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 |
|----------:|----------:|:----|----------:|-----:|----:|----:|----:|----:|-----:|----------:|---------:|
| -2.00633  | -2.00633  | OK  | 1         | 1    |  50 |   0 |   0 |  71 | 1    | 0         | 0.413223 |
| -1.64849  | -1.64849  | OK  | 0.985915  | 1    |  50 |   0 |   1 |  70 | 1    | 0.0140845 | 0.421488 |
| -1.49782  | -1.49782  | OK  | 0.971831  | 1    |  50 |   0 |   2 |  69 | 1    | 0.028169  | 0.429752 |
| -1.48962  | -1.48962  | OK  | 0.957746  | 1    |  50 |   0 |   3 |  68 | 1    | 0.0422535 | 0.438017 |
| -1.47513  | -1.47513  | OK  | 0.943662  | 1    |  50 |   0 |   4 |  67 | 1    | 0.056338  | 0.446281 |
| -1.4458   | -1.4458   | OK  | 0.929577  | 1    |  50 |   0 |   5 |  66 | 1    | 0.0704225 | 0.454545 |
| -1.40309  | -1.40309  | OK  | 0.915493  | 1    |  50 |   0 |   6 |  65 | 1    | 0.084507  | 0.46281  |
| -1.40089  | -1.40089  | OK  | 0.901408  | 1    |  50 |   0 |   7 |  64 | 1    | 0.0985915 | 0.471074 |
| -1.35552  | -1.35552  | OK  | 0.887324  | 1    |  50 |   0 |   8 |  63 | 1    | 0.112676  | 0.479339 |
| -1.31732  | -1.31732  | OK  | 0.873239  | 1    |  50 |   0 |   9 |  62 | 1    | 0.126761  | 0.487603 |
| -1.27067  | -1.27067  | OK  | 0.859155  | 1    |  50 |   0 |  10 |  61 | 1    | 0.140845  | 0.495868 |
| -1.23631  | -1.23631  | OK  | 0.84507   | 1    |  50 |   0 |  11 |  60 | 1    | 0.15493   | 0.504132 |
| -1.22502  | -1.22502  | OK  | 0.830986  | 1    |  50 |   0 |  12 |  59 | 1    | 0.169014  | 0.512397 |
| -1.16127  | -1.16127  | OK  | 0.816901  | 1    |  50 |   0 |  13 |  58 | 1    | 0.183099  | 0.520661 |
| -1.12203  | -1.12203  | OK  | 0.802817  | 1    |  50 |   0 |  14 |  57 | 1    | 0.197183  | 0.528926 |
| -1.1134   | -1.1134   | OK  | 0.788732  | 1    |  50 |   0 |  15 |  56 | 1    | 0.211268  | 0.53719  |
| -1.10908  | -1.10908  | OK  | 0.774648  | 1    |  50 |   0 |  16 |  55 | 1    | 0.225352  | 0.545455 |
| -1.09008  | -1.09008  | OK  | 0.760563  | 1    |  50 |   0 |  17 |  54 | 1    | 0.239437  | 0.553719 |
| -1.0709   | -1.0709   | OK  | 0.746479  | 1    |  50 |   0 |  18 |  53 | 1    | 0.253521  | 0.561983 |
| -1.06893  | -1.06893  | OK  | 0.732394  | 1    |  50 |   0 |  19 |  52 | 1    | 0.267606  | 0.570248 |
| -1.02123  | -1.02123  | OK  | 0.71831   | 1    |  50 |   0 |  20 |  51 | 1    | 0.28169   | 0.578512 |
| -0.988122 | -0.988122 | OK  | 0.704225  | 1    |  50 |   0 |  21 |  50 | 1    | 0.295775  | 0.586777 |
| -0.985747 | -0.985747 | OK  | 0.690141  | 1    |  50 |   0 |  22 |  49 | 1    | 0.309859  | 0.595041 |
| -0.931714 | -0.931714 | OK  | 0.676056  | 1    |  50 |   0 |  23 |  48 | 1    | 0.323944  | 0.603306 |
| -0.875996 | -0.875996 | OK  | 0.661972  | 1    |  50 |   0 |  24 |  47 | 1    | 0.338028  | 0.61157  |
| -0.869658 | -0.869658 | OK  | 0.647887  | 1    |  50 |   0 |  25 |  46 | 1    | 0.352113  | 0.619835 |
| -0.765703 | -0.765703 | OK  | 0.633803  | 1    |  50 |   0 |  26 |  45 | 1    | 0.366197  | 0.628099 |
| -0.736786 | -0.736786 | OK  | 0.619718  | 1    |  50 |   0 |  27 |  44 | 1    | 0.380282  | 0.636364 |
| -0.730793 | -0.730793 | OK  | 0.605634  | 1    |  50 |   0 |  28 |  43 | 1    | 0.394366  | 0.644628 |
| -0.727322 | -0.727322 | OK  | 0.591549  | 1    |  50 |   0 |  29 |  42 | 1    | 0.408451  | 0.652893 |
| -0.721712 | -0.721712 | OK  | 0.577465  | 1    |  50 |   0 |  30 |  41 | 1    | 0.422535  | 0.661157 |
| -0.720573 | -0.720573 | OK  | 0.56338   | 1    |  50 |   0 |  31 |  40 | 1    | 0.43662   | 0.669421 |
| -0.703506 | -0.703506 | OK  | 0.549296  | 1    |  50 |   0 |  32 |  39 | 1    | 0.450704  | 0.677686 |
| -0.696883 | -0.696883 | OK  | 0.535211  | 1    |  50 |   0 |  33 |  38 | 1    | 0.464789  | 0.68595  |
| -0.694384 | -0.694384 | OK  | 0.521127  | 1    |  50 |   0 |  34 |  37 | 1    | 0.478873  | 0.694215 |
| -0.690109 | -0.690109 | OK  | 0.507042  | 1    |  50 |   0 |  35 |  36 | 1    | 0.492958  | 0.702479 |
| -0.685877 | -0.685877 | OK  | 0.492958  | 1    |  50 |   0 |  36 |  35 | 1    | 0.507042  | 0.710744 |
| -0.666952 | -0.666952 | OK  | 0.478873  | 1    |  50 |   0 |  37 |  34 | 1    | 0.521127  | 0.719008 |
| -0.665898 | -0.665898 | OK  | 0.464789  | 1    |  50 |   0 |  38 |  33 | 1    | 0.535211  | 0.727273 |
| -0.662213 | -0.662213 | OK  | 0.450704  | 1    |  50 |   0 |  39 |  32 | 1    | 0.549296  | 0.735537 |
| -0.65559  | -0.65559  | OK  | 0.43662   | 1    |  50 |   0 |  40 |  31 | 1    | 0.56338   | 0.743802 |
| -0.608408 | -0.608408 | OK  | 0.422535  | 1    |  50 |   0 |  41 |  30 | 1    | 0.577465  | 0.752066 |
| -0.59651  | -0.59651  | OK  | 0.408451  | 1    |  50 |   0 |  42 |  29 | 1    | 0.591549  | 0.760331 |
| -0.55254  | -0.55254  | OK  | 0.394366  | 1    |  50 |   0 |  43 |  28 | 1    | 0.605634  | 0.768595 |
| -0.533475 | -0.533475 | OK  | 0.380282  | 1    |  50 |   0 |  44 |  27 | 1    | 0.619718  | 0.77686  |
| -0.518725 | -0.518725 | OK  | 0.366197  | 1    |  50 |   0 |  45 |  26 | 1    | 0.633803  | 0.785124 |
| -0.506418 | -0.506418 | OK  | 0.352113  | 1    |  50 |   0 |  46 |  25 | 1    | 0.647887  | 0.793388 |
| -0.504943 | -0.504943 | OK  | 0.338028  | 1    |  50 |   0 |  47 |  24 | 1    | 0.661972  | 0.801653 |
| -0.504393 | -0.504393 | OK  | 0.323944  | 1    |  50 |   0 |  48 |  23 | 1    | 0.676056  | 0.809917 |
| -0.446521 | -0.446521 | OK  | 0.309859  | 1    |  50 |   0 |  49 |  22 | 1    | 0.690141  | 0.818182 |
| -0.27991  | -0.27991  | OK  | 0.28169   | 1    |  50 |   0 |  51 |  20 | 1    | 0.71831   | 0.834711 |
| -0.192068 | -0.192068 | OK  | 0.211268  | 1    |  50 |   0 |  56 |  15 | 1    | 0.788732  | 0.876033 |
| -0.073232 | -0.073232 | OK  | 0.15493   | 1    |  50 |   0 |  60 |  11 | 1    | 0.84507   | 0.909091 |
|  0.1625   |  0.1625   | OK  | 0.126761  | 0.94 |  47 |   3 |  62 |   9 | 0.94 | 0.873239  | 0.900826 |
|  0.24618  |  0.24618  | OK  | 0.126761  | 0.92 |  46 |   4 |  62 |   9 | 0.92 | 0.873239  | 0.892562 |
|  0.25749  |  0.25749  | OK  | 0.112676  | 0.92 |  46 |   4 |  63 |   8 | 0.92 | 0.887324  | 0.900826 |
|  0.319812 |  0.319812 | OK  | 0.112676  | 0.88 |  44 |   6 |  63 |   8 | 0.88 | 0.887324  | 0.884298 |
|  0.401194 |  0.401194 | OK  | 0.0985915 | 0.8  |  40 |  10 |  64 |   7 | 0.8  | 0.901408  | 0.859504 |
|  0.404397 |  0.404397 | OK  | 0.0985915 | 0.78 |  39 |  11 |  64 |   7 | 0.78 | 0.901408  | 0.85124  |
|  0.425721 |  0.425721 | OK  | 0.084507  | 0.78 |  39 |  11 |  65 |   6 | 0.78 | 0.915493  | 0.859504 |
|  0.481057 |  0.481057 | OK  | 0.084507  | 0.76 |  38 |  12 |  65 |   6 | 0.76 | 0.915493  | 0.85124  |
|  0.484112 |  0.484112 | OK  | 0.0704225 | 0.76 |  38 |  12 |  66 |   5 | 0.76 | 0.929577  | 0.859504 |
|  0.48981  |  0.48981  | OK  | 0.056338  | 0.76 |  38 |  12 |  67 |   4 | 0.76 | 0.943662  | 0.867769 |
|  0.512126 |  0.512126 | OK  | 0.056338  | 0.74 |  37 |  13 |  67 |   4 | 0.74 | 0.943662  | 0.859504 |
|  0.530355 |  0.530355 | OK  | 0.0422535 | 0.74 |  37 |  13 |  68 |   3 | 0.74 | 0.957746  | 0.867769 |
|  0.634616 |  0.634616 | OK  | 0.0422535 | 0.72 |  36 |  14 |  68 |   3 | 0.72 | 0.957746  | 0.859504 |
|  0.69454  |  0.69454  | OK  | 0.0422535 | 0.7  |  35 |  15 |  68 |   3 | 0.7  | 0.957746  | 0.85124  |
|  0.707256 |  0.707256 | OK  | 0.0422535 | 0.68 |  34 |  16 |  68 |   3 | 0.68 | 0.957746  | 0.842975 |
|  0.70789  |  0.70789  | OK  | 0.028169  | 0.68 |  34 |  16 |  69 |   2 | 0.68 | 0.971831  | 0.85124  |
|  0.720385 |  0.720385 | OK  | 0.0140845 | 0.68 |  34 |  16 |  70 |   1 | 0.68 | 0.985915  | 0.859504 |
|  0.73018  |  0.73018  | OK  | 0.0140845 | 0.66 |  33 |  17 |  70 |   1 | 0.66 | 0.985915  | 0.85124  |
|  0.736639 |  0.736639 | OK  | 0.0140845 | 0.64 |  32 |  18 |  70 |   1 | 0.64 | 0.985915  | 0.842975 |
|  0.739149 |  0.739149 | OK  | 0.0140845 | 0.62 |  31 |  19 |  70 |   1 | 0.62 | 0.985915  | 0.834711 |
|  0.7443   |  0.7443   | OK  | 0         | 0.62 |  31 |  19 |  71 |   0 | 0.62 | 1         | 0.842975 |
|  0.79143  |  0.79143  | OK  | 0         | 0.6  |  30 |  20 |  71 |   0 | 0.6  | 1         | 0.834711 |
|  0.853355 |  0.853355 | OK  | 0         | 0.58 |  29 |  21 |  71 |   0 | 0.58 | 1         | 0.826446 |
|  0.85397  |  0.85397  | OK  | 0         | 0.56 |  28 |  22 |  71 |   0 | 0.56 | 1         | 0.818182 |
|  0.863088 |  0.863088 | OK  | 0         | 0.54 |  27 |  23 |  71 |   0 | 0.54 | 1         | 0.809917 |
|  0.875995 |  0.875995 | OK  | 0         | 0.52 |  26 |  24 |  71 |   0 | 0.52 | 1         | 0.801653 |
|  0.878463 |  0.878463 | OK  | 0         | 0.5  |  25 |  25 |  71 |   0 | 0.5  | 1         | 0.793388 |
|  0.87942  |  0.87942  | OK  | 0         | 0.48 |  24 |  26 |  71 |   0 | 0.48 | 1         | 0.785124 |
|  0.898505 |  0.898505 | OK  | 0         | 0.46 |  23 |  27 |  71 |   0 | 0.46 | 1         | 0.77686  |
|  0.939796 |  0.939796 | OK  | 0         | 0.44 |  22 |  28 |  71 |   0 | 0.44 | 1         | 0.768595 |
|  0.974375 |  0.974375 | OK  | 0         | 0.42 |  21 |  29 |  71 |   0 | 0.42 | 1         | 0.760331 |
|  0.993249 |  0.993249 | OK  | 0         | 0.4  |  20 |  30 |  71 |   0 | 0.4  | 1         | 0.752066 |
|  1.01022  |  1.01022  | OK  | 0         | 0.38 |  19 |  31 |  71 |   0 | 0.38 | 1         | 0.743802 |
|  1.04918  |  1.04918  | OK  | 0         | 0.36 |  18 |  32 |  71 |   0 | 0.36 | 1         | 0.735537 |
|  1.16565  |  1.16565  | OK  | 0         | 0.3  |  15 |  35 |  71 |   0 | 0.3  | 1         | 0.710744 |
|  1.35032  |  1.35032  | OK  | 0         | 0.22 |  11 |  39 |  71 |   0 | 0.22 | 1         | 0.677686 |
|  1.36194  |  1.36194  | OK  | 0         | 0.2  |  10 |  40 |  71 |   0 | 0.2  | 1         | 0.669421 |
|  1.36282  |  1.36282  | OK  | 0         | 0.18 |   9 |  41 |  71 |   0 | 0.18 | 1         | 0.661157 |
|  1.67294  |  1.67294  | OK  | 0         | 0.08 |   4 |  46 |  71 |   0 | 0.08 | 1         | 0.619835 |



labeled_formulas: B=(D+K)*A
J=(A-B)+E
output: {"Arithmetic-Relationship": []}
source: $MMTU_HOME/resources/Relationship-finding/AR/table_16525___xlsx_4e460bfd71b88a990f981802c1ef6a28d50784e4.xlsx___line_296