How to generate a training set in an automatic way?

Question

This question is related to [my previous item][1] where arithmetic with machine learning was considered. The results of the Predict command were not good because of a small size 19 of a training set

ClearAll["Global`*"];
trainingset = {"2+2" -> 4, "2+3*2" -> 8, "(12+7)*5" -> 95, "7*6" -> 42,
 "7+22" -> 29, "4+5" -> 9, "4*1+5" -> 9, "17*3+4*5" -> 41, "7+9*2" -> 25, "11+3" -> 14, 
"6+6" -> 12, "4*5+6" -> 26, "5*7" -> 35, "3*2" -> 6, "3+2" -> 5, "9*3" -> 27, 
   "3*9" -> 27, "6*3+8*2" -> 34, "5*4" -> 20};

My question is: how to generate such training set of size 200 with one or two additions and multiplications over integers from 0 to 100 in an automatic way? [1]: Why Method -> "NeuralNetwork" does not work for me?

PS. See the first example at https://reference.wolfram.com/language/tutorial/NeuralNetworksSequenceLearning.html#1013067167

Answer 1

This should work.

rn["num"] := RandomInteger[{0, 100}]
rn["op"] := RandomChoice[{"+", "*"}]

set = ToString @ Row[rn /@ Riffle[Table["num", {#}], "op"]] & /@ 
   RandomInteger[{2, 4}, 200];

set = # -> ToExpression[#] & /@ set;

Output looks like

{"94+66+34*28" -> 1112, "37*40*57" -> 84360, "34*59+27+97" -> 2130, . . .}

---

In the code above the function rn (random) makes a random number or operator as needed. So for example rn /@ {"num", "op", "num"} might give me {1, "+", 2}. From there I can merge those into a single string. So the matter is then just creating a series of "num"/"op" lists of the right form. As an example:

Riffle[Table["num", {4}], "op"] 

{"num", "op", "num", "op", "num", "op", "num"}

So this Riffle/Table expression forms the heart of a Function that I map over a list of (pseudo)random integers of the right specification.

The final step is to take our complete strings and evaluate them as input, and this is performed by ToExpression. # -> ToExpression[#] & is another Function that gives input mapped to output as a series of Rules.

The same operations written in a step by step way:

rn["num"] := RandomInteger[{0, 100}]
rn["op"] := RandomChoice[{"+", "*"}]

RandomInteger[{2, 4}, 10];

Table["num", {#}] & /@ %

Riffle[#, "op"] & /@ %

Map[rn, %, {2}]

ToString /@ Row /@ %

Thread[% -> ToExpression /@ %]

There are certainly other ways to approach this problem; this is merely what came to mind first as an expedient solution.