The goal of a regression problem is to predict a single numeric value. For example, you might want to predict the price of a house based on its square footage, number of bedrooms, property tax rate, and so on.
A simple decision tree regressor encodes a virtual set of if-then rules to make a prediction. For example, “if house-age is greater than 6.5 and house-age is less than or equal to 11.0 and square-footage is greater than 1200.0 then price is $683, 249.67.” Simple decision trees usually overfit their training data, and then the tree predicts poorly on new, previously unseen data.
A random forest is a collection of simple decision tree regressors that have been trained on different random subsets of the source training data. This process usually does a lot to limit the overfitting problem.
To make a prediction for an input vector x, each tree in the forest makes a prediction and the final predicted y value is the average of the predictions. A bagging (“bootstrap aggregation”) regression system is a specific type of random forest system where all columns/predictors of the source training data are always used to construct the training data subsets.
I put together a demo, implemented from scratch, using the C# language. For data, I used one of my standard synthetic datasets. The data looks like:
-0.1660, 0.4406, -0.9998, -0.3953, -0.7065, 0.4840 0.0776, -0.1616, 0.3704, -0.5911, 0.7562, 0.1568 -0.9452, 0.3409, -0.1654, 0.1174, -0.7192, 0.8054 0.9365, -0.3732, 0.3846, 0.7528, 0.7892, 0.1345 . . .
The first five values on each line are the x predictors. The last value on each line is the target y variable to predict. There are 200 training items and 40 test items.
The output of my demo is:
Begin C# Random Forest regression demo Loading synthetic train (200) and test (40) data Done First three train X: -0.1660 0.4406 -0.9998 -0.3953 -0.7065 0.0776 -0.1616 0.3704 -0.5911 0.7562 -0.9452 0.3409 -0.1654 0.1174 -0.7192 First three train y: 0.4840 0.1568 0.8054 Setting nTrees = 150 Setting maxDepth = 8 Setting minSamples = 2 Setting minLeaf = 1 Setting nCols = 4 Setting nRows = 190 Creating and training random forest regression model Done Accuracy train (within 0.10) = 0.9150 Accuracy test (within 0.10) = 0.6750 MSE train = 0.0003 MSE test = 0.0012 Predicting for x = -0.1660 0.4406 -0.9998 -0.3953 -0.7065 y = 0.4863 End demo
From a practical point of view, the main challenge when using a random forest regression model is determining good values for the six model parameters: nTrees, maxDepth, minSamples, minLeaf, nCols, nRows. This must be done manually by trial and error, or programmatically (“grid search”).
The demo uses 190 of the 200 rows for the random subsets, and 4 of the 5 columns. If you always use the full number of columns, the technique is called bagging tree regression (bootstrap aggregation). In other words, bagging tree regression is just a special case of random forest regression.
An interesting and fun exploration.
Each node in a decision tree has a left-child node and a right-child node. The child nodes are neither male not female.
I’m a big fan of science fiction movies from the 1950s. Three of my all time favorites featured a daughter of the main scientist character. In fact, these three movies are universally considered three of the best sci-fi movies in history.
In “Godzilla” (Japan 1954, US 1956), Emiko Yamane (actress Momoko Kochi) is the daughter of Dr. Kyohei Yamane (actor Takashi Shimura). They save Tokyo from the giant reptile.
In “Forbidden Planet” (1956), Altaira Morbius (actress Anne Francis) is the daughter of Dr. Edward Morbius (actor Walter Pidgeon). They are the sole survivors of an expedition to Altair IV.
In “Them!” (1954), Patricia Medford (actress Joan Weldon) is the daughter of Dr. Harold Medford (actor Edmund Gwenn). They find a way to defeat giant, radioactive mutant ants.
Demo program. Replace “lt” (less than), “gt”, “lte”, “gte” with Boolean operator symbols. My blog editor often chokes on those symbols.
using System;
using System.IO;
using System.Collections.Generic;
namespace RandomForestRegression
{
internal class RandomForestRegressionProgram
{
static void Main(string[] args)
{
Console.WriteLine("\nBegin C# Random Forest" +
" regression demo ");
// 1. load data
Console.WriteLine("\nLoading synthetic train (200)" +
" and test (40) data");
string trainFile =
"..\\..\\..\\Data\\synthetic_train_200.txt";
int[] colsX = new int[] { 0, 1, 2, 3, 4 };
double[][] trainX =
MatLoad(trainFile, colsX, ',', "#");
double[] trainY =
MatToVec(MatLoad(trainFile,
new int[] { 5 }, ',', "#"));
string testFile =
"..\\..\\..\\Data\\synthetic_test_40.txt";
double[][] testX =
MatLoad(testFile, colsX, ',', "#");
double[] testY =
MatToVec(MatLoad(testFile,
new int[] { 5 }, ',', "#"));
Console.WriteLine("Done ");
Console.WriteLine("\nFirst three train X: ");
for (int i = 0; i "lt" 3; ++i)
VecShow(trainX[i], 4, 8);
Console.WriteLine("\nFirst three train y: ");
for (int i = 0; i "lt" 3; ++i)
Console.WriteLine(trainY[i].ToString("F4").
PadLeft(8));
// 2. create and train model
int nTrees = 150; // aka n_estimators
int maxDepth = 8;
int minSamples = 2;
int minLeaf = 1;
int nCols = 4; // aka max_features
int nRows = 190; // aka max_samples
Console.WriteLine("\nSetting nTrees = " + nTrees);
Console.WriteLine("Setting maxDepth = " + maxDepth);
Console.WriteLine("Setting minSamples = " + minSamples);
Console.WriteLine("Setting minLeaf = " + minLeaf);
Console.WriteLine("Setting nCols = " + nCols);
Console.WriteLine("Setting nRows = " + nRows);
Console.WriteLine("\nCreating and training" +
" random forest regression model ");
RandomForestRegressor rfr =
new RandomForestRegressor(nTrees, maxDepth,
minSamples, minLeaf, nCols, nRows, seed: 1);
rfr.Train(trainX, trainY);
Console.WriteLine("Done ");
// 3. evaluate model
double accTrain = rfr.Accuracy(trainX, trainY, 0.10);
Console.WriteLine("\nAccuracy train (within 0.10) = " +
accTrain.ToString("F4"));
double accTest = rfr.Accuracy(testX, testY, 0.10);
Console.WriteLine("Accuracy test (within 0.10) = " +
accTest.ToString("F4"));
double mseTrain = rfr.MSE(trainX, trainY);
Console.WriteLine("\nMSE train = " +
mseTrain.ToString("F4"));
double mseTest = rfr.MSE(testX, testY);
Console.WriteLine("MSE test = " +
mseTest.ToString("F4"));
// 4. use model
double[] x = trainX[0];
Console.WriteLine("\nPredicting for x = ");
VecShow(x, 4, 9);
double predY = rfr.Predict(x);
Console.WriteLine("y = " + predY.ToString("F4"));
Console.WriteLine("\nEnd demo ");
Console.ReadLine();
} // Main()
// ------------------------------------------------------
// helpers for Main()
// ------------------------------------------------------
static double[][] MatLoad(string fn, int[] usecols,
char sep, string comment)
{
List"lt"double[]"gt" result =
new List"lt"double[]"gt"();
string line = "";
FileStream ifs = new FileStream(fn, FileMode.Open);
StreamReader sr = new StreamReader(ifs);
while ((line = sr.ReadLine()) != null)
{
if (line.StartsWith(comment) == true)
continue;
string[] tokens = line.Split(sep);
List"lt"double"gt" lst = new List"lt"double"gt"();
for (int j = 0; j "lt" usecols.Length; ++j)
lst.Add(double.Parse(tokens[usecols[j]]));
double[] row = lst.ToArray();
result.Add(row);
}
sr.Close(); ifs.Close();
return result.ToArray();
}
static double[] MatToVec(double[][] M)
{
int nRows = M.Length;
int nCols = M[0].Length;
double[] result = new double[nRows * nCols];
int k = 0;
for (int i = 0; i "lt" nRows; ++i)
for (int j = 0; j "lt" nCols; ++j)
result[k++] = M[i][j];
return result;
}
static void VecShow(double[] vec, int dec, int wid)
{
for (int i = 0; i "lt" vec.Length; ++i)
Console.Write(vec[i].ToString("F" + dec).PadLeft(wid));
Console.WriteLine("");
}
} // class Program
// ========================================================
public class RandomForestRegressor
{
public int nTrees;
public int maxDepth;
public int minSamples;
public int minLeaf;
public int nSplitCols; // number cols to use each split
public int nRows;
public List"lt"DecisionTreeRegressor"gt" trees;
public Random rnd;
public RandomForestRegressor(int nTrees, int maxDepth,
int minSamples, int minLeaf, int nCols, int nRows,
int seed = 0)
{
this.nTrees = nTrees;
this.maxDepth = maxDepth;
this.minSamples = minSamples;
this.minLeaf = minLeaf;
this.nRows = nRows;
this.nSplitCols = nCols; // pass to DecisionTree
this.trees = new List"lt"DecisionTreeRegressor"gt"();
this.rnd = new Random(seed);
}
// ------------------------------------------------------
public void Train(double[][] trainX, double[] trainY)
{
int nr = trainX.Length;
// int nc = trainX[0].Length;
for (int i = 0; i "lt" this.nTrees; ++i) // each tree
{
// construct data rows-subset
int[] rndRows =
GetRandomRowIdxs(nr, this.nRows, this.rnd);
double[][] subsetX =
MakeRowsSubsetX(trainX, rndRows);
double[] subsetY =
MakeSubsetY(trainY, rndRows);
// make and train curr tree
DecisionTreeRegressor dtr =
new DecisionTreeRegressor(this.maxDepth,
this.minSamples, this.minLeaf, this.nSplitCols);
// random cols will be used during splits
dtr.Train(subsetX, subsetY);
this.trees.Add(dtr);
} // i
}
// ------------------------------------------------------
public double Predict(double[] x)
{
double sum = 0.0;
for (int t = 0; t "lt" this.nTrees; ++t)
sum += this.trees[t].Predict(x);
return sum / this.nTrees;
}
// ------------------------------------------------------
public double Accuracy(double[][] dataX, double[] dataY,
double pctClose)
{
int numCorrect = 0; int numWrong = 0;
for (int i = 0; i "lt" dataX.Length; ++i)
{
double actualY = dataY[i];
double predY = this.Predict(dataX[i]);
if (Math.Abs(predY - actualY) "lt"
Math.Abs(pctClose * actualY))
++numCorrect;
else
++numWrong;
}
return (numCorrect * 1.0) / (numWrong + numCorrect);
}
// ------------------------------------------------------
public double MSE(double[][] dataX, double[] dataY)
{
int n = dataX.Length;
double sum = 0.0;
for (int i = 0; i "lt" n; ++i)
{
double actualY = dataY[i];
double predY = this.Predict(dataX[i]);
sum += (actualY - predY) * (actualY - predY);
}
return sum / n;
}
// ------------------------------------------------------
private static int[] GetRandomRowIdxs(int N, int n,
Random rnd)
{
// pick n rows from N with replacement
int[] result = new int[n];
for (int i = 0; i "lt" n; ++i)
result[i] = rnd.Next(0, N);
Array.Sort(result);
return result;
}
private static
double[][] MakeRowsSubsetX(double[][] trainX,
int[] rndRows)
{
int nCols = trainX[0].Length; // use all cols
double[][] result = new double[rndRows.Length][];
for (int i = 0; i "lt" rndRows.Length; ++i)
result[i] = new double[nCols];
for (int i = 0; i "lt" rndRows.Length; ++i)
{
for (int j = 0; j "lt" nCols; ++j)
{
int r = rndRows[i]; // random row in trainX
result[i][j] = trainX[r][j];
}
}
return result;
}
private static double[] MakeSubsetY(double[] trainY,
int[] rndRows)
{
double[] result = new double[rndRows.Length];
for (int i = 0; i "lt" rndRows.Length; ++i)
result[i] = trainY[rndRows[i]];
return result;
}
} // class RandomForestRegression
// ========================================================
public class DecisionTreeRegressor
{
public int maxDepth;
public int minSamples; // aka min_samples_split
public int minLeaf; // min number of values in a leaf
public int numSplitCols; // mostly for random forest
public List"lt"Node"gt" tree = new List"lt"Node"gt"();
public Random rnd; // order in which cols are searched
public double[][] trainX; // store data by ref
public double[] trainY;
// ------------------------------------------------------
public class Node
{
public int id;
public int colIdx; // aka featureIdx
public double thresh;
public int left; // index into List
public int right;
public double value;
public bool isLeaf;
public List"lt"int"gt" rows; // assoc rows
public Node(int id, int colIdx, double thresh,
int left, int right, double value, bool isLeaf,
List"lt"int"gt" rows)
{
this.id = id;
this.colIdx = colIdx;
this.thresh = thresh;
this.left = left;
this.right = right;
this.value = value;
this.isLeaf = isLeaf;
this.rows = rows;
}
} // class Node
// --------------------------------------------
public class StackInfo // used to build tree
{
// tree node + associated rows, not explicit data
public Node node; // node holds associated rows
public int depth;
public StackInfo(Node n, int d)
{
this.node = n;
this.depth = d;
}
}
// --------------------------------------------
public DecisionTreeRegressor(int maxDepth = 2,
int minSamples = 2, int minLeaf = 1,
int numSplitCols = -1, int seed = 0)
{
// if maxDepth = 0, tree has just a root node
// if maxDepth = 1, at most 3 nodes (root, l, r)
// if maxDepth = n, at most 2^(n+1) - 1 nodes
this.maxDepth = maxDepth;
this.minSamples = minSamples;
this.minLeaf = minLeaf;
this.numSplitCols = numSplitCols; // for ran. forest
// create full tree List with dummy nodes
int numNodes = (int)Math.Pow(2, (maxDepth + 1)) - 1;
for (int i = 0; i "lt" numNodes; ++i)
{
//this.tree.Add(null); // OK, but let's avoid ptrs
Node n = new Node(i, -1, 0.0, -1, -1, 0.0,
false, new List"lt"int"gt"());
this.tree.Add(n); // dummy node
}
this.rnd = new Random(seed);
}
public void Train(double[][] trainX, double[] trainY)
{
this.trainX = trainX;
this.trainY = trainY;
this.MakeTree();
}
// ------------------------------------------------------
public double Predict(double[] x)
{
int p = 0;
Node currNode = this.tree[p];
while (currNode.isLeaf == false &&
p "lt" this.tree.Count)
{
if (x[currNode.colIdx] "lte" currNode.thresh)
p = currNode.left;
else
p = currNode.right;
currNode = this.tree[p];
}
return this.tree[p].value;
}
// helpers: MakeTree(), BestSplit(),
// TreeTargetMean(), TreeTargetVariance()
private void MakeTree()
{
// no recursion, no pointers, List storage
if (this.numSplitCols == -1) // use all cols
this.numSplitCols = this.trainX[0].Length;
List"lt"int"gt" allRows = new List"lt"int"gt"();
for (int i = 0; i "lt" this.trainX.Length; ++i)
allRows.Add(i);
double grandMean = this.TreeTargetMean(allRows);
Node root = new Node(0, -1, 0.0, 1, 2,
grandMean, false, allRows);
Stack"lt"StackInfo"gt" stack =
new Stack"lt"StackInfo"gt"();
stack.Push(new StackInfo(root, 0));
while (stack.Count "gt" 0)
{
StackInfo info = stack.Pop();
Node currNode = info.node;
this.tree[currNode.id] = currNode;
List"lt"int"gt" currRows = info.node.rows;
int currDepth = info.depth;
if (currDepth == this.maxDepth ||
currRows.Count "lt" this.minSamples)
{
currNode.value = this.TreeTargetMean(currRows);
currNode.isLeaf = true;
continue;
}
double[] splitInfo = this.BestSplit(currRows);
int colIdx = (int)splitInfo[0];
double thresh = splitInfo[1];
if (colIdx == -1) // unable to split
{
currNode.value = this.TreeTargetMean(currRows);
currNode.isLeaf = true;
continue;
}
// got good split so at internal, non-leaf node
currNode.colIdx = colIdx;
currNode.thresh = thresh;
// make the data splits for children
// find left rows and right rows
List"lt"int"gt" leftIdxs = new List"lt"int"gt"();
List"lt"int"gt" rightIdxs = new List"lt"int"gt"();
for (int k = 0; k "lt" currRows.Count; ++k)
{
int r = currRows[k];
if (this.trainX[r][colIdx] "lte" thresh)
leftIdxs.Add(r);
else
rightIdxs.Add(r);
}
int leftID = currNode.id * 2 + 1;
Node currNodeLeft = new Node(leftID, -1, 0.0,
2 * leftID + 1, 2 * leftID + 2,
this.TreeTargetMean(leftIdxs), false, leftIdxs);
stack.Push(new StackInfo(currNodeLeft,
currDepth + 1));
int rightID = currNode.id * 2 + 2;
Node currNodeRight = new Node(rightID, -1, 0.0,
2 * rightID + 1, 2 * rightID + 2,
this.TreeTargetMean(rightIdxs), false, rightIdxs);
stack.Push(new StackInfo(currNodeRight,
currDepth + 1));
} // while
return;
} // MakeTree()
// ------------------------------------------------------
private double[] BestSplit(List"lt"int"gt" rows)
{
// implicit params numSplitCols, minLeaf, numsplitCols
// result[0] = best col idx (as double)
// result[1] = best split value
rows.Sort();
int bestColIdx = -1; // indicates bad split
double bestThresh = 0.0;
double bestVar = double.MaxValue; // smaller better
int nRows = rows.Count; // or dataY.Length
int nCols = this.trainX[0].Length;
if (nRows == 0)
{
throw new Exception("empty data in BestSplit()");
}
// process cols in scrambled order
int[] colIndices = new int[nCols];
for (int k = 0; k "lt" nCols; ++k)
colIndices[k] = k;
// shuffle, inline Fisher-Yates
int n = colIndices.Length;
for (int i = 0; i "lt" n; ++i)
{
int ri = rnd.Next(i, n); // be careful
int tmp = colIndices[i];
colIndices[i] = colIndices[ri];
colIndices[ri] = tmp;
}
// numSplitCols is usually all columns (-1)
for (int j = 0; j "lt" this.numSplitCols; ++j)
{
int colIdx = colIndices[j];
HashSet"lt"double"gt" examineds =
new HashSet"lt"double"gt"();
for (int i = 0; i "lt" nRows; ++i) // each row
{
// if curr thresh been seen, skip it
double thresh = this.trainX[rows[i]][colIdx];
if (examineds.Contains(thresh)) continue;
examineds.Add(thresh);
// get row idxs where x is lte, gt thresh
List"lt"int"gt" leftIdxs =
new List"lt"int"gt"();
List"lt"int"gt" rightIdxs =
new List"lt"int"gt"();
for (int k = 0; k "lt" nRows; ++k)
{
if (this.trainX[rows[k]][colIdx] "lte" thresh)
leftIdxs.Add(rows[k]);
else
rightIdxs.Add(rows[k]);
}
// Check if proposed split has too few values
if (leftIdxs.Count "lt" this.minLeaf ||
rightIdxs.Count "lt" this.minLeaf)
continue; // to next row
double leftVar =
this.TreeTargetVariance(leftIdxs);
double rightVar =
this.TreeTargetVariance(rightIdxs);
double weightedVar = (leftIdxs.Count * leftVar +
rightIdxs.Count * rightVar) / nRows;
if (weightedVar "lt" bestVar)
{
bestColIdx = colIdx;
bestThresh = thresh;
bestVar = weightedVar;
}
} // each row
} // j each col
double[] result = new double[2]; // out params ugly
result[0] = 1.0 * bestColIdx;
result[1] = bestThresh;
return result;
} // BestSplit()
// ------------------------------------------------------
private double TreeTargetMean(List"lt"int"gt" rows)
{
// mean of rows items in trainY: for node prediction
double sum = 0.0;
for (int i = 0; i "lt" rows.Count; ++i)
{
int r = rows[i];
sum += this.trainY[r];
}
return sum / rows.Count;
}
// ------------------------------------------------------
private double TreeTargetVariance(List"lt"int"gt" rows)
{
double mean = this.TreeTargetMean(rows);
double sum = 0.0;
for (int i = 0; i "lt" rows.Count; ++i)
{
int r = rows[i];
sum += (this.trainY[r] - mean) *
(this.trainY[r] - mean);
}
return sum / rows.Count;
}
// ------------------------------------------------------
} // class DecisionTreeRegressor
// ========================================================
} // ns
Training data:
# synthetic_train_200.txt # -0.1660, 0.4406, -0.9998, -0.3953, -0.7065, 0.4840 0.0776, -0.1616, 0.3704, -0.5911, 0.7562, 0.1568 -0.9452, 0.3409, -0.1654, 0.1174, -0.7192, 0.8054 0.9365, -0.3732, 0.3846, 0.7528, 0.7892, 0.1345 -0.8299, -0.9219, -0.6603, 0.7563, -0.8033, 0.7955 0.0663, 0.3838, -0.3690, 0.3730, 0.6693, 0.3206 -0.9634, 0.5003, 0.9777, 0.4963, -0.4391, 0.7377 -0.1042, 0.8172, -0.4128, -0.4244, -0.7399, 0.4801 -0.9613, 0.3577, -0.5767, -0.4689, -0.0169, 0.6861 -0.7065, 0.1786, 0.3995, -0.7953, -0.1719, 0.5569 0.3888, -0.1716, -0.9001, 0.0718, 0.3276, 0.2500 0.1731, 0.8068, -0.7251, -0.7214, 0.6148, 0.3297 -0.2046, -0.6693, 0.8550, -0.3045, 0.5016, 0.2129 0.2473, 0.5019, -0.3022, -0.4601, 0.7918, 0.2613 -0.1438, 0.9297, 0.3269, 0.2434, -0.7705, 0.5171 0.1568, -0.1837, -0.5259, 0.8068, 0.1474, 0.3307 -0.9943, 0.2343, -0.3467, 0.0541, 0.7719, 0.5581 0.2467, -0.9684, 0.8589, 0.3818, 0.9946, 0.1092 -0.6553, -0.7257, 0.8652, 0.3936, -0.8680, 0.7018 0.8460, 0.4230, -0.7515, -0.9602, -0.9476, 0.1996 -0.9434, -0.5076, 0.7201, 0.0777, 0.1056, 0.5664 0.9392, 0.1221, -0.9627, 0.6013, -0.5341, 0.1533 0.6142, -0.2243, 0.7271, 0.4942, 0.1125, 0.1661 0.4260, 0.1194, -0.9749, -0.8561, 0.9346, 0.2230 0.1362, -0.5934, -0.4953, 0.4877, -0.6091, 0.3810 0.6937, -0.5203, -0.0125, 0.2399, 0.6580, 0.1460 -0.6864, -0.9628, -0.8600, -0.0273, 0.2127, 0.5387 0.9772, 0.1595, -0.2397, 0.1019, 0.4907, 0.1611 0.3385, -0.4702, -0.8673, -0.2598, 0.2594, 0.2270 -0.8669, -0.4794, 0.6095, -0.6131, 0.2789, 0.4700 0.0493, 0.8496, -0.4734, -0.8681, 0.4701, 0.3516 0.8639, -0.9721, -0.5313, 0.2336, 0.8980, 0.1412 0.9004, 0.1133, 0.8312, 0.2831, -0.2200, 0.1782 0.0991, 0.8524, 0.8375, -0.2102, 0.9265, 0.2150 -0.6521, -0.7473, -0.7298, 0.0113, -0.9570, 0.7422 0.6190, -0.3105, 0.8802, 0.1640, 0.7577, 0.1056 0.6895, 0.8108, -0.0802, 0.0927, 0.5972, 0.2214 0.1982, -0.9689, 0.1870, -0.1326, 0.6147, 0.1310 -0.3695, 0.7858, 0.1557, -0.6320, 0.5759, 0.3773 -0.1596, 0.3581, 0.8372, -0.9992, 0.9535, 0.2071 -0.2468, 0.9476, 0.2094, 0.6577, 0.1494, 0.4132 0.1737, 0.5000, 0.7166, 0.5102, 0.3961, 0.2611 0.7290, -0.3546, 0.3416, -0.0983, -0.2358, 0.1332 -0.3652, 0.2438, -0.1395, 0.9476, 0.3556, 0.4170 -0.6029, -0.1466, -0.3133, 0.5953, 0.7600, 0.4334 -0.4596, -0.4953, 0.7098, 0.0554, 0.6043, 0.2775 0.1450, 0.4663, 0.0380, 0.5418, 0.1377, 0.2931 -0.8636, -0.2442, -0.8407, 0.9656, -0.6368, 0.7429 0.6237, 0.7499, 0.3768, 0.1390, -0.6781, 0.2185 -0.5499, 0.1850, -0.3755, 0.8326, 0.8193, 0.4399 -0.4858, -0.7782, -0.6141, -0.0008, 0.4572, 0.4197 0.7033, -0.1683, 0.2334, -0.5327, -0.7961, 0.1776 0.0317, -0.0457, -0.6947, 0.2436, 0.0880, 0.3345 0.5031, -0.5559, 0.0387, 0.5706, -0.9553, 0.3107 -0.3513, 0.7458, 0.6894, 0.0769, 0.7332, 0.3170 0.2205, 0.5992, -0.9309, 0.5405, 0.4635, 0.3532 -0.4806, -0.4859, 0.2646, -0.3094, 0.5932, 0.3202 0.9809, -0.3995, -0.7140, 0.8026, 0.0831, 0.1600 0.9495, 0.2732, 0.9878, 0.0921, 0.0529, 0.1289 -0.9476, -0.6792, 0.4913, -0.9392, -0.2669, 0.5966 0.7247, 0.3854, 0.3819, -0.6227, -0.1162, 0.1550 -0.5922, -0.5045, -0.4757, 0.5003, -0.0860, 0.5863 -0.8861, 0.0170, -0.5761, 0.5972, -0.4053, 0.7301 0.6877, -0.2380, 0.4997, 0.0223, 0.0819, 0.1404 0.9189, 0.6079, -0.9354, 0.4188, -0.0700, 0.1907 -0.1428, -0.7820, 0.2676, 0.6059, 0.3936, 0.2790 0.5324, -0.3151, 0.6917, -0.1425, 0.6480, 0.1071 -0.8432, -0.9633, -0.8666, -0.0828, -0.7733, 0.7784 -0.9444, 0.5097, -0.2103, 0.4939, -0.0952, 0.6787 -0.0520, 0.6063, -0.1952, 0.8094, -0.9259, 0.4836 0.5477, -0.7487, 0.2370, -0.9793, 0.0773, 0.1241 0.2450, 0.8116, 0.9799, 0.4222, 0.4636, 0.2355 0.8186, -0.1983, -0.5003, -0.6531, -0.7611, 0.1511 -0.4714, 0.6382, -0.3788, 0.9648, -0.4667, 0.5950 0.0673, -0.3711, 0.8215, -0.2669, -0.1328, 0.2677 -0.9381, 0.4338, 0.7820, -0.9454, 0.0441, 0.5518 -0.3480, 0.7190, 0.1170, 0.3805, -0.0943, 0.4724 -0.9813, 0.1535, -0.3771, 0.0345, 0.8328, 0.5438 -0.1471, -0.5052, -0.2574, 0.8637, 0.8737, 0.3042 -0.5454, -0.3712, -0.6505, 0.2142, -0.1728, 0.5783 0.6327, -0.6297, 0.4038, -0.5193, 0.1484, 0.1153 -0.5424, 0.3282, -0.0055, 0.0380, -0.6506, 0.6613 0.1414, 0.9935, 0.6337, 0.1887, 0.9520, 0.2540 -0.9351, -0.8128, -0.8693, -0.0965, -0.2491, 0.7353 0.9507, -0.6640, 0.9456, 0.5349, 0.6485, 0.1059 -0.0462, -0.9737, -0.2940, -0.0159, 0.4602, 0.2606 -0.0627, -0.0852, -0.7247, -0.9782, 0.5166, 0.2977 0.0478, 0.5098, -0.0723, -0.7504, -0.3750, 0.3335 0.0090, 0.3477, 0.5403, -0.7393, -0.9542, 0.4415 -0.9748, 0.3449, 0.3736, -0.1015, 0.8296, 0.4358 0.2887, -0.9895, -0.0311, 0.7186, 0.6608, 0.2057 0.1570, -0.4518, 0.1211, 0.3435, -0.2951, 0.3244 0.7117, -0.6099, 0.4946, -0.4208, 0.5476, 0.1096 -0.2929, -0.5726, 0.5346, -0.3827, 0.4665, 0.2465 0.4889, -0.5572, -0.5718, -0.6021, -0.7150, 0.2163 -0.7782, 0.3491, 0.5996, -0.8389, -0.5366, 0.6516 -0.5847, 0.8347, 0.4226, 0.1078, -0.3910, 0.6134 0.8469, 0.4121, -0.0439, -0.7476, 0.9521, 0.1571 -0.6803, -0.5948, -0.1376, -0.1916, -0.7065, 0.7156 0.2878, 0.5086, -0.5785, 0.2019, 0.4979, 0.2980 0.2764, 0.1943, -0.4090, 0.4632, 0.8906, 0.2960 -0.8877, 0.6705, -0.6155, -0.2098, -0.3998, 0.7107 -0.8398, 0.8093, -0.2597, 0.0614, -0.0118, 0.6502 -0.8476, 0.0158, -0.4769, -0.2859, -0.7839, 0.7715 0.5751, -0.7868, 0.9714, -0.6457, 0.1448, 0.1175 0.4802, -0.7001, 0.1022, -0.5668, 0.5184, 0.1090 0.4458, -0.6469, 0.7239, -0.9604, 0.7205, 0.0779 0.5175, 0.4339, 0.9747, -0.4438, -0.9924, 0.2879 0.8678, 0.7158, 0.4577, 0.0334, 0.4139, 0.1678 0.5406, 0.5012, 0.2264, -0.1963, 0.3946, 0.2088 -0.9938, 0.5498, 0.7928, -0.5214, -0.7585, 0.7687 0.7661, 0.0863, -0.4266, -0.7233, -0.4197, 0.1466 0.2277, -0.3517, -0.0853, -0.1118, 0.6563, 0.1767 0.3499, -0.5570, -0.0655, -0.3705, 0.2537, 0.1632 0.7547, -0.1046, 0.5689, -0.0861, 0.3125, 0.1257 0.8186, 0.2110, 0.5335, 0.0094, -0.0039, 0.1391 0.6858, -0.8644, 0.1465, 0.8855, 0.0357, 0.1845 -0.4967, 0.4015, 0.0805, 0.8977, 0.2487, 0.4663 0.6760, -0.9841, 0.9787, -0.8446, -0.3557, 0.1509 -0.1203, -0.4885, 0.6054, -0.0443, -0.7313, 0.4854 0.8557, 0.7919, -0.0169, 0.7134, -0.1628, 0.2002 0.0115, -0.6209, 0.9300, -0.4116, -0.7931, 0.4052 -0.7114, -0.9718, 0.4319, 0.1290, 0.5892, 0.3661 0.3915, 0.5557, -0.1870, 0.2955, -0.6404, 0.2954 -0.3564, -0.6548, -0.1827, -0.5172, -0.1862, 0.4622 0.2392, -0.4959, 0.5857, -0.1341, -0.2850, 0.2470 -0.3394, 0.3947, -0.4627, 0.6166, -0.4094, 0.5325 0.7107, 0.7768, -0.6312, 0.1707, 0.7964, 0.2757 -0.1078, 0.8437, -0.4420, 0.2177, 0.3649, 0.4028 -0.3139, 0.5595, -0.6505, -0.3161, -0.7108, 0.5546 0.4335, 0.3986, 0.3770, -0.4932, 0.3847, 0.1810 -0.2562, -0.2894, -0.8847, 0.2633, 0.4146, 0.4036 0.2272, 0.2966, -0.6601, -0.7011, 0.0284, 0.2778 -0.0743, -0.1421, -0.0054, -0.6770, -0.3151, 0.3597 -0.4762, 0.6891, 0.6007, -0.1467, 0.2140, 0.4266 -0.4061, 0.7193, 0.3432, 0.2669, -0.7505, 0.6147 -0.0588, 0.9731, 0.8966, 0.2902, -0.6966, 0.4955 -0.0627, -0.1439, 0.1985, 0.6999, 0.5022, 0.3077 0.1587, 0.8494, -0.8705, 0.9827, -0.8940, 0.4263 -0.7850, 0.2473, -0.9040, -0.4308, -0.8779, 0.7199 0.4070, 0.3369, -0.2428, -0.6236, 0.4940, 0.2215 -0.0242, 0.0513, -0.9430, 0.2885, -0.2987, 0.3947 -0.5416, -0.1322, -0.2351, -0.0604, 0.9590, 0.3683 0.1055, 0.7783, -0.2901, -0.5090, 0.8220, 0.2984 -0.9129, 0.9015, 0.1128, -0.2473, 0.9901, 0.4776 -0.9378, 0.1424, -0.6391, 0.2619, 0.9618, 0.5368 0.7498, -0.0963, 0.4169, 0.5549, -0.0103, 0.1614 -0.2612, -0.7156, 0.4538, -0.0460, -0.1022, 0.3717 0.7720, 0.0552, -0.1818, -0.4622, -0.8560, 0.1685 -0.4177, 0.0070, 0.9319, -0.7812, 0.3461, 0.3052 -0.0001, 0.5542, -0.7128, -0.8336, -0.2016, 0.3803 0.5356, -0.4194, -0.5662, -0.9666, -0.2027, 0.1776 -0.2378, 0.3187, -0.8582, -0.6948, -0.9668, 0.5474 -0.1947, -0.3579, 0.1158, 0.9869, 0.6690, 0.2992 0.3992, 0.8365, -0.9205, -0.8593, -0.0520, 0.3154 -0.0209, 0.0793, 0.7905, -0.1067, 0.7541, 0.1864 -0.4928, -0.4524, -0.3433, 0.0951, -0.5597, 0.6261 -0.8118, 0.7404, -0.5263, -0.2280, 0.1431, 0.6349 0.0516, -0.8480, 0.7483, 0.9023, 0.6250, 0.1959 -0.3212, 0.1093, 0.9488, -0.3766, 0.3376, 0.2735 -0.3481, 0.5490, -0.3484, 0.7797, 0.5034, 0.4379 -0.5785, -0.9170, -0.3563, -0.9258, 0.3877, 0.4121 0.3407, -0.1391, 0.5356, 0.0720, -0.9203, 0.3458 -0.3287, -0.8954, 0.2102, 0.0241, 0.2349, 0.3247 -0.1353, 0.6954, -0.0919, -0.9692, 0.7461, 0.3338 0.9036, -0.8982, -0.5299, -0.8733, -0.1567, 0.1187 0.7277, -0.8368, -0.0538, -0.7489, 0.5458, 0.0830 0.9049, 0.8878, 0.2279, 0.9470, -0.3103, 0.2194 0.7957, -0.1308, -0.5284, 0.8817, 0.3684, 0.2172 0.4647, -0.4931, 0.2010, 0.6292, -0.8918, 0.3371 -0.7390, 0.6849, 0.2367, 0.0626, -0.5034, 0.7039 -0.1567, -0.8711, 0.7940, -0.5932, 0.6525, 0.1710 0.7635, -0.0265, 0.1969, 0.0545, 0.2496, 0.1445 0.7675, 0.1354, -0.7698, -0.5460, 0.1920, 0.1728 -0.5211, -0.7372, -0.6763, 0.6897, 0.2044, 0.5217 0.1913, 0.1980, 0.2314, -0.8816, 0.5006, 0.1998 0.8964, 0.0694, -0.6149, 0.5059, -0.9854, 0.1825 0.1767, 0.7104, 0.2093, 0.6452, 0.7590, 0.2832 -0.3580, -0.7541, 0.4426, -0.1193, -0.7465, 0.5657 -0.5996, 0.5766, -0.9758, -0.3933, -0.9572, 0.6800 0.9950, 0.1641, -0.4132, 0.8579, 0.0142, 0.2003 -0.4717, -0.3894, -0.2567, -0.5111, 0.1691, 0.4266 0.3917, -0.8561, 0.9422, 0.5061, 0.6123, 0.1212 -0.0366, -0.1087, 0.3449, -0.1025, 0.4086, 0.2475 0.3633, 0.3943, 0.2372, -0.6980, 0.5216, 0.1925 -0.5325, -0.6466, -0.2178, -0.3589, 0.6310, 0.3568 0.2271, 0.5200, -0.1447, -0.8011, -0.7699, 0.3128 0.6415, 0.1993, 0.3777, -0.0178, -0.8237, 0.2181 -0.5298, -0.0768, -0.6028, -0.9490, 0.4588, 0.4356 0.6870, -0.1431, 0.7294, 0.3141, 0.1621, 0.1632 -0.5985, 0.0591, 0.7889, -0.3900, 0.7419, 0.2945 0.3661, 0.7984, -0.8486, 0.7572, -0.6183, 0.3449 0.6995, 0.3342, -0.3113, -0.6972, 0.2707, 0.1712 0.2565, 0.9126, 0.1798, -0.6043, -0.1413, 0.2893 -0.3265, 0.9839, -0.2395, 0.9854, 0.0376, 0.4770 0.2690, -0.1722, 0.9818, 0.8599, -0.7015, 0.3954 -0.2102, -0.0768, 0.1219, 0.5607, -0.0256, 0.3949 0.8216, -0.9555, 0.6422, -0.6231, 0.3715, 0.0801 -0.2896, 0.9484, -0.7545, -0.6249, 0.7789, 0.4370 -0.9985, -0.5448, -0.7092, -0.5931, 0.7926, 0.5402
Test data:
# synthetic_test_40.txt # 0.7462, 0.4006, -0.0590, 0.6543, -0.0083, 0.1935 0.8495, -0.2260, -0.0142, -0.4911, 0.7699, 0.1078 -0.2335, -0.4049, 0.4352, -0.6183, -0.7636, 0.5088 0.1810, -0.5142, 0.2465, 0.2767, -0.3449, 0.3136 -0.8650, 0.7611, -0.0801, 0.5277, -0.4922, 0.7140 -0.2358, -0.7466, -0.5115, -0.8413, -0.3943, 0.4533 0.4834, 0.2300, 0.3448, -0.9832, 0.3568, 0.1360 -0.6502, -0.6300, 0.6885, 0.9652, 0.8275, 0.3046 -0.3053, 0.5604, 0.0929, 0.6329, -0.0325, 0.4756 -0.7995, 0.0740, -0.2680, 0.2086, 0.9176, 0.4565 -0.2144, -0.2141, 0.5813, 0.2902, -0.2122, 0.4119 -0.7278, -0.0987, -0.3312, -0.5641, 0.8515, 0.4438 0.3793, 0.1976, 0.4933, 0.0839, 0.4011, 0.1905 -0.8568, 0.9573, -0.5272, 0.3212, -0.8207, 0.7415 -0.5785, 0.0056, -0.7901, -0.2223, 0.0760, 0.5551 0.0735, -0.2188, 0.3925, 0.3570, 0.3746, 0.2191 0.1230, -0.2838, 0.2262, 0.8715, 0.1938, 0.2878 0.4792, -0.9248, 0.5295, 0.0366, -0.9894, 0.3149 -0.4456, 0.0697, 0.5359, -0.8938, 0.0981, 0.3879 0.8629, -0.8505, -0.4464, 0.8385, 0.5300, 0.1769 0.1995, 0.6659, 0.7921, 0.9454, 0.9970, 0.2330 -0.0249, -0.3066, -0.2927, -0.4923, 0.8220, 0.2437 0.4513, -0.9481, -0.0770, -0.4374, -0.9421, 0.2879 -0.3405, 0.5931, -0.3507, -0.3842, 0.8562, 0.3987 0.9538, 0.0471, 0.9039, 0.7760, 0.0361, 0.1706 -0.0887, 0.2104, 0.9808, 0.5478, -0.3314, 0.4128 -0.8220, -0.6302, 0.0537, -0.1658, 0.6013, 0.4306 -0.4123, -0.2880, 0.9074, -0.0461, -0.4435, 0.5144 0.0060, 0.2867, -0.7775, 0.5161, 0.7039, 0.3599 -0.7968, -0.5484, 0.9426, -0.4308, 0.8148, 0.2979 0.7811, 0.8450, -0.6877, 0.7594, 0.2640, 0.2362 -0.6802, -0.1113, -0.8325, -0.6694, -0.6056, 0.6544 0.3821, 0.1476, 0.7466, -0.5107, 0.2592, 0.1648 0.7265, 0.9683, -0.9803, -0.4943, -0.5523, 0.2454 -0.9049, -0.9797, -0.0196, -0.9090, -0.4433, 0.6447 -0.4607, 0.1811, -0.2389, 0.4050, -0.0078, 0.5229 0.2664, -0.2932, -0.4259, -0.7336, 0.8742, 0.1834 -0.4507, 0.1029, -0.6294, -0.1158, -0.6294, 0.6081 0.8948, -0.0124, 0.9278, 0.2899, -0.0314, 0.1534 -0.1323, -0.8813, -0.0146, -0.0697, 0.6135, 0.2386
.NET Test Automation Recipes
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