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 |
|------:|:--------------------------|--------:|------:|--------:|----------:|----------:|----------:|--------:|-----------------:|-----------------:|----:|-----------------:|----:|-----------------:|
| 58003 | Agar-Blunt-Onida 58-3     |  235    |  1.5  | 12.2625 |  19.1641  | 0.122324  |  19.2864  | 67854.4 |      1.30867e+06 | 488134           |   0 |      1.7968e+06  |   0 |      1.7968e+06  |
| 61001 | Alcester-Hudson 61-1      |  336.5  |  1.25 | 13.0237 |  25.8374  | 0.0959785 |  25.9334  | 67854.4 |      1.75969e+06 | 656366           |   0 |      2.41606e+06 |   0 |      2.41606e+06 |
| 11001 | Andes Central 11-1        |  318    |  1.75 | 12.885  |  24.6799  | 0.135817  |  24.8157  | 67854.4 |      1.68385e+06 | 628077           |   0 |      2.31193e+06 |   0 |      2.31193e+06 |
| 38001 | Arlington 38-1            |  276    |  0.75 | 12.57   |  21.957   | 0.0596659 |  22.0167  | 67854.4 |      1.49393e+06 | 557236           |   0 |      2.05117e+06 |   0 |      2.05117e+06 |
| 21001 | Armour 21-1               |  184.25 |  0.5  | 12      |  15.3542  | 0.0416667 |  15.3958  | 67854.4 |      1.04467e+06 | 389664           |   0 |      1.43434e+06 |   0 |      1.43434e+06 |
| 49001 | Baltic 49-1               |  561    |  2    | 14.7075 |  38.1438  | 0.135985  |  38.2798  | 67854.4 |      2.59745e+06 | 968849           |   0 |      3.5663e+06  |   0 |      3.5663e+06  |
| 61002 | Beresford 61-2            |  715.24 |  7.75 | 15      |  47.6827  | 0.516667  |  48.1993  | 67854.4 |      3.27054e+06 |      1.21991e+06 |   0 |      4.49045e+06 |   0 |      4.49045e+06 |
| 25001 | Big Stone City 25-1       |   86    |  0    | 12      |   7.16667 | 0         |   7.16667 | 67854.4 | 486290           | 181386           |   0 | 667676           |   0 | 667676           |
| 52001 | Bison 52-1                |  137    |  0    | 12      |  11.4167  | 0         |  11.4167  | 67854.4 | 774671           | 288952           |   0 |      1.06362e+06 |   0 |      1.06362e+06 |
| 22001 | Bowdle 22-1               |  118    |  0    | 12      |   9.83333 | 0         |   9.83333 | 67854.4 | 667235           | 248879           |   0 | 916113           |   0 | 916113           |
| 49002 | Brandon Valley 49-2       | 4866.7  | 14    | 15      | 324.447   | 0.933333  | 325.38    | 67854.4 |      2.20785e+07 |      8.23526e+06 |   0 |      3.03137e+07 |   0 |      3.03137e+07 |
| 30003 | Bridgewater -Emery 30-3   |  330    |  1    | 12.975  |  25.4335  | 0.0770713 |  25.5106  | 67854.4 |      1.73101e+06 | 645665           |   0 |      2.37667e+06 |   0 |      2.37667e+06 |
| 45004 | Britton - Hecla 45-4      |  453.14 |  5.5  | 13.8986 |  32.6034  | 0.395725  |  32.9991  | 67854.4 |      2.23914e+06 | 835197           |   0 |      3.07433e+06 |   0 |      3.07433e+06 |
| 26002 | Burke 26-2                |  225.44 |  0    | 12.1908 |  18.4926  | 0         |  18.4926  | 67854.4 |      1.25481e+06 | 468043           |   0 |      1.72285e+06 |   0 |      1.72285e+06 |
| 43001 | Canistota 43-1            |  248.42 |  1    | 12.3631 |  20.0936  | 0.0808855 |  20.1745  | 67854.4 |      1.36893e+06 | 510609           |   0 |      1.87954e+06 |   0 |      1.87954e+06 |
| 28001 | Castlewood 28-1           |  319.29 |  3.25 | 12.8947 |  24.7614  | 0.252042  |  25.0134  | 67854.4 |      1.69727e+06 | 633082           |   0 |      2.33035e+06 |   0 |      2.33035e+06 |
| 60001 | Centerville 60-1          |  280.13 |  0.25 | 12.601  |  22.2308  | 0.0198397 |  22.2507  | 67854.4 |      1.5098e+06  | 563157           |   0 |      2.07296e+06 |   0 |      2.07296e+06 |
| 39001 | Chester 39-1              |  541    |  5.75 | 14.5575 |  37.163   | 0.394985  |  37.558   | 67854.4 |      2.54847e+06 | 950580           |   0 |      3.49905e+06 |   0 |      3.49905e+06 |
| 12002 | Clark 12-2                |  449    | 18.75 | 13.8675 |  32.3779  | 1.35208   |  33.7299  | 67854.4 |      2.28872e+06 | 853694           |   0 |      3.14242e+06 |   0 |      3.14242e+06 |
| 50005 | Colman-Egan 50-5          |  274.91 |  1.75 | 12.5618 |  21.8846  | 0.139311  |  22.0239  | 67854.4 |      1.49442e+06 | 557417           |   0 |      2.05183e+06 |   0 |      2.05183e+06 |
| 59003 | Colome Consolidated 59-3  |  191    |  0    | 12      |  15.9167  | 0         |  15.9167  | 67854.4 |      1.08002e+06 | 402846           |   0 |      1.48286e+06 |   0 |      1.48286e+06 |
| 21003 | Corsica-Stickney 21-3     |  267    |  0.5  | 12.5025 |  21.3557  | 0.039992  |  21.3957  | 67854.4 |      1.45179e+06 | 541519           |   0 |      1.99331e+06 |   0 |      1.99331e+06 |
| 16001 | Custer 16-1               |  922.99 |  0.25 | 15      |  61.5327  | 0.0166667 |  61.5493  | 67854.4 |      4.17639e+06 |      1.55779e+06 |   0 |      5.73419e+06 |   0 |      5.73419e+06 |
| 61008 | Dakota Valley 61-8        | 1375.5  |  5.25 | 15      |  91.7     | 0.35      |  92.05    | 67854.4 |      6.246e+06   |      2.32976e+06 |   0 |      8.57575e+06 |   0 |      8.57575e+06 |
| 38002 | De Smet 38-2              |  298.26 |  0.25 | 12.737  |  23.4169  | 0.0196279 |  23.4365  | 67854.4 |      1.59027e+06 | 593171           |   0 |      2.18344e+06 |   0 |      2.18344e+06 |
| 49003 | Dell Rapids 49-3          |  988.38 |  1    | 15      |  65.892   | 0.0666667 |  65.9587  | 67854.4 |      4.47558e+06 |      1.66939e+06 |   0 |      6.14498e+06 |   0 |      6.14498e+06 |
| 19004 | Deuel 19-4                |  529    |  1    | 14.4675 |  36.5647  | 0.0691204 |  36.6338  | 67854.4 |      2.48577e+06 | 927191           |   0 |      3.41296e+06 |   0 |      3.41296e+06 |
| 51001 | Douglas 51-1              | 2804.14 |  1.75 | 15      | 186.943   | 0.116667  | 187.059   | 67854.4 |      1.26928e+07 |      4.73441e+06 |   0 |      1.74272e+07 |   0 |      1.74272e+07 |
| 64002 | Dupree 64-2               |  369    |  0    | 13.2675 |  27.8123  | 0         |  27.8123  | 67854.4 |      1.88719e+06 | 703921           |   0 |      2.59111e+06 |   0 |      2.59111e+06 |
| 20001 | Eagle Butte 20-1          |  347.84 |  0    | 13.1088 |  26.5348  | 0         |  26.5348  | 67854.4 |      1.80051e+06 | 671589           |   0 |      2.47209e+06 |   0 |      2.47209e+06 |
| 23001 | Edgemont 23-1             |  159    |  0.5  | 12      |  13.25    | 0.0416667 |  13.2917  | 67854.4 | 901898           | 336408           |   0 |      1.23831e+06 |   0 |      1.23831e+06 |
| 22005 | Edmunds Central 22-5      |  130    |  0.5  | 12      |  10.8333  | 0.0416667 |  10.875   | 67854.4 | 737916           | 275243           |   0 |      1.01316e+06 |   0 |      1.01316e+06 |
| 61007 | Elk Point-Jefferson 61-7  |  693    |  1    | 15      |  46.2     | 0.0666667 |  46.2667  | 67854.4 |      3.1394e+06  |      1.17099e+06 |   0 |      4.31039e+06 |   0 |      4.31039e+06 |
| 28002 | Estelline 28-2            |  262.13 |  1.75 | 12.466  |  21.0276  | 0.140382  |  21.168   | 67854.4 |      1.43634e+06 | 535756           |   0 |      1.9721e+06  |   0 |      1.9721e+06  |
| 17001 | Ethan 17-1                |  274    |  0.5  | 12.555  |  21.824   | 0.0398248 |  21.8638  | 67854.4 |      1.48355e+06 | 553366           |   0 |      2.03692e+06 |   0 |      2.03692e+06 |
| 44001 | Eureka 44-1               |  154.2  |  0.25 | 12      |  12.85    | 0.0208333 |  12.8708  | 67854.4 | 873342           | 325757           |   0 |      1.1991e+06  |   0 |      1.1991e+06  |
| 46002 | Faith 46-2                |  168    |  0    | 12      |  14       | 0         |  14       | 67854.4 | 949961           | 354336           |   0 |      1.3043e+06  |   0 |      1.3043e+06  |
| 24004 | Faulkton Area 24-4        |  359    |  4    | 13.1925 |  27.2124  | 0.303203  |  27.5156  | 67854.4 |      1.86706e+06 | 696412           |   0 |      2.56347e+06 |   0 |      2.56347e+06 |
| 50003 | Flandreau 50-3            |  723    | 20.75 | 15      |  48.2     | 1.38333   |  49.5833  | 67854.4 |      3.36445e+06 |      1.25494e+06 |   0 |      4.61938e+06 |   0 |      4.61938e+06 |
| 14001 | Florence 14-1             |  293.05 |  0    | 12.6979 |  23.0787  | 0         |  23.0787  | 67854.4 |      1.56599e+06 | 584114           |   0 |      2.1501e+06  |   0 |      2.1501e+06  |
| 33001 | Freeman 33-1              |  382.07 |  9.5  | 13.3655 |  28.5862  | 0.710784  |  29.297   | 67854.4 |      1.98793e+06 | 741498           |   0 |      2.72943e+06 |   0 |      2.72943e+06 |
| 49004 | Garretson 49-4            |  465    |  1.25 | 13.9875 |  33.244   | 0.0893655 |  33.3333  | 67854.4 |      2.26181e+06 | 843656           |   0 |      3.10547e+06 |   0 |      3.10547e+06 |
| 63001 | Gayville-Volin 63-1       |  275    |  0.25 | 12.5625 |  21.8905  | 0.0199005 |  21.9104  | 67854.4 |      1.48672e+06 | 554546           |   0 |      2.04127e+06 |   0 |      2.04127e+06 |
| 53001 | Gettysburg 53-1           |  228    |  0.25 | 12.21   |  18.6732  | 0.020475  |  18.6937  | 67854.4 |      1.26845e+06 | 473131           |   0 |      1.74158e+06 |   0 |      1.74158e+06 |
| 26004 | Gregory 26-4              |  407    |  0.25 | 13.5525 |  30.0314  | 0.0184468 |  30.0498  | 67854.4 |      2.03901e+06 | 760551           |   0 |      2.79956e+06 |   0 |      2.79956e+06 |
| 27001 | Haakon 27-1               |  309    |  0.25 | 12.8175 |  24.1077  | 0.0195046 |  24.1272  | 67854.4 |      1.63713e+06 | 610651           |   0 |      2.24778e+06 |   0 |      2.24778e+06 |
| 28003 | Hamlin 28-3               |  838    |  4.5  | 15      |  55.8667  | 0.3       |  56.1667  | 67854.4 |      3.81115e+06 |      1.42156e+06 |   0 |      5.23271e+06 |   0 |      5.23271e+06 |
| 30001 | Hanson 30-1               |  382    |  4.5  | 13.365  |  28.5821  | 0.3367    |  28.9188  | 67854.4 |      1.96227e+06 | 731926           |   0 |      2.69419e+06 |   0 |      2.69419e+06 |
| 31001 | Harding County 31-1       |  210.25 |  0    | 12.0769 |  17.4093  | 0         |  17.4093  | 67854.4 |      1.1813e+06  | 440624           |   0 |      1.62192e+06 |   0 |      1.62192e+06 |
| 41002 | Harrisburg 41-2           | 5710.32 | 25.75 | 15      | 380.688   | 1.71667   | 382.405   | 67854.4 |      2.59478e+07 |      9.67854e+06 |   0 |      3.56264e+07 |   0 |      3.56264e+07 |
| 14002 | Henry 14-2                |  181.01 |  0    | 12      |  15.0842  | 0         |  15.0842  | 67854.4 |      1.02353e+06 | 381775           |   0 |      1.4053e+06  |   0 |      1.4053e+06  |
| 34002 | Highmore-Harrold 34-2     |  218    |  0    | 12.135  |  17.9646  | 0         |  17.9646  | 67854.4 |      1.21897e+06 | 454677           |   0 |      1.67365e+06 |   0 |      1.67365e+06 |
| 51002 | Hill City 51-2            |  502.55 |  3.25 | 14.2691 |  35.2194  | 0.227764  |  35.4472  | 67854.4 |      2.40525e+06 | 897156           |   0 |      3.3024e+06  |   0 |      3.3024e+06  |
| 23002 | Hot Springs 23-2          |  765.86 |  1    | 15      |  51.0573  | 0.0666667 |  51.124   | 67854.4 |      3.46899e+06 |      1.29393e+06 |   0 |      4.76292e+06 |   0 |      4.76292e+06 |
| 48003 | Howard 48-3               |  348    |  3.25 | 13.11   |  26.5446  | 0.247902  |  26.7925  | 67854.4 |      1.81799e+06 | 678110           |   0 |      2.4961e+06  |   0 |      2.4961e+06  |
| 22006 | Ipswich Public 22-6       |  418    |  9.5  | 13.635  |  30.6564  | 0.696736  |  31.3531  | 67854.4 |      2.12745e+06 | 793538           |   0 |      2.92099e+06 |   0 |      2.92099e+06 |
| 13003 | Irene-Wakonda 13-3        |  293.57 |  0    | 12.7018 |  23.1125  | 0         |  23.1125  | 67854.4 |      1.56829e+06 | 584970           |   0 |      2.15326e+06 |   0 |      2.15326e+06 |
| 37003 | Jones County 37-3         |  187    |  0    | 12      |  15.5833  | 0         |  15.5833  | 67854.4 |      1.0574e+06  | 394409           |   0 |      1.45181e+06 |   0 |      1.45181e+06 |
| 35002 | Kadoka Area 35-2          |  325    |  0    | 12.9375 |  25.1208  | 0         |  25.1208  | 67854.4 |      1.70455e+06 | 635799           |   0 |      2.34035e+06 |   0 |      2.34035e+06 |
| 38003 | Lake Preston 38-3         |  177    |  0.75 | 12      |  14.75    | 0.0625    |  14.8125  | 67854.4 |      1.00509e+06 | 374900           |   0 |      1.37999e+06 |   0 |      1.37999e+06 |
| 45005 | Langford Area 45-5        |  227    |  1.25 | 12.2025 |  18.6027  | 0.102438  |  18.7052  | 67854.4 |      1.26923e+06 | 473422           |   0 |      1.74265e+06 |   0 |      1.74265e+06 |
| 40001 | Lead-Deadwood 40-1        |  688.64 |  2.5  | 15      |  45.9093  | 0.166667  |  46.076   | 67854.4 |      3.12646e+06 |      1.16617e+06 |   0 |      4.29263e+06 |   0 |      4.29263e+06 |
| 52004 | Lemmon 52-4               |  267    |  0    | 12.5025 |  21.3557  | 0         |  21.3557  | 67854.4 |      1.44908e+06 | 540507           |   0 |      1.98959e+06 |   0 |      1.98959e+06 |
| 41004 | Lennox 41-4               | 1137.84 |  0.25 | 15      |  75.856   | 0.0166667 |  75.8727  | 67854.4 |      5.14829e+06 |      1.92031e+06 |   0 |      7.06861e+06 |   0 |      7.06861e+06 |
| 42001 | Lyman 42-1                |  352    |  0    | 13.14   |  26.7884  | 0         |  26.7884  | 67854.4 |      1.81771e+06 | 678007           |   0 |      2.49572e+06 |   0 |      2.49572e+06 |
| 39002 | Madison Central 39-2      | 1139.21 |  6.75 | 15      |  75.9473  | 0.45      |  76.3973  | 67854.4 |      5.18389e+06 |      1.93359e+06 |   0 |      7.11749e+06 |   0 |      7.11749e+06 |
| 60003 | Marion 60-3               |  195    |  1    | 12      |  16.25    | 0.0833333 |  16.3333  | 67854.4 |      1.10829e+06 | 413391           |   0 |      1.52168e+06 |   0 |      1.52168e+06 |
| 43007 | McCook Central 43-7       |  403.89 |  1.75 | 13.5292 |  29.8533  | 0.12935   |  29.9826  | 67854.4 |      2.03445e+06 | 758850           |   0 |      2.7933e+06  |   0 |      2.7933e+06  |
| 15001 | McIntosh 15-1             |  148    |  0    | 12      |  12.3333  | 0         |  12.3333  | 67854.4 | 836871           | 312153           |   0 |      1.14902e+06 |   0 |      1.14902e+06 |
| 15002 | McLaughlin 15-2           |  416    |  1.5  | 13.62   |  30.5433  | 0.110132  |  30.6535  | 67854.4 |      2.07997e+06 | 775829           |   0 |      2.8558e+06  |   0 |      2.8558e+06  |
| 46001 | Meade 46-1                | 3080.14 |  0.5  | 15      | 205.343   | 0.0333333 | 205.376   | 67854.4 |      1.39357e+07 |      5.198e+06   |   0 |      1.91337e+07 |   0 |      1.91337e+07 |
| 25004 | Milbank 25-4              |  970.46 | 11.5  | 15      |  64.6973  | 0.766667  |  65.464   | 67854.4 |      4.44202e+06 |      1.65687e+06 |   0 |      6.09889e+06 |   0 |      6.09889e+06 |
| 29004 | Miller 29-4               |  447    |  2.25 | 13.8525 |  32.2685  | 0.162426  |  32.431   | 67854.4 |      2.20058e+06 | 820818           |   0 |      3.0214e+06  |   0 |      3.0214e+06  |
| 17002 | Mitchell 17-2             | 2747.4  | 22.5  | 15      | 183.16    | 1.5       | 184.66    | 67854.4 |      1.253e+07   |      4.67369e+06 |   0 |      1.72037e+07 |   0 |      1.72037e+07 |
| 62006 | Mobridge-Pollock 62-6     |  621    |  0    | 15      |  41.4     | 0         |  41.4     | 67854.4 |      2.80917e+06 |      1.04782e+06 |   0 |      3.85699e+06 |   0 |      3.85699e+06 |
| 43002 | Montrose 43-2             |  243    |  2.75 | 12.3225 |  19.72    | 0.223169  |  19.9432  | 67854.4 |      1.35323e+06 | 504756           |   0 |      1.85799e+06 |   0 |      1.85799e+06 |
| 17003 | Mount Vernon 17-3         |  256    |  0    | 12.42   |  20.6119  | 0         |  20.6119  | 67854.4 |      1.39861e+06 | 521681           |   0 |      1.92029e+06 |   0 |      1.92029e+06 |
| 51003 | New Underwood 51-3        |  287    |  0.25 | 12.6525 |  22.6833  | 0.0197589 |  22.703   | 67854.4 |      1.5405e+06  | 574606           |   0 |      2.11511e+06 |   0 |      2.11511e+06 |
| 56007 | Northwestern Area 56-7    |  303    |  0    | 12.7725 |  23.7228  | 0         |  23.7228  | 67854.4 |      1.6097e+06  | 600418           |   0 |      2.21012e+06 |   0 |      2.21012e+06 |
| 23003 | Oelrichs 23-3             |  139    |  0    | 12      |  11.5833  | 0         |  11.5833  | 67854.4 | 785980           | 293170           |   0 |      1.07915e+06 |   0 |      1.07915e+06 |
| 65001 | Oglala Lakota County 65-1 | 1802.2  |  1.25 | 15      | 120.147   | 0.0833333 | 120.23    | 67854.4 |      8.15813e+06 |      3.04298e+06 |   0 |      1.12011e+07 |   0 |      1.12011e+07 |
| 60004 | Parker 60-4               |  481.2  |  4    | 14.109  |  34.1059  | 0.283507  |  34.3894  | 67854.4 |      2.33347e+06 | 870385           |   0 |      3.20386e+06 |   0 |      3.20386e+06 |
| 33003 | Parkston 33-3             |  514.4  |  2.75 | 14.244  |  36.1135  | 0.193064  |  36.3065  | 67854.4 |      2.46356e+06 | 918906           |   0 |      3.38246e+06 |   0 |      3.38246e+06 |
| 11005 | Platte-Geddes 11-5        |  500.63 |  4.5  | 14.2547 |  35.1203  | 0.315685  |  35.436   | 67854.4 |      2.40449e+06 | 896873           |   0 |      3.30136e+06 |   0 |      3.30136e+06 |
| 56004 | Redfield 56-4             |  547.2  |  0.5  | 14.604  |  37.4692  | 0.0342372 |  37.5034  | 67854.4 |      2.54477e+06 | 949200           |   0 |      3.49397e+06 |   0 |      3.49397e+06 |
| 54004 | Rosholt 54-4              |  242    |  3.5  | 12.315  |  19.6508  | 0.284206  |  19.935   | 67854.4 |      1.35268e+06 | 504549           |   0 |      1.85723e+06 |   0 |      1.85723e+06 |
| 62005 | Selby 62-5                |  170    |  0    | 12      |  14.1667  | 0         |  14.1667  | 67854.4 | 961270           | 358554           |   0 |      1.31982e+06 |   0 |      1.31982e+06 |
| 54002 | Sisseton 54-2             |  933.23 |  3    | 15      |  62.2153  | 0.2       |  62.4153  | 67854.4 |      4.23515e+06 |      1.57971e+06 |   0 |      5.81487e+06 |   0 |      5.81487e+06 |
| 15003 | Smee 15-3                 |  174.4  |  0.25 | 12      |  14.5333  | 0.0208333 |  14.5542  | 67854.4 | 987564           | 368361           |   0 |      1.35593e+06 |   0 |      1.35593e+06 |
| 26005 | South Central 26-5        |   70    |  0    | 12      |   5.83333 | 0         |   5.83333 | 67854.4 | 395817           | 147640           |   0 | 543457           |   0 | 543457           |
| 40002 | Spearfish 40-2            | 2414.98 |  3.25 | 15      | 160.999   | 0.216667  | 161.215   | 67854.4 |      1.09392e+07 |      4.08031e+06 |   0 |      1.50195e+07 |   0 |      1.50195e+07 |
| 57001 | Stanley County 57-1       |  416    |  0    | 13.62   |  30.5433  | 0         |  30.5433  | 67854.4 |      2.0725e+06  | 773042           |   0 |      2.84554e+06 |   0 |      2.84554e+06 |
| 54006 | Summit 54-6               |  165    |  2    | 12      |  13.75    | 0.166667  |  13.9167  | 67854.4 | 944307           | 352226           |   0 |      1.29653e+06 |   0 |      1.29653e+06 |
| 41005 | Tea Area 41-5             | 2174.56 |  7.25 | 15      | 144.971   | 0.483333  | 145.454   | 67854.4 |      9.86969e+06 |      3.68139e+06 |   0 |      1.35511e+07 |   0 |      1.35511e+07 |
| 20003 | Timber Lake 20-3          |  339    |  0.25 | 13.0425 |  25.9919  | 0.0191681 |  26.0111  | 67854.4 |      1.76497e+06 | 658333           |   0 |      2.4233e+06  |   0 |      2.4233e+06  |
| 33005 | Tripp-Delmont 33-5        |  161.01 |  1.75 | 12      |  13.4175  | 0.145833  |  13.5633  | 67854.4 | 920331           | 343284           |   0 |      1.26362e+06 |   0 |      1.26362e+06 |
| 49006 | Tri-Valley 49-6           |  971.5  |  8.25 | 15      |  64.7667  | 0.55      |  65.3167  | 67854.4 |      4.43202e+06 |      1.65314e+06 |   0 |      6.08517e+06 |   0 |      6.08517e+06 |
| 13001 | Vermillion 13-1           | 1344.95 |  1.25 | 15      |  89.6633  | 0.0833333 |  89.7467  | 67854.4 |      6.0897e+06  |      2.27146e+06 |   0 |      8.36116e+06 |   0 |      8.36116e+06 |
| 60006 | Viborg-Hurley 60-6        |  381.17 |  1.75 | 13.3588 |  28.5333  | 0.131     |  28.6643  | 67854.4 |      1.945e+06   | 725484           |   0 |      2.67048e+06 |   0 |      2.67048e+06 |
| 11004 | Wagner 11-4               |  800    |  0    | 15      |  53.3333  | 0         |  53.3333  | 67854.4 |      3.6189e+06  |      1.34985e+06 |   0 |      4.96875e+06 |   0 |      4.96875e+06 |
| 51005 | Wall 51-5                 |  268.51 |  0    | 12.5138 |  21.4571  | 0         |  21.4571  | 67854.4 |      1.45596e+06 | 543072           |   0 |      1.99903e+06 |   0 |      1.99903e+06 |
| 14004 | Watertown 14-4            | 3835.73 | 11    | 15      | 255.715   | 0.733333  | 256.449   | 67854.4 |      1.74012e+07 |      6.49063e+06 |   0 |      2.38918e+07 |   0 |      2.38918e+07 |
| 18003 | Waubay 18-3               |  175    |  0    | 12      |  14.5833  | 0         |  14.5833  | 67854.4 | 989543           | 369100           |   0 |      1.35864e+06 |   0 |      1.35864e+06 |
| 14005 | Waverly 14-5              |  257    |  0    | 12.4275 |  20.6799  | 0         |  20.6799  | 67854.4 |      1.40322e+06 | 523403           |   0 |      1.92663e+06 |   0 |      1.92663e+06 |
| 18005 | Webster Area 18-5         |  534    |  0.5  | 14.505  |  36.8149  | 0.0344709 |  36.8494  | 67854.4 |      2.50039e+06 | 932646           |   0 |      3.43304e+06 |   0 |      3.43304e+06 |
| 36002 | Wessington Springs 36-2   |  370.6  |  4.75 | 13.2795 |  27.9077  | 0.357694  |  28.2654  | 67854.4 |      1.91793e+06 | 715388           |   0 |      2.63332e+06 |   0 |      2.63332e+06 |
| 49007 | West Central 49-7         | 1429    |  1.5  | 15      |  95.2667  | 0.1       |  95.3667  | 67854.4 |      6.47105e+06 |      2.4137e+06  |   0 |      8.88475e+06 |   0 |      8.88475e+06 |
| 47001 | White River 47-1          |  384    |  0.25 | 13.38   |  28.6996  | 0.0186846 |  28.7182  | 67854.4 |      1.94866e+06 | 726849           |   0 |      2.67551e+06 |   0 |      2.67551e+06 |
| 54007 | Wilmot 54-7               |  214    |  0    | 12.105  |  17.6786  | 0         |  17.6786  | 67854.4 |      1.19957e+06 | 447441           |   0 |      1.64701e+06 |   0 |      1.64701e+06 |
| 59002 | Winner 59-2               |  715    |  0.5  | 15      |  47.6667  | 0.0333333 |  47.7     | 67854.4 |      3.23665e+06 |      1.20727e+06 |   0 |      4.44393e+06 |   0 |      4.44393e+06 |
| 55004 | Woonsocket 55-4           |  258    |  0.25 | 12.435  |  20.7479  | 0.0201045 |  20.768   | 67854.4 |      1.4092e+06  | 525631           |   0 |      1.93483e+06 |   0 |      1.93483e+06 |
| 63003 | Yankton 63-3              | 2821.06 | 10.75 | 15      | 188.071   | 0.716667  | 188.787   | 67854.4 |      1.281e+07   |      4.77815e+06 |   0 |      1.75882e+07 |   0 |      1.75882e+07 |



label: F=C/E
G=D/E
H=F+G
J=H*I
M=J+K+L
labeled_formulas: F=C/E
G=D/E
H=F+G
J=H*I
N=A*L
N=C*L
N=E*L
N=F*L
N=H*L
N=I*L
O=J+K
N=J*L
N=K*L
N=L*M
O=L+M
N=L*O
M=J+K+L
N=(A+C)*L
N=(A+E)*L
O=(E/A)+M
N=(A+F)*L
O=(F/A)+M
N=(A+H)*L
O=(H/A)+M
N=(A+I)*L
N=(A+J)*L
N=(A+K)*L
N=(A*L)*M
O=(A*L)+M
N=(A*L)*O
N=(C+E)*L
N=(C+F)*L
O=(G/C)+M
N=(C+H)*L
N=(C+I)*L
N=(C+J)*L
N=(C+K)*L
N=(C*L)*M
O=(C*L)+M
N=(C*L)*O
N=(E+F)*L
N=(E+H)*L
N=(E+I)*L
N=(E+J)*L
N=(E+K)*L
N=(E*L)*M
O=(E*L)+M
N=(E*L)*O
N=(F+I)*L
N=(F+J)*L
N=(F+K)*L
N=(F*L)*M
O=(F*L)+M
N=(F*L)*O
O=(H*I)+K
N=(H+I)*L
N=(H+J)*L
N=(H+K)*L
N=(H*L)*M
O=(H*L)+M
N=(H*L)*O
N=(I+J)*L
N=(I+K)*L
N=(I*L)*M
O=(I*L)+M
N=(I*L)*O
N=(J+K)*L
output: {"Arithmetic-Relationship": ["F=C/E", "G=D/E", "H=F+G", "J=H*I", "M=J+K+L"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_743357___xlsx_f18f2b2d80f1c1c13566cc790089b1a343fbf97a.xlsx___line_629