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 |
|----:|----:|----:|-------:|-------:|------------:|------:|------------:|-----:|------:|------:|-----:|-----:|------:|-------:|------------:|
|   1 | 197 | 197 |  52951 |  52951 | 1.04313e+07 | 38809 | 2.80381e+09 |    0 | 22561 |  1118 |  382 | 2052 |  1881 | -78173 | 2.81433e+09 |
|   9 | 159 | 159 |  53743 |  53743 | 8.54514e+06 | 25281 | 2.88831e+09 |    0 | 16535 |  2717 |  209 | 2400 |  1476 |  28950 | 2.89704e+09 |
|  10 | 141 | 141 |  53109 |  53109 | 7.48837e+06 | 19881 | 2.82057e+09 |    0 | 23821 |  1102 |  184 | 2076 |  1168 |  20876 | 2.82823e+09 |
|  13 | 280 | 280 |  49049 |  49049 | 1.37337e+07 | 78400 | 2.4058e+09  |    0 | 19992 |  1999 |  582 | 1927 |  -477 | -30104 | 2.41971e+09 |
|  15 | 174 | 174 |  59790 |  59790 | 1.04035e+07 | 30276 | 3.57484e+09 |  200 | 20082 |  1336 |  492 | 1898 |  1260 |  18803 | 3.58544e+09 |
|  16 | 171 | 171 |  80773 |  80773 | 1.38122e+07 | 29241 | 6.52428e+09 |  600 | 26716 |  3873 |  559 | 1808 |   510 |  23080 | 6.53834e+09 |
|  17 | 167 | 167 |  71130 |  71130 | 1.18787e+07 | 27889 | 5.05948e+09 | 9212 | 25223 |  5560 |  356 | 1816 |  2350 |  18774 | 5.07159e+09 |
|  18 | 161 | 161 |  82490 |  82490 | 1.32809e+07 | 25921 | 6.8046e+09  | 6007 | 21106 |  1737 |  439 | 1384 |  -288 |  23802 | 6.81813e+09 |
|  19 | 173 | 173 |  98172 |  98172 | 1.69838e+07 | 29929 | 9.63774e+09 |  500 | 17799 |  1847 | 1628 | 1962 |  1591 |  33848 | 9.65501e+09 |
|  20 | 161 | 161 |  90685 |  90685 | 1.46003e+07 | 25921 | 8.22377e+09 | 2690 | 28038 |  4415 |  -12 | 2446 | -3308 |  13480 | 8.23862e+09 |
|  21 | 167 | 167 |  97771 |  97771 | 1.63278e+07 | 27889 | 9.55917e+09 |  600 | 37284 |  2827 |  480 | 2296 |  1709 |  22965 | 9.57579e+09 |
|  22 | 153 | 153 |  87129 |  87129 | 1.33307e+07 | 23409 | 7.59146e+09 | 1740 | 24236 |  5836 |   79 | 3175 |   798 |  18898 | 7.60505e+09 |
|  23 | 201 | 201 |  95910 |  95910 | 1.92779e+07 | 40401 | 9.19873e+09 | 2074 | 27244 |  3387 |  188 | 1287 | -2025 |  38699 | 9.21831e+09 |
|  25 | 227 | 227 |  89041 |  89041 | 2.02123e+07 | 51529 | 7.9283e+09  | 1880 | 26719 |  4383 |  769 | 2205 |  2493 | -44140 | 7.94874e+09 |
|  26 | 150 | 150 |  92165 |  92165 | 1.38248e+07 | 22500 | 8.49439e+09 | 3602 | 14727 | 10231 |  593 | 2289 | -2051 |  36311 | 8.50848e+09 |
|  27 | 142 | 142 |  88981 |  88981 | 1.26353e+07 | 20164 | 7.91762e+09 |  744 | 27880 |  7734 |  414 | 1891 |   386 |  19865 | 7.93051e+09 |
|  28 | 104 | 104 |  95898 |  95898 | 9.97339e+06 | 10816 | 9.19643e+09 |  960 | 21872 |  -684 |  425 | 2288 |   178 |  19013 | 9.20665e+09 |
|  29 | 121 | 121 |  96245 |  96245 | 1.16456e+07 | 14641 | 9.2631e+09  |    0 | 18705 |  8329 |  483 | 2223 |  -262 |  16228 | 9.275e+09   |
|  30 |  99 |  99 | 106364 | 106364 | 1.053e+07   |  9801 | 1.13133e+10 |    0 | 23835 |  2540 |  417 | 1683 | -1356 |  37637 | 1.13241e+10 |
|  31 | 150 | 150 |  90564 |  90564 | 1.35846e+07 | 22500 | 8.20184e+09 | 1950 | 25605 |  5862 |  222 | 1586 |   486 |  -1121 | 8.21566e+09 |
|  32 | 144 | 144 |  98418 |  98418 | 1.41722e+07 | 20736 | 9.6861e+09  | 1540 | 17763 |  6998 |   49 | 1751 | -1924 |  34757 | 9.70055e+09 |
|  33 | 154 | 154 | 110436 | 110436 | 1.70071e+07 | 23716 | 1.21961e+10 | 2693 | 32379 |  8131 |  818 | 2082 |  1547 |  26419 | 1.22134e+10 |
|  34 | 130 | 130 | 102042 | 102042 | 1.32655e+07 | 16900 | 1.04126e+10 | 1060 | 19324 |  6026 | 1015 | 1714 |   132 |  21134 | 1.04261e+10 |
|  35 | 202 | 202 | 124413 | 124413 | 2.51314e+07 | 40804 | 1.54786e+10 | 3519 | 22412 |  9120 | 1255 | 2173 | -2337 |  18578 | 1.55041e+10 |
|  36 |  51 |  51 | 116897 | 116897 | 5.96175e+06 |  2601 | 1.36649e+10 | 1520 | 29998 |  6798 |   68 | 1779 |  1195 |  91520 | 1.36712e+10 |
|  37 | 148 | 148 |  97083 |  97083 | 1.43683e+07 | 21904 | 9.42511e+09 | 1080 |  9112 |  6627 |  565 | 1324 |  1164 | -73753 | 9.43964e+09 |
|  38 | 153 | 153 | 104727 | 104727 | 1.60232e+07 | 23409 | 1.09677e+10 | 3230 | 38616 |  5892 |  369 | 1523 | -1839 |  30443 | 1.09841e+10 |
|  39 |  83 |  83 |  95622 |  95622 | 7.93663e+06 |  6889 | 9.14357e+09 |  953 | 22690 |  3450 | -182 | 2087 |   454 |  17725 | 9.15175e+09 |
|  40 | 101 | 101 |  96438 |  96438 | 9.74024e+06 | 10201 | 9.30029e+09 | 1244 | 14703 |  5259 |  709 | 2095 |   868 |  26402 | 9.31028e+09 |
|  41 | 140 | 140 | 114995 | 114995 | 1.60993e+07 | 19600 | 1.32239e+10 |    0 | 28764 |  2294 | 1006 | 1304 | -1990 |  -3789 | 1.32402e+10 |
|  42 | 132 | 132 | 105337 | 105337 | 1.39045e+07 | 17424 | 1.10959e+10 |  160 | 27253 |  8155 |  521 | 1667 |  1869 |  15090 | 1.11101e+10 |
|  43 | 112 | 112 |  98989 |  98989 | 1.10868e+07 | 12544 | 9.79882e+09 | 2480 | 24419 |  1621 |  514 | 1040 |   329 |   -945 | 9.81015e+09 |
|  44 | 127 | 127 | 124352 | 124352 | 1.57927e+07 | 16129 | 1.54634e+10 | 1800 | 26011 |   902 |  917 | 2880 | -1897 |  30405 | 1.54795e+10 |
|  45 | 139 | 139 | 115875 | 115875 | 1.61066e+07 | 19321 | 1.3427e+10  | 1417 | 24492 |  5158 |  -77 | 1281 |  2959 |  14781 | 1.34434e+10 |
|  46 | 156 | 156 | 113035 | 113035 | 1.76335e+07 | 24336 | 1.27769e+10 | 1820 | 31158 |  2901 |  450 | 2259 |   417 |  15613 | 1.27948e+10 |
|  47 | 126 | 126 | 119106 | 119106 | 1.50074e+07 | 15876 | 1.41862e+10 | 3338 | 32213 | 14426 |  120 | 1394 | -2659 |  40968 | 1.42016e+10 |
|  49 | 209 | 209 |  98938 |  98938 | 2.0678e+07  | 43681 | 9.78873e+09 | 1866 | 26737 |  1694 |  853 | 1657 |   601 | -20127 | 9.80966e+09 |
|  50 | 124 | 124 | 108606 | 108606 | 1.34671e+07 | 15376 | 1.17953e+10 | 3676 | 31084 |  9040 |  498 | 2266 |  -284 |  18236 | 1.1809e+10  |
|  51 | 131 | 131 | 106396 | 106396 | 1.39379e+07 | 17161 | 1.13201e+10 | 1197 | 33278 |  2099 |  605 | 1952 |   668 |  15176 | 1.13343e+10 |
|  52 | 144 | 144 | 106778 | 106778 | 1.5376e+07  | 20736 | 1.14015e+10 |  241 | 32657 |  9328 |  483 | 1852 |  1409 |  25245 | 1.14172e+10 |
|  53 |  93 |  93 | 124805 | 124805 | 1.16069e+07 |  8649 | 1.55763e+10 |  500 | 29794 |  4268 |  788 | 1704 | -1771 |   6493 | 1.55882e+10 |
|  54 | 199 | 199 | 110153 | 110153 | 2.19204e+07 | 39601 | 1.21337e+10 | 1910 | 38431 |  5407 |  529 | 1882 |   453 |  21851 | 1.21559e+10 |
|  55 | 170 | 170 | 117276 | 117276 | 1.99369e+07 | 28900 | 1.37537e+10 |  800 | 27640 |  9305 | -180 |  977 |  1310 |      7 | 1.37739e+10 |
|  56 | 186 | 186 | 112055 | 112055 | 2.08422e+07 | 34596 | 1.25563e+10 |  980 | 28657 |  1803 | -242 |  846 | -2844 |  17192 | 1.25775e+10 |
|  57 | 200 | 200 | 114765 | 114765 | 2.2953e+07  | 40000 | 1.3171e+10  | 1695 | 36425 |  8839 |  859 | 2856 |  1532 |  14864 | 1.31943e+10 |
|  58 | 146 | 146 | 128007 | 128007 | 1.8689e+07  | 21316 | 1.63858e+10 | 1560 | 27720 | 10944 | -492 | 1864 |  1400 |  10121 | 1.64048e+10 |
|  59 | 222 | 222 | 116811 | 116811 | 2.5932e+07  | 49284 | 1.36448e+10 | 2249 | 27941 |  5775 |  245 | 1141 | -3513 |   7946 | 1.36711e+10 |
|  60 |  73 |  73 | 115899 | 115899 | 8.46063e+06 |  5329 | 1.34326e+10 | 1594 | 30950 | 12750 |  717 |  486 |  1746 | 188040 | 1.34415e+10 |



label: F=B*D
G=B*C
H=D*E
labeled_formulas: F=B*D
G=B*C
H=D*E
C=(L/H)+B
C=(L/P)+B
output: {"Arithmetic-Relationship": ["F=B*D", "G=B*C", "H=D*E"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_772173___xlsx_f64e988e517713ad92999a3138c3cfcb03fe429b.xlsx___line_721