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        | U   |
|------:|:---------|:--------|:----|:----------|:----------|:----------|:-------|----:|----:|----:|----:|----:|----:|----:|----:|-------------:|------------:|:---------|:---------|:----|
| 14701 | deletion | de novo | VIP | 14701.x6  | 14701.x3  | 14701.x7  | Mother |   0 |  37 |  37 |  13 |  43 |  56 |   0 |  19 | 6.68672e-97  | 1           | Paternal | Paternal | Y   |
| 14703 | deletion | de novo | VIP | 14703.x1  | 14703.x2  | 14703.x3  | Mother |   0 |  16 |  16 |  20 |  59 |  79 |   0 |  17 | 1.09881e-30  | 1           | Paternal | Paternal | Y   |
| 14704 | deletion | de novo | VIP | 14704.x3  | 14704.x6  | 14703.x3  | Mother |   0 |  29 |  29 |  16 |  49 |  65 |   0 |  18 | 7.4976e-66   | 1           | Paternal | Paternal | Y   |
| 14709 | deletion | de novo | VIP | 14709.x10 | 14709.x11 | 14709.x13 | Mother |   0 |   0 |   0 |  28 |  67 |  95 |   0 |  17 | 1            | 6.69327e-15 | Maternal | Maternal | Y   |
| 14711 | deletion | de novo | VIP | 14711.x6  | 14711.x3  | 14711.x7  | Mother |   0 |  37 |  37 |   9 |  49 |  58 |   0 |  17 | 1.48728e-90  | 1           | Paternal | Paternal | Y   |
| 14713 | deletion | de novo | VIP | 14713.x3  | 14713.x6  | 14713.x7  | Mother |   0 |   9 |   9 |  18 |  68 |  86 |   0 |  17 | 1.7139e-17   | 1           | Paternal | Paternal | Y   |
| 14716 | deletion | de novo | VIP | 14716.x1  | 14716.x2  | 14716.x3  | Mother |   0 |  46 |  46 |   3 |  46 |  49 |   0 |  17 | 1.02934e-125 | 1           | Paternal | Paternal | Y   |
| 14731 | deletion | de novo | VIP | 14731.x6  | 14731.x7  | 14731.x8  | Mother |   0 |  48 |  48 |   0 |  45 |  45 |   0 |  19 | 5.58893e-121 | 1           | Paternal | Paternal | Y   |
| 14733 | deletion | de novo | VIP | 14733.x14 | 14733.x13 | 14733.x15 | Mother |   0 |  37 |  37 |   4 |  54 |  58 |   0 |  17 | 3.13241e-93  | 1           | Paternal | Paternal | Y   |
| 14736 | deletion | de novo | VIP | 14736.x3  | 14736.x6  | 14736.x7  | Mother |   0 |   6 |   6 |   5 |  83 |  88 |   0 |  18 | 4.42015e-16  | 1           | Paternal | Paternal | Y   |
| 14737 | deletion | de novo | VIP | 14737.x5  | 14737.x6  | 14737.x7  | Mother |   0 |   9 |   9 |  24 |  62 |  86 |   0 |  17 | 6.42629e-13  | 1           | Paternal | Paternal | Y   |
| 14744 | deletion | de novo | VIP | 14744.x3  | 14744.x4  | 14744.x5  | Mother |   0 |   0 |   0 |  54 |  41 |  95 |   0 |  17 | 1            | 1.52635e-25 | Maternal | Maternal | Y   |
| 14747 | deletion | de novo | VIP | 14747.x9  | 14747.x8  | 14747.x10 | Mother |   0 |   9 |   9 |  16 |  69 |  85 |   0 |  18 | 1.00745e-17  | 1           | Paternal | Paternal | Y   |
| 14754 | deletion | de novo | VIP | 14754.x3  | 14754.x6  | 14754.x7  | Mother |   0 |  19 |  19 |  18 |  57 |  75 |   0 |  18 | 8.13687e-40  | 1           | Paternal | Paternal | Y   |
| 14763 | deletion | de novo | VIP | 14763.x3  | 14763.x6  | 14763.x7  | Mother |   0 |  24 |  24 |   6 |  65 |  71 |   0 |  17 | 2.38432e-61  | 1           | Paternal | Paternal | Y   |
| 14772 | deletion | de novo | VIP | 14772.x10 | 14772.x11 | 14772.x12 | Mother |   0 |  22 |  22 |   8 |  64 |  72 |   0 |  18 | 1.63387e-52  | 1           | Paternal | Paternal | Y   |
| 14777 | deletion | de novo | VIP | 14777.x1  | 14777.x2  | 14777.x3  | Mother |   0 |  14 |  14 |  18 |  63 |  81 |   0 |  17 | 8.54083e-34  | 1           | Paternal | Paternal | Y   |
| 14779 | deletion | de novo | VIP | 14779.x6  | 14779.x3  | 14779.x7  | Mother |   0 |   0 |   0 |  22 |  72 |  94 |   0 |  18 | 0.999996     | 3.82044e-06 | Maternal | Paternal | N   |
| 14781 | deletion | de novo | VIP | 14781.x14 | 14781.x15 | 14781.x16 | Mother |   0 |  10 |  10 |  11 |  70 |  81 |   0 |  21 | 5.15097e-21  | 1           | Paternal | Paternal | Y   |
| 14782 | deletion | de novo | VIP | 14782.x1  | 14782.x2  | 14782.x3  | Mother |   0 |  24 |  24 |   9 |  62 |  71 |   0 |  17 | 1.0141e-63   | 1           | Paternal | Paternal | Y   |
| 14796 | deletion | de novo | VIP | 14796.x1  | 14796.x2  | 14796.x3  | Mother |   0 |  26 |  26 |  28 |  41 |  69 |   0 |  17 | 1.09262e-58  | 1           | Paternal | Paternal | Y   |
| 14799 | deletion | de novo | VIP | 14799.x4  | 14799.x3  | 14799.x1  | Mother |   0 |  20 |  20 |   1 |  74 |  75 |   0 |  17 | 6.12913e-59  | 1           | Paternal | Paternal | Y   |
| 14802 | deletion | de novo | VIP | 14802.x3  | 14802.x6  | 14802.x7  | Mother |   0 |  20 |  20 |  15 |  60 |  75 |   0 |  17 | 1.411e-50    | 1           | Paternal | Paternal | Y   |
| 14809 | deletion | de novo | VIP | 14809.x3  | 14809.x2  | 14809.x1  | Mother |   0 |  51 |  51 |   7 |  37 |  44 |   0 |  17 | 7.63899e-141 | 1           | Paternal | Paternal | Y   |
| 14823 | deletion | de novo | VIP | 14823.x11 | 14823.x13 | 14823.x14 | Mother |   0 |  20 |  20 |  14 |  60 |  74 |   0 |  18 | 3.64157e-43  | 1           | Paternal | Paternal | Y   |
| 14830 | deletion | de novo | VIP | 14830.x3  | 14830.x6  | 14830.x7  | Mother |   0 |  39 |  39 |   7 |  48 |  55 |   0 |  18 | 3.53726e-99  | 1           | Paternal | Paternal | Y   |
| 14838 | deletion | de novo | VIP | 14838.x2  | 14838.x1  | 14838.x3  | Mother |   0 |  47 |  47 |   5 |  43 |  48 |   0 |  17 | 7.03878e-129 | 1           | Paternal | Paternal | Y   |
| 14840 | deletion | de novo | VIP | 14840.x19 | 14840.x20 | 14840.x22 | Mother |   0 |  19 |  19 |   6 |  70 |  76 |   0 |  17 | 6.66776e-46  | 1           | Paternal | Paternal | Y   |
| 14850 | deletion | de novo | VIP | 14850.x20 | 14850.x21 | 14850.x22 | Mother |   0 |  19 |  19 |   5 |  69 |  74 |   0 |  19 | 9.50727e-47  | 1           | Paternal | Paternal | Y   |
| 14863 | deletion | de novo | VIP | 14863.x3  | 14863.x6  | 14863.x7  | Mother |   0 |  36 |  36 |   7 |  51 |  58 |   0 |  18 | 1.37947e-96  | 1           | Paternal | Paternal | Y   |
| 14893 | deletion | de novo | VIP | 14893.x6  | 14893.x3  | 14893.x7  | Mother |   0 |  42 |  42 |   5 |  46 |  51 |   0 |  19 | 4.53479e-107 | 1           | Paternal | Paternal | Y   |
| 14904 | deletion | de novo | VIP | 14904.x3  | 14904.x6  | 14904.x7  | Mother |   0 |   0 |   0 |   8 |  51 |  59 |   0 |  53 | 0.999984     | 1.58619e-05 | Maternal | Paternal | N   |
| 14913 | deletion | de novo | VIP | 14913.x2  | 14913.x3  | 14913.x1  | Mother |   0 |   0 |   0 |   6 |  87 |  93 |   0 |  19 | 0.000596678  | 0.999403    | Paternal | Maternal | N   |
| 14701 | deletion | de novo | VIP | 14701.x6  | 14701.x3  | 14701.x7  | Father |   0 |   0 |   0 |  70 |  23 |  93 |   0 |  19 | 1.97257e-13  | 1           | Paternal | Paternal | Y   |
| 14702 | deletion | de novo | VIP | 14702.x1  | 14702.x2  | 14702.x3  | Father |   0 |   0 |   0 |  52 |  42 |  94 |   0 |  18 | 3.03093e-17  | 1           | Paternal | Paternal | Y   |
| 14703 | deletion | de novo | VIP | 14703.x1  | 14703.x2  | 14703.x3  | Father |   0 |   0 |   0 |  66 |  29 |  95 |   0 |  17 | 4.7571e-13   | 1           | Paternal | Paternal | Y   |
| 14704 | deletion | de novo | VIP | 14704.x3  | 14704.x6  | 14704.x7  | Father |   0 |   0 |   0 |  62 |  32 |  94 |   0 |  18 | 3.58387e-14  | 1           | Paternal | Paternal | Y   |
| 14711 | deletion | de novo | VIP | 14711.x6  | 14711.x3  | 14711.x7  | Father |   0 |   0 |   0 |  61 |  34 |  95 |   0 |  17 | 2.86276e-15  | 1           | Paternal | Paternal | Y   |
| 14713 | deletion | de novo | VIP | 14713.x3  | 14713.x6  | 14713.x7  | Father |   0 |   0 |   0 |  58 |  37 |  95 |   0 |  17 | 1.84904e-12  | 1           | Paternal | Paternal | Y   |
| 14714 | deletion | de novo | VIP | 14714.x12 | 14714.x11 | 14714.x18 | Father |   0 |   0 |   0 |  66 |  28 |  94 |   0 |  18 | 2.04752e-07  | 1           | Paternal | Paternal | Y   |
| 14716 | deletion | de novo | VIP | 14716.x1  | 14716.x2  | 14716.x3  | Father |   0 |   0 |   0 |  66 |  29 |  95 |   0 |  17 | 4.06087e-13  | 1           | Paternal | Paternal | Y   |
| 14718 | deletion | de novo | VIP | 14718.x1  | 14718.x4  | 14718.x5  | Father |   0 |   0 |   0 |  63 |  31 |  94 |   0 |  18 | 7.6733e-15   | 1           | Paternal | Paternal | Y   |
| 14726 | deletion | de novo | VIP | 14726.x10 | 14726.x11 | 14726.x12 | Father |   0 |   0 |   0 |  65 |  30 |  95 |   0 |  17 | 2.33448e-13  | 1           | Paternal | Paternal | Y   |
| 14731 | deletion | de novo | VIP | 14731.x6  | 14731.x7  | 14731.x8  | Father |   0 |   0 |   0 |  62 |  31 |  93 |   0 |  19 | 1.58173e-11  | 1           | Paternal | Paternal | Y   |
| 14733 | deletion | de novo | VIP | 14733.x14 | 14733.x13 | 14733.x15 | Father |   0 |   0 |   0 |  55 |  39 |  94 |   0 |  18 | 8.92342e-16  | 1           | Paternal | Paternal | Y   |
| 14736 | deletion | de novo | VIP | 14736.x3  | 14736.x6  | 14736.x7  | Father |   0 |   0 |   0 |  83 |  11 |  94 |   0 |  18 | 0.0178297    | 0.98217     | Paternal | Paternal | Y   |
| 14737 | deletion | de novo | VIP | 14737.x5  | 14737.x6  | 14737.x7  | Father |   0 |   0 |   0 |  73 |  22 |  95 |   0 |  17 | 6.44245e-09  | 1           | Paternal | Paternal | Y   |
| 14747 | deletion | de novo | VIP | 14747.x9  | 14747.x8  | 14747.x10 | Father |   0 |   0 |   0 |  63 |  31 |  94 |   0 |  18 | 7.87989e-13  | 1           | Paternal | Paternal | Y   |
| 14754 | deletion | de novo | VIP | 14754.x3  | 14754.x6  | 14754.x7  | Father |   0 |   0 |   0 |  38 |  56 |  94 |   0 |  18 | 3.05279e-25  | 1           | Paternal | Paternal | Y   |
| 14763 | deletion | de novo | VIP | 14763.x3  | 14763.x6  | 14763.x7  | Father |   0 |   0 |   0 |  68 |  27 |  95 |   0 |  17 | 5.46049e-10  | 1           | Paternal | Paternal | Y   |
| 14772 | deletion | de novo | VIP | 14772.x10 | 14772.x11 | 14772.x12 | Father |   0 |   0 |   0 |  69 |  25 |  94 |   0 |  18 | 1.58893e-12  | 1           | Paternal | Paternal | Y   |
| 14777 | deletion | de novo | VIP | 14777.x1  | 14777.x2  | 14777.x3  | Father |   0 |   0 |   0 |  71 |  24 |  95 |   0 |  17 | 2.97435e-10  | 1           | Paternal | Paternal | Y   |
| 14778 | deletion | de novo | VIP | 14778.x10 | 14778.x11 | 14778.x12 | Father |   0 |   0 |   0 |  71 |  23 |  94 |   0 |  18 | 9.84477e-10  | 1           | Paternal | Paternal | Y   |
| 14779 | deletion | de novo | VIP | 14779.x6  | 14779.x3  | 14779.x7  | Father |   0 |   0 |   0 |  68 |  26 |  94 |   0 |  18 | 7.42679e-12  | 1           | Paternal | Paternal | Y   |
| 14781 | deletion | de novo | VIP | 14781.x14 | 14781.x15 | 14781.x16 | Father |   0 |   0 |   0 |  64 |  27 |  91 |   0 |  21 | 1.56402e-09  | 1           | Paternal | Paternal | Y   |
| 14782 | deletion | de novo | VIP | 14782.x1  | 14782.x2  | 14782.x3  | Father |   0 |   0 |   0 |  50 |  45 |  95 |   0 |  17 | 3.86966e-18  | 1           | Paternal | Paternal | Y   |
| 14791 | deletion | de novo | VIP | 14791.x24 | 14791.x25 | 14791.x26 | Father |   0 |   0 |   0 |  53 |  40 |  93 |   0 |  19 | 1.49541e-15  | 1           | Paternal | Paternal | Y   |
| 14795 | deletion | de novo | VIP | 14795.x16 | 14795.x15 | 14795.x17 | Father |   0 |   0 |   0 |  93 |   2 |  95 |   0 |  17 | 0.961796     | 0.038204    | Maternal | Paternal | N   |
| 14796 | deletion | de novo | VIP | 14796.x1  | 14796.x2  | 14796.x3  | Father |   0 |   0 |   0 |  65 |  30 |  95 |   0 |  17 | 1.53858e-13  | 1           | Paternal | Paternal | Y   |
| 14797 | deletion | de novo | VIP | 14797.x6  | 14797.x7  | 14797.x8  | Father |   0 |   0 |   0 |  46 |  48 |  94 |   0 |  18 | 3.95209e-20  | 1           | Paternal | Paternal | Y   |
| 14799 | deletion | de novo | VIP | 14799.x4  | 14799.x3  | 14799.x1  | Father |   0 |   0 |   0 |  69 |  26 |  95 |   0 |  17 | 3.1917e-11   | 1           | Paternal | Paternal | Y   |
| 14802 | deletion | de novo | VIP | 14802.x3  | 14802.x6  | 14802.x7  | Father |   0 |   0 |   0 |  64 |  31 |  95 |   0 |  17 | 1.44463e-10  | 1           | Paternal | Paternal | Y   |
| 14809 | deletion | de novo | VIP | 14809.x3  | 14809.x2  | 14809.x1  | Father |   0 |   0 |   0 |  70 |  25 |  95 |   0 |  17 | 2.19536e-12  | 1           | Paternal | Paternal | Y   |
| 14823 | deletion | de novo | VIP | 14823.x11 | 14823.x13 | 14823.x14 | Father |   0 |   0 |   0 |  69 |  25 |  94 |   0 |  18 | 5.67482e-15  | 1           | Paternal | Paternal | Y   |
| 14824 | deletion | de novo | VIP | 14824.x11 | 14824.x10 | 14824.x12 | Father |   0 |   0 |   0 |  44 |  51 |  95 |   0 |  17 | 3.29038e-20  | 1           | Paternal | Paternal | Y   |
| 14830 | deletion | de novo | VIP | 14830.x3  | 14830.x6  | 14830.x7  | Father |   0 |   0 |   0 |  51 |  43 |  94 |   0 |  18 | 1.17346e-18  | 1           | Paternal | Paternal | Y   |
| 14838 | deletion | de novo | VIP | 14838.x2  | 14838.x1  | 14838.x3  | Father |   0 |   0 |   0 |  82 |  12 |  94 |   0 |  18 | 0.000133238  | 0.999867    | Paternal | Paternal | Y   |
| 14840 | deletion | de novo | VIP | 14840.x19 | 14840.x20 | 14840.x22 | Father |   0 |   0 |   0 |  75 |  20 |  95 |   0 |  17 | 3.01243e-15  | 1           | Paternal | Paternal | Y   |
| 14850 | deletion | de novo | VIP | 14850.x20 | 14850.x21 | 14850.x22 | Father |   0 |   0 |   0 |  69 |  23 |  92 |   0 |  20 | 7.23338e-09  | 1           | Paternal | Paternal | Y   |
| 14863 | deletion | de novo | VIP | 14863.x3  | 14863.x6  | 14863.x7  | Father |   0 |   0 |   0 |  81 |  13 |  94 |   0 |  18 | 7.72396e-07  | 0.999999    | Paternal | Paternal | Y   |
| 14893 | deletion | de novo | VIP | 14893.x6  | 14893.x3  | 14893.x7  | Father |   0 |   0 |   0 |  47 |  46 |  93 |   0 |  19 | 1.15106e-20  | 1           | Paternal | Paternal | Y   |
| 14904 | deletion | de novo | VIP | 14904.x3  | 14904.x6  | 14904.x7  | Father |   0 |   0 |   0 |  42 |  17 |  59 |   0 |  53 | 3.12611e-08  | 1           | Paternal | Paternal | Y   |
| 14956 | deletion | de novo | VIP | 14956.x3  | 14956.x6  | 14956.x7  | Father |   0 |   0 |   0 |  51 |  44 |  95 |   0 |  17 | 3.47298e-20  | 1           | Paternal | Paternal | Y   |
| 14965 | deletion | de novo | VIP | 14965.x20 | 14965.x21 | 14965.x22 | Father |   0 |   0 |   0 |  66 |  25 |  91 |   0 |  21 | 1.12049e-15  | 1           | Paternal | Paternal | Y   |



labeled_formulas: K=J*R
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_702106___xlsx_f16db0e8a1c378b4d004c6e57f1e96298fd95087.xlsx___line_590