What's wrong with FindFormula after I set the value of x from 100 to 1000?

Question

The first code here.

x = 100;
list4 = Table[i^2, {i, 3, x}]; list5 = Table[3 i, {i, 3, x}];
Transpose[{list4, list5}] // FindFormula

Output:

3. #1^0.5 &

The second one

x = 1000;
list4 = Table[i^2, {i, 3, x}]; list5 = Table[3 i, {i, 3, x}];
Transpose[{list4, list5}] // FindFormula

Output:

\!\(
TagBox[GridBox[{
{"\[Piecewise]", GridBox[{
{
RowBox[{
RowBox[{"-", "215.59113232341036`"}], "-", 
RowBox[{"462.8447599959154`", " ", 
RowBox[{"Log", "[", 
RowBox[{
RowBox[{"-", "1.`"}], "+", "#1"}], "]"}]}], "+", 
RowBox[{"510.22846254395745`", " ", 
RowBox[{"Log", "[", "#1", "]"}]}], "+", 
RowBox[{"0.0076258318162933944`", " ", "#1"}]}], 
RowBox[{"9.`", "<=", "#1", "<", "63221.253155283164`"}]},
{
RowBox[{
RowBox[{"-", "3396.8684645398685`"}], "+", 
RowBox[{"365.162688790241`", " ", 
RowBox[{"Log", "[", "#1", "]"}]}], "+", 
RowBox[{"0.0014401159532839128`", " ", "#1"}]}], 
RowBox[{"63221.253155283164`", "<=", "#1", "<", "705500.890275878`"}]},
{
RowBox[{
RowBox[{"-", "7319.177400203924`"}], "+", 
RowBox[{"687.8323472075917`", " ", 
RowBox[{"Log", "[", "#1", "]"}]}], "+", 
RowBox[{"0.0008165452390911563`", " ", "#1"}]}], 
RowBox[{"705500.890275878`", "<=", "#1", "<", "1.`*^6"}]},
{"0", 
TagBox["True",
"PiecewiseDefault",
AutoDelete->True]}
},
AllowedDimensions->{2, Automatic},
Editable->True,
GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{1.}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.84]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}},
Selectable->True]}
},
GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}},
GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{1.}}},
GridBoxSpacings->{"Columns" -> {
Offset[0.27999999999999997`], {
Offset[0.35]}, 
Offset[0.27999999999999997`]}, "Rows" -> {
Offset[0.2], {
Offset[0.4]}, 
Offset[0.2]}}],
"Piecewise",
DeleteWithContents->True,
Editable->False,
SelectWithContents->True,
Selectable->False,
StripWrapperBoxes->True]\)

Is there a means for me find the exact Formula after I set x to 1000?

Answer 1

Clear["Global`*"]

FindFormula uses a randomized approach with the allowed TargetFunctions {Plus, Times, Power, Sin, Cos, Tan, Cot, Log, Sqrt, Csc, Sec, Abs, Exp} within the TimeConstraint. Using a large number of data points uses the available time dealing with all of the data. Generally, it is better to limit the amount of data used. Alternatively, restrict the set of TargetFunctions and increase the TimeConstraint. Because the approach is randomized, you generally need to specify the RandomSeeding option to get reproducible results.

x = 1000;
list4 = Table[i^2, {i, 3, x}]; list5 = Table[3 i, {i, 3, x}];

f1 = With[{n = 10},
   Transpose[{list4[[1 ;; n]], list5[[1 ;; n]]}] // 
    FindFormula[#, RandomSeeding -> 1234] &] // Rationalize

(* 3 Sqrt[#1] & *)

f2 = Transpose[{list4, list5}] //
   FindFormula[#,
     TargetFunctions -> {Times, Power},
     TimeConstraint -> 15,
     RandomSeeding -> 1234] & //
  Simplify

Answer 2

It seems to work properly

x = 100;
list4 = Table[i^2, {i, 3, x}]; list5 = Table[3 i, {i, 3, x}];
data = Transpose[{list4, list5}];
fy = FindFormula[data, y]
Show[ListPlot[data, PlotStyle -> Red], Plot[fy, {y, 0, 10000}]]