0.3705 | Note 3    |   554364 |   2304195 |        0 |   2858559 |   5204998 |   2346439 |   33340 |   0 |   390531 |   357191 |   2703630 | 116902           |   0 | 100112                            | 381308 |   18618245 |



label: K=J-I
P=K+O
I=F+G+H
O=N-M-L
labeled_formulas: K=J-I
P=K+O
R=B*M
R=C*M
R=D*M
R=F*M
R=G*M
R=H*M
R=I*M
R=J*M
R=K*M
R=L*M
N=L+O
R=M*N
R=M*O
R=M*P
R=M*Q
R=M*T
R=M*U
I=F+G+H
O=N-M-L
R=(B+C)*M
R=(B+D)*M
R=(B+F)*M
R=(B+G)*M
R=(B*H)*M
R=(B+I)*M
R=(B+J)*M
R=(B+K)*M
R=(B+L)*M
R=(B*M)*N
R=(B*M)*O
R=(B*M)*P
R=(B*M)*Q
R=(B*M)*T
R=(B*M)*U
R=(C+D)*M
R=(C+F)*M
R=(C+G)*M
R=(C*H)*M
output: {"Arithmetic-Relationship": ["K=J-I", "P=K+O", "I=F+G+H", "O=N-M-L"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_13045___xlsx_094fc42878ea22b2956ea99486bcfd761d3d63ff.xlsx___line_27