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 |
|:----------------|:----|:---------------------------|---------:|---------:|------:|-----:|-----:|-----:|------:|------:|-----:|
| 806 BRYAN ST    | J   | 1                          | 10334.5  | 0.237247 |  26.9 | 34.9 |  6.8 | 12.8 |  19.6 |  27.6 | 21.5 |
| 811 BRYAN ST    | I   | 20                         | 27002.6  | 0.619895 | 112.6 | 21.5 | 16.9 | 34.7 |  51.6 |  32.3 | 20   |
| 812 BRYAN ST    | J   | 2                          | 12351.3  | 0.283548 |  33.4 | 43.9 | 11.1 | 19   |  30.1 |  27.6 | 15   |
| 817 BRYAN ST    | I   | 19                         | 14691.2  | 0.337264 |  31.6 | 77.5 |  7.8 | 11.2 |  19   |  29.8 | 22.5 |
| 818 BRYAN ST    | J   | 4                          | 15559    | 0.357186 |  35.9 | 61.6 | 16.8 | 30   |  46.8 |  37.2 | 15   |
| 823 BRYAN ST    | I   | 18                         | 14968.3  | 0.343624 |  31.1 | 87.7 | 22   | 10.9 |  32.9 |  26.1 | 17.7 |
| 824 BRYAN ST    | J   | 6                          |  9475.48 | 0.217527 |  24.8 | 23.1 | 12.5 | 15.2 |  27.7 |  20   | 34   |
| 828 BRYAN ST    | J   | 8                          |  7782.57 | 0.178663 |  23.7 | 23.2 |  4.7 | 17.1 |  21.8 |  20   | 27   |
| 829 BRYAN ST    | I   | 17                         | 14957.7  | 0.343381 |  22.1 | 66.8 |  3.1 | 14.8 |  17.9 |  26.1 | 23   |
| 611 DANIELS ST  | D   | 1, 2, 3                    | 21493.6  | 0.493424 |  24   | 28.1 | 28   | 13.6 |  41.6 | 110.5 | 14   |
| 612 DANIELS ST  | C   | 43                         | 14380.4  | 0.330129 |  24.2 | 38.6 |  7.3 | 12.5 |  19.8 |  25   | 16   |
| 618 DANIELS ST  | C   | 40                         | 11625    | 0.266874 |  38.9 | 32.2 | 14.9 | 16.8 |  31.7 |  25   | 16   |
| 622 DANIELS ST  | C   | 37(part), 38, 39(remnant)  | 13405.5  | 0.307747 |  36.5 | 22   | 24.6 | 24.5 |  49.1 |  31.4 | 20.7 |
| 626 DANIELS ST  | C   | 35, 36, 37(part)           | 14286.3  | 0.327969 |  35.6 | 58.1 |  6.1 | 28.2 |  34.3 |  31.4 | 17.2 |
| 630 DANIELS ST  | C   | 34                         |  7990.21 | 0.18343  |  15   | 54   | 17.3 |  7.4 |  24.7 |  16.7 | 32.5 |
| 634 DANIELS ST  | C   | 33                         |  7535.89 | 0.173    |  15.2 | 21.1 |  8.7 | 16.6 |  25.3 |  16.7 | 34.2 |
| 702 DANIELS ST  | E   | 1 (part)                   | 12455.5  | 0.285938 |  23.3 | 14.3 | 22.8 |  9.9 |  32.7 |  19.6 | 14.7 |
| 708 DANIELS ST  | E   | 2, 3, 4(part)              | 11792.2  | 0.270712 |  31.6 | 44.5 | 12.3 | 18.4 |  30.7 |  22.4 | 14   |
| 712 DANIELS ST  | E   | 4(part), 5, 6              | 13627.9  | 0.312853 |  27.5 | 58.1 | 10.1 | 21.5 |  31.6 |  28.8 | 14   |
| 800 DANIELS ST  | G   | 12                         | 14869.2  | 0.341351 |  25.9 | 25.6 | 25.5 | 33.7 |  59.2 |  33.9 | 18   |
| 810 DANIELS ST  | G   | 13, 14                     |  9231.42 | 0.211924 |  32   | 43.7 |  5.7 |  8.4 |  14.1 |  20.6 | 14.5 |
| 814 DANIELS ST  | G   | 15, 16                     |  9464.68 | 0.217279 |  34.5 | 40.5 | 11.2 |  9.7 |  20.9 |  20.6 | 17   |
| 818 DANIELS ST  | G   | 17, 18                     | 10440.1  | 0.239672 |  32.8 | 41   | 16   |  9.4 |  25.4 |  24.9 | 14   |
| 822 DANIELS ST  | G   | 19, 20                     | 10975.3  | 0.251959 |  29.2 | 50   | 14.1 |  6.3 |  20.4 |  24.9 | 15   |
| 826 DANIELS ST  | G   | 21, 22                     | 11355.9  | 0.260696 |  29.8 | 29.1 | 20.3 |  4   |  24.3 |  22.2 | 14   |
| 830 DANIELS ST  | G   | 23, 24                     | 10316.9  | 0.236843 |  29   | 36.2 | 17.7 |  7.5 |  25.2 |  13.4 | 14.5 |
| 836 DANIELS ST  | G   | 1                          | 12466    | 0.286179 |  17.5 |  5.3 | 15.9 | 22.1 |  38   |  13.4 | 14   |
| 902 DANIELS ST  | H   | 27                         | 13474.2  | 0.309325 |  29.9 |  9.2 | 32.6 |  9.7 |  42.3 |  18.9 | 18   |
| 908 DANIELS ST  | H   | 28                         | 10455.1  | 0.240015 |  27.4 | 30.7 |  9.1 |  0   |   9.1 |  10.3 | 16   |
| 706 GRAHAM ST   | C   | 31, 32                     | 16358.3  | 0.375535 |  30.6 | 62.8 | 24.1 | 21.9 |  46   |  44.1 | 14   |
| 709 GRAHAM ST   | E   | 1(part), 14                | 10525.4  | 0.24163  |  17.8 |  2.1 | 11.1 | 10.2 |  21.3 |  19.6 | 17   |
| 710 GRAHAM ST   | C   | 29, 30                     | 11702.6  | 0.268655 |  34.9 | 32.9 | 22   | 14.9 |  36.9 |  22.3 | 15   |
| 714 GRAHAM ST   | C   | 27, 28                     | 11375.6  | 0.261147 |  22.2 | 20.5 |  5.1 | 20.3 |  25.4 |  22.3 | 15.5 |
| 715 GRAHAM ST   | E   | 12, 13                     |  9398.24 | 0.215754 |  27.3 | 32.9 |  8.8 |  4.4 |  13.2 |  17.2 | 16   |
| 718 GRAHAM ST   | C   | 25, 26                     | 10415.4  | 0.239104 |  25.7 | 45.2 |  9   |  3.4 |  12.4 |  20   | 14   |
| 719 GRAHAM ST   | E   | 10, 11                     |  9765.94 | 0.224195 |  29.5 | 27.6 |  5.7 | 12.4 |  18.1 |  17.2 | 28.2 |
| 722 GRAHAM ST   | C   | 23, 24                     | 11899.6  | 0.273176 |  30.3 | 68.8 |  6   |  7.4 |  13.4 |  20   | 11   |
| 727 GRAHAM ST   | E   | 9                          | 13086.6  | 0.300427 |  24.4 | 27.8 | 14.3 | 35   |  49.3 |  28.3 | 16   |
| 805 GRAHAM ST   | G   | 10                         | 17356.5  | 0.39845  |  17   | 23.4 | 38.2 | 36.5 |  74.7 |  30.8 | 16   |
| 806 GRAHAM ST   | H   | 12, 13, 14(part)           | 12233.3  | 0.280838 |  25.9 | 71.2 | 14.5 | 13.1 |  27.6 |  24.4 | 16.5 |
| 809 GRAHAM ST   | G   | 8, 9                       | 12197.9  | 0.280026 |  31.3 | 68.8 |  8.9 |  9.7 |  18.6 |  26.5 | 13.5 |
| 812 GRAHAM ST   | H   | 14(part), 15, 16           | 11859.1  | 0.272247 |  36.5 | 39.4 | 10.4 |  3.4 |  13.8 |  24.4 | 16.5 |
| 813 GRAHAM ST   | G   | 6, 7                       | 12636.5  | 0.290094 |  29.4 | 70.3 |  5.4 | 16.8 |  22.2 |  22.9 | 15   |
| 816 GRAHAM ST   | H   | 18                         | 13959.9  | 0.320476 |  34.5 | 46.6 | 27.3 |  1.2 |  28.5 |  11.7 | 29.5 |
| 817 GRAHAM ST   | G   | 4, 5                       | 11327.9  | 0.260053 |  32.3 | 56.3 | 17.3 | 10.5 |  27.8 |  22.9 | 14.5 |
| 820 GRAHAM ST   | H   | 19, 20                     | 20122.8  | 0.461956 |  48.7 | 35.1 |  9.2 | 10.3 |  19.5 |  11.7 | 17.3 |
| 823 GRAHAM ST   | G   | 3                          | 12153.4  | 0.279003 |  29   | 32.7 | 12.7 |  6.9 |  19.6 |  13.3 | 16   |
| 824 GRAHAM ST   | H   | 21, 22                     | 14660.5  | 0.336558 |  52.6 | 32.8 |  9.1 | 24.3 |  33.4 |  22.7 | 17.5 |
| 828 GRAHAM ST   | H   | 23, 24                     | 14010.9  | 0.321646 |  10.7 | 51   | 13.7 | 10.5 |  24.2 |  24.2 | 17   |
| 829 GRAHAM ST   | G   | 2                          | 10904.5  | 0.250332 |  29.1 | 22.4 |  0.6 |  6.4 |   7   |  13.3 | 15   |
| 832 GRAHAM ST   | H   | 25, 26                     | 16472.6  | 0.378159 |  32.2 | 78.2 | 13.8 | 12.5 |  26.3 |  21.7 | 16.5 |
| 1002 JAMES PL   | K   | 3, 4(part)                 | 14954.6  | 0.34331  |  29.3 | 41.8 |  8.2 |  9   |  17.2 |  16.2 | 17.5 |
| 1003 JAMES PL   | I   | 1                          | 14567.6  | 0.334426 |  16.6 | 20   | 31.5 | 26.2 |  57.7 |  41.4 | 26.5 |
| 1006 JAMES PL   | K   | 4(part), 5                 |  9498.74 | 0.218061 |  29.7 | 40.7 | 14.2 | 10.8 |  25   |  23.5 | 17   |
| 1007 JAMES PL   | I   | 22                         | 11390.6  | 0.261492 |  31   | 40.1 | 13.4 | 27.7 |  41.1 |  38   | 15.5 |
| 1010 JAMES PL   | K   | 6, 7                       | 11905.2  | 0.273306 |  28.7 | 43.4 |  7.9 | 19.4 |  27.3 |  24.6 | 16   |
| 1014 JAMES PL   | K   | 8, 9                       | 12693.6  | 0.291404 |  27.3 | 31.4 | 12.5 | 23.7 |  36.2 |  32   | 16   |
| 1017 JAMES PL   | I   | 21                         | 15132.7  | 0.347398 |  41.7 | 54.2 |  7.6 | 10.7 |  18.3 |  38   | 16   |
| 1018 JAMES PL   | K   | 10, 11                     | 10596.2  | 0.243256 |  28.5 | 56   | 11.6 | 22.7 |  34.3 |  31.7 | 17   |
| 1022 JAMES PL   | K   | 12                         | 11709.1  | 0.268803 |  25.4 | 29   |  9   | 25.5 |  34.5 |  31.7 | 15.5 |
| 611 SMEDES PL   | C   | 1, 2, 3, 4                 | 29170.4  | 0.669661 |  33.8 | 42.9 | 68.6 | 31.3 |  99.9 |  45   | 18   |
| 612 SMEDES PL   | B   | 1                          | 14406.3  | 0.330723 |  30   | 65.3 | 10.4 | 11.9 |  22.3 |  21.5 | 16   |
| 613 SMEDES PL   | C   | 5                          | 11600.1  | 0.266302 |  42.8 | 22.4 | 13.4 |  7.3 |  20.7 |  20.5 | 14.8 |
| 618 SMEDES PL   | B   | 4, 5, 6                    | 13682.4  | 0.314104 |  40.2 | 42   |  6.5 | 16.2 |  22.7 |  21.5 | 17   |
| 619 SMEDES PL   | C   | 7, 8                       | 10278.3  | 0.235957 |  32.1 | 32.2 | 11.8 | 11.9 |  23.7 |  20.5 | 17.5 |
| 622 SMEDES PL   | B   | 7, 8                       |  9892.42 | 0.227099 |  39.3 | 18.9 | 13.6 | 17.9 |  31.5 |  29.9 | 17   |
| 625 SMEDES PL   | C   | 10                         | 14442.5  | 0.331554 |  36.1 | 30.5 | 18.9 | 28.3 |  47.2 |  31.1 | 17.2 |
| 626 SMEDES PL   | B   | 10                         |  9469.13 | 0.217381 |  37.9 | 39.6 | 16.1 | 16.6 |  32.7 |  31.4 | 17   |
| 630 SMEDES PL   | B   | 11, 12                     |  9275.8  | 0.212943 |  39.6 | 41.1 | 14.3 | 13.6 |  27.9 |  29.7 | 15.5 |
| 631 SMEDES PL   | C   | 12, 13                     |  9860.49 | 0.226366 |  34   | 29.5 |  8.8 |  9.2 |  18   |  16.4 | 18   |
| 634 SMEDES PL   | B   | 13, 14                     |  9469.24 | 0.217384 |  32.4 | 23.7 | 16.1 |  8.9 |  25   |  29.7 | 16   |
| 635 SMEDES PL   | C   | 14, 15                     |  9468.59 | 0.217369 |  41.2 | 46.4 |  7.2 |  9.9 |  17.1 |  16.4 | 14.2 |
| 638 SMEDES PL   | B   | 15, 16                     | 10828.9  | 0.248596 |  38   | 25.6 | 28.8 | 11.2 |  40   |  38   | 15.5 |
| 639 SMEDES PL   | C   | 16, 17, 18(part)           | 13147.6  | 0.301827 |  41.7 | 21.5 |  9.1 |  8.9 |  18   |  20   | 14.5 |
| 703 SMEDES PL   | H   | 8, 9                       | 16893.4  | 0.387819 |  37.1 | 34.8 | 24.8 | 18.5 |  43.3 |  44.6 | 16   |
| 706 SMEDES PL   | H   | 5                          | 13335.1  | 0.306133 |  28.2 | 16.7 | 14.5 | 15.7 |  30.2 |  48.1 | 16.2 |
| 707 SMEDES PL   | H   | 7                          | 10896.4  | 0.250148 |  32.3 | 12.3 | 20   | 14.2 |  34.2 |  43   | 16.2 |
| 710 SMEDES PL   | H   | 6                          | 35672.2  | 0.81892  |  74.9 | 40.2 | 15.8 | 16   |  31.8 |  43   | 24.7 |
| 1707 SUTTON DR  | A   | 1                          | 13758    | 0.31584  |  25.2 | 29.6 | 10   | 30.1 |  40.1 |  35.8 | 23.7 |
| 1804 SUTTON DR  | H   | 1, 2                       | 18889.8  | 0.433651 |  34.6 | 17.4 | 19.4 | 52.4 |  71.8 |  39.9 | 18   |
| 1806 SUTTON DR  | H   | 3                          |  9087.71 | 0.208625 |  20.2 | 24.4 | 17.6 |  5.1 |  22.7 |  14.4 | 36   |
| 1807 SUTTON DR  | B   | 17, 18(part)               | 18736.4  | 0.430127 |  30.5 | 37.6 |  9.3 | 40.7 |  50   |  37.9 | 15.5 |
| 1810 SUTTON DR  | H   | 4                          |  7642.06 | 0.175438 |  14.5 | 30.6 |  3.6 | 22.1 |  25.7 |  14.4 | 29   |
| 1901 SUTTON DR  | C   | 18(part), 19, 20           | 18957.8  | 0.435211 |  29.5 | 21.5 | 40.6 | 20.9 |  61.5 |  39.9 | 28.2 |
| 1905 SUTTON DR  | C   | 21, 22                     | 13844.2  | 0.317819 |  24.5 | 27.6 | 20.9 |  1.1 |  22   |  35.4 | 26   |
| 1908 SUTTON DR  | H   | 10, 11                     | 16929.3  | 0.388644 |  30.3 | 11.8 | 30.2 | 39.2 |  69.4 |  28.3 | 17.1 |
| 2007 SUTTON DR  | E   | 7(part), 8                 | 11237.4  | 0.257976 |  31.8 | 22.7 |  1.5 |  8.2 |   9.7 |  22.5 | 18   |
| 2008 SUTTON DR  | G   | 11                         | 11685.5  | 0.268262 |  24.6 | 92   |  6.2 | 12.8 |  19   |  30.8 | 14.5 |
| 2015 SUTTON DR  | E   | 7(part)                    | 13059.1  | 0.299795 |  32.5 | 18.1 | 17.7 | 16.7 |  34.4 |  22.5 | 14   |
| 911 WADE AVE    | H   | 29                         | 11507.7  | 0.26418  |  53.1 | 40   | 11.1 | 11.3 |  22.4 |  10.3 | 32   |
| 611 WOODBURN RD | B   | 30                         | 15529.4  | 0.356506 |  28.5 | 76.4 | 13.4 | 11.6 |  25   |  35.1 | 15   |
| 615 WOODBURN RD | B   | 27 (part), 28, 29          | 13081.3  | 0.300305 |  28.7 | 68.4 | 23.5 | 12   |  35.5 |  29.4 | 18   |
| 616 WOODBURN RD | A   | 6                          |  9861.98 | 0.2264   |  35.7 | 48.8 | 28.6 |  6.3 |  34.9 |  25.3 | 17   |
| 622 WOODBURN RD | A   | 5                          | 10064.4  | 0.231047 |  42   | 36.9 | 18.9 |  9   |  27.9 |  25.3 | 16.5 |
| 623 WOODBURN RD | B   | 25(part),26, 27(part)      | 12043.9  | 0.27649  |  26.4 | 62.1 | 17.1 |  8.5 |  25.6 |  21.7 | 18.2 |
| 625 WOODBURN RD | B   | 23, 24, 25(part)           | 13652.8  | 0.313424 |  34.9 | 64.6 | 13.1 | 16.1 |  29.2 |  21.7 | 14   |
| 626 WOODBURN RD | A   | 4                          |  9612.22 | 0.220666 |  31.8 | 38.3 | 19.2 |  4.8 |  24   |  17.8 | 16.5 |
| 627 WOODBURN RD | B   | 20, 21, 22                 | 15273    | 0.35062  |  25.3 | 61.2 | 28.9 | 16.6 |  45.5 |  45.2 | 17   |
| 628 WOODBURN RD | A   | 3                          |  9937.06 | 0.228124 |  33.1 | 40.4 | 13   |  7   |  20   |  17.8 | 16.5 |
| 630 WOODBURN RD | A   | 2                          |  9903.11 | 0.227344 |  36.3 | 31.6 | 12.3 |  6.2 |  18.5 |  19.4 | 17.5 |
| 635 WOODBURN RD | B   | 18(part), 19               | 15845.9  | 0.363771 |  18.4 | 27.4 | 22.5 | 27.5 |  50   |  37.9 | 16.3 |
| 700 WOODBURN RD | K   | 1                          | 10854.1  | 0.249175 |  29.2 | 25.4 | 28   |  5.5 |  33.5 |  15.9 | 16.2 |
| 706 WOODBURN RD | K   | 2                          |  9978.82 | 0.229082 |  32.1 | 34   |  9.5 |  6.8 |  16.3 |  15.9 | 12   |
| 709 WOODBURN RD | H   | 50, 51, 52                 | 14016.7  | 0.32178  |  18.6 | 34.4 | 20.6 |  1.2 |  21.8 |  12.6 | 31.7 |
| 803 WOODBURN RD | H   | 47(part), 48, 49           | 12437.6  | 0.285527 |  26   | 26.8 | 10.4 | 15.4 |  25.8 |  12.6 | 21   |
| 808 WOODBURN RD | I   | 2, 3, 4                    | 13932.8  | 0.319853 |  37   | 30.8 | 30.4 | 15.4 |  45.8 |  30.2 | 24   |
| 809 WOODBURN RD | H   | 44(part), 45, 46, 47(part) | 15220.8  | 0.349421 |  54   | 35   |  7.5 |  8.5 |  16   |  18.4 | 17.5 |
| 813 WOODBURN RD | H   | 42, 43, 44(part)           | 13275    | 0.304753 |  54.4 | 21.1 |  9.8 | 14.6 |  24.4 |  18.4 | 16.2 |
| 814 WOODBURN RD | I   | 5, 6, 7                    | 18614.3  | 0.427326 |  36.3 | 64.9 | 14.8 | 30.8 |  45.6 |  30.2 | 17.5 |
| 817 WOODBURN RD | H   | 39, 40, 41                 | 17901.3  | 0.410958 |  44.4 | 40   | 19.6 | 20.6 |  40.2 |  34.2 | 16.1 |
| 818 WOODBURN RD | I   | 8,9                        | 13277.9  | 0.304819 |  38.6 | 64.2 | 11   |  5.8 |  16.8 |  16   | 16.5 |
| 821 WOODBURN RD | H   | 37, 38                     | 12015.2  | 0.27583  |  39.1 | 45   | 15   |  2.2 |  17.2 |  13.6 | 17   |
| 822 WOODBURN RD | I   | 10, 11                     | 12391.9  | 0.28448  |  33.9 | 88.8 |  9.8 |  6.9 |  16.7 |  16   | 16.5 |
| 825 WOODBURN RD | H   | 35, 36                     | 11955.5  | 0.274461 |  47.1 | 41.4 | 10.9 |  3.1 |  14   |  13.6 | 17   |
| 826 WOODBURN RD | I   | 12, 13                     | 12375.4  | 0.284101 |  31.4 | 78.5 | 20.4 |  6.3 |  26.7 |  14.3 | 18   |
| 828 WOODBURN RD | I   | 14                         | 11879.6  | 0.272718 |  33.7 | 61.2 |  7.6 | 10.9 |  18.5 |  14.3 | 18   |
| 829 WOODBURN RD | H   | 2                          | 12639.7  | 0.290167 |  49.3 | 53.2 | 14.5 | 13   |  27.5 |  17.6 | 16   |
| 833 WOODBURN RD | H   | 1                          | 12568.6  | 0.288534 |  48.8 | 60.8 |  9   | 16.4 |  25.4 |  22.1 | 37   |
| 837 WOODBURN RD | H   | 30                         | 15434.5  | 0.354327 |  38.7 | 13.2 | 32.3 | 32.4 |  64.7 |  29.8 | 15.5 |
| 838 WOODBURN RD | I   | 14                         | 18480.5  | 0.424253 |  33.9 | 18.1 | 59   | 53.6 | 112.6 |  70.1 | 17.3 |



label: J=H+I
labeled_formulas: J=H+I
output: {"Arithmetic-Relationship": ["J=H+I"]}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_95272___xlsx_8564c2388c465b4ee784da146978b9d915ecdab7.xlsx___line_388