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 |
|------:|--------:|---------:|--------:|--------:|-------:|-------:|------------:|---------:|------------:|----:|-----------------:|-----------------:|--------:|---------:|---------:|---------:|---------:|---------:|---------:|
| 42522 | 81809.8 |  93629.5 | 35632.5 | 5600.25 | 216672 | 123974 | 1.68446e+06 | 28458.9  | 1.71292e+06 | 169 | 865951           | 818507           | 2754.12 | 13500.8  | 12204    | 0.510789 | 0.489211 | 0.542028 | 0.457972 |
| 42552 | 77174   | 100106   | 37541   | 3089.25 | 217910 | 124067 | 1.65871e+06 | 15091.1  | 1.67381e+06 | 166 | 825017           | 833697           | 1393.81 | 13697.3  |     0    | 0.493732 | 0.506268 | 0.526434 | 0.473566 |
| 42583 | 84430.8 | 107268   | 40049   | 3763.25 | 235511 | 133076 | 1.77083e+06 | 14661    | 1.78549e+06 | 154 | 908780           | 862053           | 1825.41 | 12718.1  |   117.56 | 0.510035 | 0.489965 | 0.528552 | 0.471448 |
| 42614 | 81902   | 100229   | 35027.5 | 2698.5  | 219857 | 123795 | 1.68897e+06 | 15229.4  | 1.7042e+06  | 144 | 885700           | 803269           | 1187.16 | 13758    |   284.21 | 0.5205   | 0.4795   | 0.531843 | 0.468157 |
| 42644 | 88796.2 | 114093   | 32711.8 | 2966.25 | 238567 | 134344 | 1.86525e+06 | 13776.6  | 1.87902e+06 | 155 | 969861           | 895385           | 1588.63 | 10732    |  1456    | 0.517398 | 0.482602 | 0.509324 | 0.490676 |
| 42675 | 94158.5 | 101861   | 36412   | 3724    | 236155 | 133214 | 1.90454e+06 | 18757    | 1.92329e+06 | 151 |      1.05744e+06 | 847093           | 2251    | 15164    |  1342    | 0.551364 | 0.448636 | 0.552901 | 0.447099 |
| 42705 | 86917   |  97712.2 | 39193.8 | 5801.25 | 229624 | 130173 | 1.8029e+06  | 18842.4  | 1.82174e+06 | 153 | 960082           | 842816           | 1768.94 | 16546    |   527.44 | 0.528138 | 0.471862 | 0.549205 | 0.450795 |
| 42736 | 89766.5 | 101302   | 31465.5 | 5982.5  | 228516 | 128420 | 1.84162e+06 | 16126.3  | 1.85775e+06 | 147 |      1.00012e+06 | 841495           | 1418.37 | 14707.9  |     0    | 0.539117 | 0.460883 | 0.530519 | 0.469481 |
| 42767 | 85826.5 |  96921.2 | 30437   | 7190.75 | 220376 | 124607 | 1.75554e+06 | 12143.5  | 1.76768e+06 | 138 | 940112           | 815429           | 2582.55 |  9561    |     0    | 0.533293 | 0.466707 | 0.52757  | 0.47243  |
| 42795 | 92384   |  99664.8 | 32487.8 | 7611.75 | 232148 | 131800 | 1.86459e+06 | 15647.8  | 1.88024e+06 | 146 | 993143           | 871448           | 1575.18 | 14072.6  |     0    | 0.529038 | 0.470962 | 0.537897 | 0.462103 |
| 42826 | 85623   | 101114   | 34927.2 | 3532.25 | 225196 | 128321 | 1.82679e+06 | 17533.3  | 1.84432e+06 | 157 | 936611           | 890175           | 2576    | 14957.3  |     0    | 0.509232 | 0.490768 | 0.535312 | 0.464688 |
| 42856 | 85824   | 100594   | 56015.8 | 4438    | 246871 | 141218 | 1.80071e+06 | 14056    | 1.81477e+06 | 143 | 926077           | 874634           | 1639    | 12417    |     0    | 0.511204 | 0.488796 | 0.574549 | 0.425451 |
| 42887 | 81533.8 | 103006   | 44037   | 3098    | 231675 | 132764 | 1.75319e+06 | 14050    | 1.76724e+06 | 142 | 873812           | 879373           | 1017    | 12988.2  |    44.72 | 0.49504  | 0.50496  | 0.542013 | 0.457987 |
| 42917 | 75702.8 | 109215   | 46854.8 | 2457.25 | 234230 | 134104 | 1.72827e+06 | 13294    | 1.74156e+06 | 148 | 810213           | 918054           | 1491.69 | 11802.3  |     0    | 0.466079 | 0.533921 | 0.523236 | 0.476764 |
| 42948 | 75430   | 113188   | 50063.8 | 1923    | 240604 | 136826 | 1.72883e+06 | 16816.9  | 1.74565e+06 | 149 | 798839           | 929996           | 2327    | 14489.9  |     0    | 0.458949 | 0.541051 | 0.521577 | 0.478423 |
| 42979 | 76794.2 | 109716   | 49844.2 | 1461    | 237816 | 135042 | 1.7265e+06  | 12189    | 1.73869e+06 | 139 | 818034           | 908462           | 2093    |  9534    |   562    | 0.471847 | 0.528153 | 0.532507 | 0.467493 |
| 43009 | 87749.8 | 125075   | 51182.5 | 1482.25 | 265490 | 149595 | 1.95781e+06 | 15395.8  | 1.9732e+06  | 153 | 965888           | 991918           | 2305.51 | 12956.8  |   133.49 | 0.490704 | 0.509296 | 0.523306 | 0.476694 |
| 43040 | 87695   | 110673   | 40057.2 | 2145    | 240570 | 135469 | 1.90336e+06 | 19975    | 1.92333e+06 | 137 | 977509           | 925849           | 2161.77 | 17813.2  |     0    | 0.509361 | 0.490639 | 0.53104  | 0.46896  |
| 43070 | 90240.8 | 105867   | 39364   | 2053    | 237524 | 134594 | 1.8974e+06  | 19897    | 1.9173e+06  | 147 |      1.0104e+06  | 886999           | 2604    | 17293    |     0    | 0.52835  | 0.47165  | 0.545648 | 0.454352 |
| 43101 | 76293.5 | 104150   | 37882.5 | 2208    | 220534 | 125369 | 1.71143e+06 | 17505.7  | 1.72893e+06 | 137 | 844304           | 867124           | 4000    | 13505.6  |     0    | 0.490651 | 0.509349 | 0.517726 | 0.482274 |
| 43132 | 82103.8 | 100368   | 34156   | 2099    | 218726 | 122919 | 1.727e+06   | 13526.6  | 1.74052e+06 | 131 | 909753           | 817245           | 2416    | 11110.6  |     0    | 0.524077 | 0.475923 | 0.53153  | 0.46847  |
| 43160 | 98648.2 | 113122   | 38151.5 | 2308    | 252230 | 142869 | 2.07172e+06 | 19355    | 2.09107e+06 | 147 |      1.10445e+06 | 967271           | 3283    | 16072    |     0    | 0.529743 | 0.470257 | 0.542361 | 0.457639 |
| 43191 | 86251.2 |  97606.8 | 33311   | 2112    | 219281 | 124936 | 1.81756e+06 | 12501.2  | 1.83006e+06 | 143 | 949522           | 868039           | 1874.25 | 10607.9  |    19    | 0.519876 | 0.480124 | 0.545247 | 0.454753 |
| 43221 | 85157.2 | 108592   | 40552   | 2589    | 236890 | 134802 | 1.87094e+06 | 20161.4  | 1.8911e+06  | 142 | 926553           | 944385           | 2526    | 17635.4  |     0    | 0.49129  | 0.50871  | 0.530664 | 0.469336 |
| 43252 | 80595.5 | 105955   | 35615   | 1674    | 223840 | 127265 | 1.7702e+06  | 15868.7  | 1.78607e+06 | 131 | 865480           | 904717           | 2186    | 13682.7  |     0    | 0.485797 | 0.514203 | 0.519169 | 0.480831 |
| 43282 | 82853   | 120132   | 48182   | 1512    | 252679 | 143531 | 1.90602e+06 | 17835.4  | 1.92386e+06 | 142 | 892715           |      1.0133e+06  | 3392.51 | 14442.9  |     0    | 0.465787 | 0.534213 | 0.518583 | 0.481417 |
| 43313 | 83512.2 | 117042   | 56726.8 | 1540    | 258820 | 146726 | 1.8442e+06  | 19001.2  | 1.86321e+06 | 149 | 880288           | 963916           | 3477.13 | 15524.1  |     0    | 0.474325 | 0.525675 | 0.541839 | 0.458161 |
| 43344 | 65587.8 | 108980   | 44970.2 | 1816.25 | 221355 | 124736 | 1.57374e+06 | 12031.9  | 1.58578e+06 | 128 | 694835           | 878909           | 3425.02 |  8606.92 |     0    | 0.440327 | 0.559673 | 0.499461 | 0.500539 |
| 43374 | 83576.8 | 127676   | 58615.8 |  669    | 270538 | 150931 | 1.93156e+06 | 11738.2  | 1.9433e+06  | 142 | 920858           |      1.0107e+06  | 2871    |  8867.25 |     0    | 0.47534  | 0.52466  | 0.525592 | 0.474408 |
| 43405 | 77788.8 | 112218   | 47841   | 2042    | 239890 | 133711 | 1.77903e+06 | 12620.2  | 1.79165e+06 | 130 | 872493           | 906538           | 1834.77 | 10785.4  |     0    | 0.488001 | 0.511999 | 0.523697 | 0.476303 |
| 43435 | 75418   | 111566   | 52045.5 | 2091    | 241120 | 135091 | 1.78203e+06 | 17283.9  | 1.79932e+06 | 133 | 844334           | 937699           | 4428.09 | 12855.8  |     0    | 0.471714 | 0.528286 | 0.52863  | 0.47137  |
| 43466 | 77948.2 | 109756   | 50537.8 | 1868    | 240110 | 134638 | 1.77564e+06 | 15085.8  | 1.79073e+06 | 129 | 859501           | 916143           | 1691.71 | 13394.1  |     0    | 0.480917 | 0.519083 | 0.535112 | 0.464888 |
| 43497 | 76641.8 | 105357   | 44037.8 | 2115    | 228151 | 127596 | 1.69176e+06 | 13561.1  | 1.70532e+06 | 113 | 838116           | 853642           | 1666.4  | 11894.7  |     0    | 0.492449 | 0.507551 | 0.528945 | 0.471055 |
| 43525 | 89282   | 107040   | 41711.8 | 2002    | 240035 | 135146 | 1.90986e+06 | 12673    | 1.92253e+06 | 128 | 983839           | 926019           | 1965    | 10708    |     0    | 0.512764 | 0.487236 | 0.545727 | 0.454273 |
| 43556 | 85378   | 119266   | 38579.5 | 2710    | 245933 | 138996 | 1.96962e+06 | 13018    | 1.98264e+06 | 126 | 939488           |      1.03013e+06 | 2522    | 10496    |     0    | 0.47513  | 0.52487  | 0.504029 | 0.495971 |
| 43586 | 88064.5 | 119592   | 51173.2 | 2064    | 260894 | 146018 | 1.97126e+06 | 15645    | 1.98691e+06 | 127 | 964796           |      1.00647e+06 | 3467    | 12079    |    99    | 0.487346 | 0.512654 | 0.533696 | 0.466304 |
| 43617 | 76535.2 | 112664   | 48622.2 | 1507.75 | 239329 | 134371 | 1.77343e+06 | 12197    | 1.78563e+06 | 123 | 832834           | 940598           | 3002    |  9195    |     0    | 0.46809  | 0.53191  | 0.522952 | 0.477048 |
| 43647 | 80954.8 | 125260   | 56696   | 2649    | 265559 | 149163 | 1.88634e+06 | 15294    | 1.90164e+06 | 135 | 873501           |      1.01284e+06 | 2315    | 12979    |     0    | 0.460559 | 0.539441 | 0.518343 | 0.481657 |
| 43678 | 80654.8 | 121542   | 54405.2 | 1073    | 257675 | 143327 | 1.829e+06   | 15363.2  | 1.84436e+06 | 133 | 871555           | 957442           | 1808.2  | 13455    |   100    | 0.473557 | 0.526443 | 0.524148 | 0.475852 |
| 43709 | 71560.5 | 114642   | 52765.5 | 2447    | 241416 | 134948 | 1.67813e+06 | 11469.2  | 1.6896e+06  | 125 | 774026           | 904104           | 1140.2  | 10244    |    85    | 0.45881  | 0.54119  | 0.514988 | 0.485012 |
| 43739 | 83556.5 | 124142   | 57427.2 | 1850    | 266976 | 148242 | 1.87005e+06 | 12757    | 1.88281e+06 | 128 | 917732           | 952322           | 1057    | 11700    |     0    | 0.487988 | 0.512012 | 0.528076 | 0.471924 |
| 43770 | 77241   | 103410   | 44991.5 | 1339    | 226982 | 126063 | 1.70907e+06 | 10508    | 1.71958e+06 | 122 | 875942           | 833129           | 1508    |  9000    |     0    | 0.51027  | 0.48973  | 0.538513 | 0.461487 |
| 43800 | 78284.8 | 103710   | 41854.2 | 1052.25 | 224902 | 125281 | 1.71509e+06 | 13918.2  | 1.72901e+06 | 125 | 884642           | 830445           | 1215.22 | 12703    |     0    | 0.512351 | 0.487649 | 0.534184 | 0.465816 |
| 43831 | 79328   | 108884   | 36655.5 | 2366    | 227234 | 126634 | 1.77211e+06 |  9003    | 1.78111e+06 | 121 | 901985           | 870121           |  544    |  8459    |     0    | 0.506723 | 0.493277 | 0.510415 | 0.489585 |
| 43862 | 80834   |  97559   | 27917.5 | 1505.25 | 207816 | 114959 | 1.6636e+06  |  9484    | 1.67308e+06 | 111 | 896084           | 767511           | 1400    |  8084    |     0    | 0.536426 | 0.463574 | 0.523307 | 0.476693 |
| 43891 | 90761   |  99129   | 26347.2 | 3078    | 219315 | 122655 | 1.83935e+06 |  8552    | 1.8479e+06  | 112 | 968667           | 870679           | 1340    |  7212    |     0    | 0.524925 | 0.475075 | 0.533972 | 0.466028 |
| 43922 | 71158.2 | 100310   | 32604.5 | 3171.25 | 207244 | 116459 | 1.65517e+06 | 11800    | 1.66697e+06 | 114 | 801749           | 853421           |  392    | 10653    |   755    | 0.481415 | 0.518585 | 0.500679 | 0.499321 |
| 43952 | 72160   |  87669.2 | 39940   | 2068    | 201837 | 112913 | 1.56848e+06 |  4587    | 1.57307e+06 | 106 | 820509           | 747969           |  373    |  4193    |    21    | 0.521843 | 0.478157 | 0.555398 | 0.444602 |
| 43983 | 71591   |  95502.2 | 41840.8 | 1735.25 | 210669 | 117525 | 1.5758e+06  |  5444    | 1.58124e+06 | 106 | 797769           | 778029           |  508    |  4936    |     0    | 0.504842 | 0.495158 | 0.538435 | 0.461565 |
| 44013 | 68593.8 | 105692   | 45383.5 | 1359    | 221028 | 122446 | 1.5867e+06  |  3790    | 1.59049e+06 | 113 | 753431           | 833265           |  624    |  3166    |     0    | 0.474103 | 0.525897 | 0.515669 | 0.484331 |
| 44044 | 75325   | 120914   | 50159.8 |  950    | 247348 | 136144 | 1.74299e+06 |  4482    | 1.74747e+06 | 126 | 823449           | 919540           |  791    |  3691    |     0    | 0.471676 | 0.528324 | 0.50732  | 0.49268  |
| 44075 | 75525.8 | 121115   | 57704   | 2094    | 256438 | 140636 | 1.75128e+06 |  4256    | 1.75554e+06 | 119 | 834146           | 917134           |  526    |  3730    |     0    | 0.475451 | 0.524549 | 0.519539 | 0.480461 |
| 44105 | 83705   | 131770   | 57644.2 | 1096    | 274215 | 149675 | 1.92222e+06 |  6053    | 1.92827e+06 | 132 | 939078           | 983140           |  462    |  5591    |     0    | 0.487245 | 0.512755 | 0.515469 | 0.484531 |
| 44136 | 89031.8 | 125214   | 64844.2 |  778    | 279868 | 152755 | 2.00167e+06 |  5074    | 2.00675e+06 | 134 |      1.02715e+06 | 974520           |  677    |  4397    |     0    | 0.512187 | 0.487813 | 0.549816 | 0.450184 |
| 44166 | 82670.2 | 123218   | 53175.2 | 1338    | 260401 | 143262 | 1.92248e+06 |  7572    | 1.93005e+06 | 134 | 953023           | 969455           |  390    |  7182    |     0    | 0.493984 | 0.506016 | 0.521678 | 0.478322 |
| 44197 | 84688   | 130777   | 54730   |  774    | 270969 | 148450 | 1.97581e+06 |  7084    | 1.98289e+06 | 129 | 969391           |      1.00642e+06 | 1495    |  5589    |     0    | 0.489632 | 0.510368 | 0.514517 | 0.485483 |
| 44228 | 87466.2 | 110274   | 48493.5 | 2291.5  | 248526 | 136803 | 1.8713e+06  |  7459    | 1.87876e+06 | 117 |      1.00152e+06 | 869780           | 1398    |  6061    |     0    | 0.53382  | 0.46618  | 0.547066 | 0.452934 |
| 44256 | 94845.8 | 130066   | 51092   | 3510    | 279514 | 155311 | 2.11736e+06 |  9218.25 | 2.12658e+06 | 128 |      1.06257e+06 |      1.05479e+06 | 1078    |  8140.25 |     0    | 0.50017  | 0.49983  | 0.522112 | 0.477888 |
| 44287 | 95618.2 | 137954   | 50909   | 1924    | 286405 | 159688 | 2.20381e+06 | 13328    | 2.21714e+06 | 134 |      1.05554e+06 |      1.14827e+06 | 2021    | 11307    |     0    | 0.476994 | 0.523006 | 0.511608 | 0.488392 |
| 44317 | 99717.2 | 144916   | 67970   | 2338    | 314942 | 176081 | 2.29167e+06 |  8563    | 2.30023e+06 | 139 |      1.09429e+06 |      1.19738e+06 |  586    |  7977    |     0    | 0.475984 | 0.524016 | 0.532439 | 0.467561 |
| 44348 | 78853   | 138737   | 61368.8 | 2387    | 281346 | 156857 | 2.00129e+06 |  7915    | 2.00921e+06 | 133 | 865271           |      1.13602e+06 | 1038    |  6877    |     0    | 0.43117  | 0.56883  | 0.498396 | 0.501604 |
| 44378 | 81067.5 | 142963   | 66842   | 2254    | 293126 | 164227 | 2.07538e+06 |  8977    | 2.08436e+06 | 126 | 888744           |      1.18664e+06 | 1007    |  7970    |     0    | 0.426871 | 0.573129 | 0.504593 | 0.495407 |



label: S=(B+D)/F
T=(C+E)/F
labeled_formulas: S=(B+D)/F
T=(C+E)/F
output: {"Arithmetic-Relationship": ["S=(B+D)/F", "T=(C+E)/F"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_537477___xlsx_ae35cc103bfc687e1627c12fdf22d0fa0d537fb9.xlsx___line_505