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 |
|------:|-----:|-----:|-----:|-----:|-----:|----:|-----:|----:|----:|----:|-----:|------:|-----:|------:|
| 41643 | 1880 | 2031 | 1412 | 5323 | 1058 | 112 | 1170 |   3 | 180 | 183 | 6676 |  6869 |  739 |  7608 |
| 41650 | 2348 | 2382 | 1011 | 5741 | 1635 |  67 | 1702 |   5 | 103 | 108 | 7551 |  8292 | 1092 |  9384 |
| 41657 | 2324 | 2581 |  954 | 5859 | 1591 |  75 | 1666 |  28 | 155 | 183 | 7708 |  6952 | 1153 |  8105 |
| 41664 | 2498 | 2858 | 1049 | 6405 | 1638 |  82 | 1720 |   6 | 152 | 158 | 8283 |  6926 | 1057 |  7983 |
| 41671 | 2662 | 2629 | 1194 | 6485 | 1736 |  78 | 1814 |  20 | 167 | 187 | 8486 |  7106 | 1011 |  8117 |
| 41678 | 2647 | 2754 | 1175 | 6576 | 1549 |  94 | 1643 |   1 | 168 | 169 | 8388 |  7638 |  991 |  8629 |
| 41685 | 2828 | 2671 | 1064 | 6563 | 1737 | 167 | 1904 |  12 | 187 | 199 | 8666 |  6816 |  927 |  7743 |
| 41692 | 2909 | 3014 | 1280 | 7203 | 1617 | 160 | 1777 |   7 | 197 | 204 | 9184 |  5971 | 1062 |  7033 |
| 41699 | 2821 | 2779 | 1371 | 6971 | 1768 | 221 | 1989 |   4 | 187 | 191 | 9151 |  5042 |  739 |  5781 |
| 41706 | 2994 | 2614 | 1303 | 6911 | 1626 | 254 | 1880 |  30 | 165 | 195 | 8986 |  5246 |  888 |  6134 |
| 41713 | 2810 | 2591 | 1185 | 6586 | 1593 | 303 | 1896 |  10 | 213 | 223 | 8705 |  6066 |  866 |  6932 |
| 41720 | 2615 | 1946 |  948 | 5509 | 1274 | 178 | 1452 |  10 | 161 | 171 | 7132 |  4577 |  666 |  5243 |
| 41727 | 2465 | 2309 |  915 | 5689 | 1491 | 230 | 1721 |  16 | 199 | 215 | 7625 |  4286 |  836 |  5122 |
| 41734 | 2706 | 2395 | 1029 | 6130 | 1322 | 181 | 1503 |   9 | 214 | 223 | 7856 |  4640 | 1086 |  5726 |
| 41741 | 2991 | 2720 | 1023 | 6734 | 1429 | 142 | 1571 |  28 | 178 | 206 | 8511 |  5460 | 1144 |  6604 |
| 41748 | 2997 | 2454 |  916 | 6367 | 1124 | 136 | 1260 |  10 | 281 | 291 | 7918 |  4969 | 1001 |  5970 |
| 41755 | 2401 | 2358 |  868 | 5627 | 1088 | 118 | 1206 |  64 | 186 | 250 | 7083 |  3818 |  785 |  4603 |
| 41762 | 3291 | 2877 |  921 | 7089 | 1328 | 164 | 1492 |   7 | 168 | 175 | 8756 |  4937 | 1042 |  5979 |
| 41769 | 3082 | 2344 |  933 | 6359 | 1298 | 126 | 1424 |  24 | 184 | 208 | 7991 |  4586 |  894 |  5480 |
| 41776 | 3535 | 2848 | 1065 | 7448 | 1330 | 116 | 1446 |   9 | 195 | 204 | 9098 |  5463 | 1038 |  6501 |
| 41783 | 3313 | 2881 | 1381 | 7575 | 1300 | 167 | 1467 |   7 | 199 | 206 | 9248 |  6521 |  802 |  7323 |
| 41790 | 3239 | 2567 | 1161 | 6967 | 1309 | 130 | 1439 |   5 | 164 | 169 | 8575 |  7021 |  925 |  7946 |
| 41797 | 2598 | 2259 | 1158 | 6015 | 1286 | 127 | 1413 |  10 | 181 | 191 | 7619 |  9101 |  771 |  9872 |
| 41804 | 2451 | 2105 | 1389 | 5945 | 1378 | 125 | 1503 |  36 | 143 | 179 | 7627 | 10325 |  766 | 11091 |
| 41811 | 2156 | 1937 | 1045 | 5138 | 1424 | 123 | 1547 |  11 | 148 | 159 | 6844 | 10948 | 1001 | 11949 |
| 41818 | 2007 | 1714 | 1086 | 4807 | 1376 | 140 | 1516 |  35 | 164 | 199 | 6522 | 12361 |  997 | 13358 |
| 41825 | 2091 | 1625 |  927 | 4643 | 1366 | 126 | 1492 |   1 | 187 | 188 | 6323 | 14359 |  911 | 15270 |
| 41832 | 1856 | 1610 |  909 | 4375 | 1486 | 151 | 1637 |  14 | 184 | 198 | 6210 | 11823 |  756 | 12579 |
| 41839 | 1518 | 1172 |  554 | 3244 |  970 |  84 | 1054 |   1 | 143 | 144 | 4442 |  9665 |  870 | 10535 |
| 41846 | 2140 | 1754 |  871 | 4765 | 1290 |  76 | 1366 |   6 | 136 | 142 | 6273 | 12887 |  673 | 13560 |
| 41853 | 2562 | 1787 |  901 | 5250 | 1572 | 139 | 1711 |   9 | 157 | 166 | 7127 | 12738 |  903 | 13641 |
| 41860 | 2490 | 1906 |  805 | 5201 | 1692 | 109 | 1801 |  13 | 167 | 180 | 7182 | 12684 |  863 | 13547 |
| 41867 | 2963 | 2004 |  794 | 5761 | 1718 | 100 | 1818 |   5 | 183 | 188 | 7767 | 11136 | 1184 | 12320 |
| 41874 | 3214 | 2035 |  761 | 6010 | 1774 | 116 | 1890 |   4 | 171 | 175 | 8075 | 11167 | 1096 | 12263 |
| 41881 | 3398 | 1948 |  558 | 5904 | 1732 | 147 | 1879 |   6 | 166 | 172 | 7955 | 11978 |  813 | 12791 |
| 41888 | 3101 | 1928 |  707 | 5736 | 1812 | 149 | 1961 |   6 | 145 | 151 | 7848 | 13129 | 1310 | 14439 |
| 41895 | 3093 | 1929 |  562 | 5584 | 1977 | 150 | 2127 |  10 | 156 | 166 | 7877 | 12504 | 1691 | 14195 |
| 41902 | 3732 | 1966 |  507 | 6205 | 1364 |  98 | 1462 |   2 | 147 | 149 | 7816 | 11120 | 1576 | 12696 |
| 41909 | 3665 | 2182 |  427 | 6274 | 1651 | 142 | 1793 |   6 | 171 | 177 | 8244 | 11847 | 1295 | 13142 |
| 41916 | 3844 | 2078 |  365 | 6287 | 1611 | 117 | 1728 |  19 | 174 | 193 | 8208 | 12414 | 1315 | 13729 |
| 41923 | 4000 | 2228 |  452 | 6680 | 1892 | 135 | 2027 |  18 | 163 | 181 | 8888 | 11489 | 1207 | 12696 |
| 41930 | 3896 | 2380 |  386 | 6662 | 1904 |  74 | 1978 |   8 | 171 | 179 | 8819 | 10388 | 1196 | 11584 |
| 41937 | 4114 | 2647 |  439 | 7200 | 1759 |  98 | 1857 |   8 | 157 | 165 | 9222 |  9642 | 1127 | 10769 |
| 41944 | 3851 | 2582 |  507 | 6940 | 2157 | 105 | 2262 |  13 | 188 | 201 | 9403 | 10886 |  638 | 11524 |
| 41951 | 3938 | 2510 |  426 | 6874 | 2088 |  89 | 2177 |  27 | 118 | 145 | 9196 |  9401 |  947 | 10348 |
| 41958 | 3914 | 2343 |  401 | 6658 | 2219 | 105 | 2324 |  15 | 107 | 122 | 9104 |  9085 |  798 |  9883 |
| 41965 | 3725 | 3002 |  419 | 7146 | 2141 | 109 | 2250 |  20 | 136 | 156 | 9552 |  8792 | 1099 |  9891 |
| 41972 | 3888 | 2719 |  383 | 6990 | 2212 | 107 | 2319 |  10 | 120 | 130 | 9439 |  7069 | 1462 |  8531 |
| 41979 | 3438 | 2770 |  460 | 6668 | 2157 | 118 | 2275 |  48 | 138 | 186 | 9129 |  8433 |  978 |  9411 |
| 41986 | 3461 | 2682 |  548 | 6691 | 2144 | 105 | 2249 |  15 | 121 | 136 | 9076 |  7955 | 1021 |  8976 |
| 41993 | 3489 | 2404 |  610 | 6503 | 2182 | 144 | 2326 |  12 | 109 | 121 | 8950 |  7886 |  668 |  8554 |
| 42000 | 2023 | 1571 |  382 | 3976 |  556 |  35 |  591 |   0 |   6 |   6 | 4573 |  2536 |  121 |  2657 |



label: H=F+G
O=M+N
L=E+H+K
labeled_formulas: H=F+G
O=M+N
L=E+H+K
output: {"Arithmetic-Relationship": ["H=F+G", "O=M+N", "L=E+H+K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_505204___xlsx_d418f34936d8532db8f608bf498911f65891f526.xlsx___line_754