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 |
|------:|-----:|-----:|-----:|-----:|-----:|----:|-----:|----:|----:|----:|------:|-----:|-----:|-----:|
| 40551 | 2260 | 2368 | 1354 | 5982 | 1514 | 151 | 1665 |   4 | 162 | 166 |  7813 | 3910 |  465 | 4375 |
| 40558 | 3309 | 3049 | 1424 | 7782 | 1544 | 228 | 1772 |   1 |  75 |  76 |  9630 | 3818 |  929 | 4747 |
| 40565 | 3539 | 2996 | 1353 | 7888 | 2055 | 378 | 2433 |  10 | 152 | 162 | 10483 | 3975 |  917 | 4892 |
| 40572 | 4011 | 3002 | 1253 | 8266 | 1634 | 319 | 1953 |   5 | 123 | 128 | 10347 | 3518 | 1056 | 4574 |
| 40579 | 3253 | 3208 | 1431 | 7892 | 1848 | 214 | 2062 |   8 | 134 | 142 | 10096 | 3476 |  543 | 4019 |
| 40586 | 3143 | 3057 | 1275 | 7475 | 1802 | 239 | 2041 |   0 | 100 | 100 |  9616 | 3610 |  733 | 4343 |
| 40593 | 3624 | 3081 | 1332 | 8037 | 1716 | 170 | 1886 |   2 |  99 | 101 | 10024 | 3341 |  478 | 3819 |
| 40600 | 3530 | 3130 | 1541 | 8201 | 1741 | 140 | 1881 |   0 | 125 | 125 | 10207 | 3181 |  529 | 3710 |
| 40607 | 3506 | 3104 | 1234 | 7844 | 1602 | 190 | 1792 |   5 | 110 | 115 |  9751 | 3082 |  596 | 3678 |
| 40614 | 3483 | 2740 | 1315 | 7538 | 1590 | 295 | 1885 |   1 | 113 | 114 |  9537 | 3080 |  434 | 3514 |
| 40621 | 2832 | 2679 | 1174 | 6685 | 1298 | 177 | 1475 |   6 | 118 | 124 |  8284 | 3288 |  361 | 3649 |
| 40628 | 3373 | 2855 | 1353 | 7581 | 1562 | 146 | 1708 |   6 |  94 | 100 |  9389 | 2841 |  420 | 3261 |
| 40635 | 2940 | 2787 | 1276 | 7003 | 1048 | 123 | 1171 |   6 | 117 | 123 |  8297 | 2927 |  684 | 3611 |
| 40642 | 3152 | 2707 | 1074 | 6933 | 1448 | 156 | 1604 |   1 |  72 |  73 |  8610 | 3137 |  643 | 3780 |
| 40649 | 3121 | 2545 | 1220 | 6886 | 1098 | 149 | 1247 |   0 | 106 | 106 |  8239 | 3215 |  668 | 3883 |
| 40656 | 3000 | 2608 | 1020 | 6628 | 1329 | 132 | 1461 |   1 | 120 | 121 |  8210 | 3087 |  316 | 3403 |
| 40663 | 2396 | 2020 |  904 | 5320 |  870 |  81 |  951 |   1 |  98 |  99 |  6370 | 2870 |  665 | 3535 |
| 40670 | 2860 | 2208 | 1178 | 6246 | 1318 | 144 | 1462 |   1 |  79 |  80 |  7788 | 2953 |  648 | 3601 |
| 40677 | 2959 | 2654 | 1511 | 7124 | 1179 | 172 | 1351 |   2 |  50 |  52 |  8527 | 3231 |  874 | 4105 |
| 40684 | 2730 | 2626 | 1359 | 6715 | 1557 | 218 | 1775 |   0 |  87 |  87 |  8577 | 4105 |  819 | 4924 |
| 40691 | 2990 | 2469 | 1613 | 7072 | 1208 | 143 | 1351 |   8 |  76 |  84 |  8507 | 4466 |  567 | 5033 |
| 40698 | 2702 | 2229 | 1408 | 6339 | 1914 | 175 | 2089 |   1 |  73 |  74 |  8502 | 5111 |  578 | 5689 |
| 40705 | 2667 | 2207 | 1542 | 6416 | 1505 | 204 | 1709 |   1 |  62 |  63 |  8188 | 4670 |  408 | 5078 |
| 40712 | 2585 | 2149 | 1190 | 5924 | 2267 | 228 | 2495 |   2 |  61 |  63 |  8482 | 5018 |  697 | 5715 |
| 40719 | 2973 | 2071 | 1394 | 6438 | 1602 | 138 | 1740 |   1 | 106 | 107 |  8285 | 5038 |  368 | 5406 |
| 40726 | 2247 | 2031 | 1474 | 5752 | 2146 | 174 | 2320 |   0 | 114 | 114 |  8186 | 6032 |  555 | 6587 |
| 40733 | 2210 | 1976 | 1038 | 5224 | 1728 | 128 | 1856 |   1 |  76 |  77 |  7157 | 5584 |  594 | 6178 |
| 40740 | 1459 |  952 |  705 | 3116 |  935 | 131 | 1066 |   5 |  96 | 101 |  4283 | 3473 |  345 | 3818 |
| 40747 | 1846 | 1574 |  833 | 4253 | 1628 | 132 | 1760 |   8 |  68 |  76 |  6089 | 6657 |  668 | 7325 |
| 40754 | 2102 | 1761 |  934 | 4797 | 1774 | 154 | 1928 |   0 |  87 |  87 |  6812 | 5582 |  974 | 6556 |
| 40761 | 2213 | 1885 | 1030 | 5128 | 1845 | 158 | 2003 |   1 | 123 | 124 |  7255 | 6626 |  991 | 7617 |
| 40768 | 2981 | 2013 |  897 | 5891 | 1760 | 139 | 1899 |   3 | 101 | 104 |  7894 | 6436 |  981 | 7417 |
| 40775 | 3413 | 1893 | 1061 | 6367 | 1671 | 216 | 1887 |  10 |  66 |  76 |  8330 | 6272 | 1050 | 7322 |
| 40782 | 3523 | 2328 |  988 | 6839 | 1874 | 112 | 1986 |   5 |  93 |  98 |  8923 | 6129 |  957 | 7086 |
| 40789 | 3616 | 1978 |  864 | 6458 | 1589 |  95 | 1684 |   2 | 124 | 126 |  8268 | 6346 |  876 | 7222 |
| 40796 | 3842 | 2471 |  840 | 7153 | 1866 | 103 | 1969 |   0 | 109 | 109 |  9231 | 8118 | 1017 | 9135 |
| 40803 | 4008 | 2347 |  923 | 7278 | 1847 | 135 | 1982 |   0 | 140 | 140 |  9400 | 7574 | 1146 | 8720 |
| 40810 | 4530 | 2253 |  976 | 7759 | 1893 | 100 | 1993 |   2 | 129 | 131 |  9883 | 7178 | 1116 | 8294 |
| 40817 | 4142 | 2283 | 1182 | 7607 | 1952 | 115 | 2067 |  11 | 150 | 161 |  9835 | 7282 | 1055 | 8337 |
| 40824 | 4554 | 2389 | 1004 | 7947 | 1851 | 151 | 2002 |   4 | 143 | 147 | 10096 | 6847 | 1103 | 7950 |
| 40831 | 4005 | 2361 |  924 | 7290 | 2008 | 129 | 2137 |   8 | 128 | 136 |  9563 | 6687 |  917 | 7604 |
| 40838 | 4349 | 2422 |  939 | 7710 | 2331 | 142 | 2473 |   3 |  92 |  95 | 10278 | 6746 | 1167 | 7913 |
| 40845 | 3920 | 2157 |  926 | 7003 | 2717 | 129 | 2846 |   0 | 137 | 137 |  9986 | 6430 |  805 | 7235 |
| 40852 | 3215 | 2023 |  971 | 6209 | 2619 | 149 | 2768 |   0 | 133 | 133 |  9110 | 6895 |  590 | 7485 |
| 40859 | 2942 | 2288 |  814 | 6044 | 2323 | 125 | 2448 |   1 | 137 | 138 |  8630 | 7335 |  834 | 8169 |
| 40866 | 3034 | 2428 | 1211 | 6673 | 2260 | 122 | 2382 |   4 | 117 | 121 |  9176 | 5549 | 1091 | 6640 |
| 40873 | 3381 | 2471 | 1016 | 6868 | 2286 | 117 | 2403 |   5 | 129 | 134 |  9405 | 5910 |  933 | 6843 |
| 40880 | 3552 | 2920 | 1300 | 7772 | 1697 | 136 | 1833 |   1 | 162 | 163 |  9768 | 6261 |  890 | 7151 |
| 40887 | 3531 | 2599 |  968 | 7098 | 2398 | 127 | 2525 |   2 |  76 |  78 |  9701 | 7069 |  495 | 7564 |
| 40894 | 2940 | 2460 |  907 | 6307 | 2302 | 133 | 2435 |   3 | 162 | 165 |  8907 | 7273 |  816 | 8089 |
| 40901 | 2742 | 2311 |  978 | 6031 | 1850 | 124 | 1974 |  10 | 106 | 116 |  8121 | 5787 |  529 | 6316 |
| 40908 | 2072 | 1954 |  877 | 4903 |  599 |  83 |  682 |   1 |  84 |  85 |  5670 | 3880 |  604 | 4484 |



label: H=F+G
K=I+J
O=M+N
L=E+H+K
labeled_formulas: H=F+G
K=I+J
O=M+N
L=E+H+K
output: {"Arithmetic-Relationship": ["H=F+G", "K=I+J", "O=M+N", "L=E+H+K"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_505201___xlsx_d418f34936d8532db8f608bf498911f65891f526.xlsx___line_751