tests/testthat/test-trees.R

In jmwerner/ArtisanalMachineLearning: Hand Made Pure Organic Machine Learning

context("random forest testing")

data(iris)
data = iris[,1:4]
names(data) = letters[1:4]
response = data$d
data$d = NULL

test_that("Single split is calculated correctly", {
    one_split = .find_one_split(data, response, sum_of_squares)

    expect_equal(one_split$split_column_name, "c")
    expect_equal(one_split$criterion_value, 18.4066)
    expect_equal(one_split$split_value, 2.45)

    expect_type(one_split$split_column_name, "character")
    expect_type(one_split$criterion_value, "double")
    expect_type(one_split$split_value, "double")

    expect_equal(dim(one_split), c(1, 3))
})

test_that("Single column split is calculated correctly", {
    one_split = .find_one_column_split(data, "a", response, sum_of_squares)
    expect_equal(one_split$split_column_name, "a")
    expect_equal(one_split$criterion_value, 30.59534)
    expect_equal(one_split$split_value, 5.55)
    expect_type(one_split$split_column_name, "character")
    expect_type(one_split$criterion_value, "double")
    expect_type(one_split$split_value, "double")
    expect_equal(dim(one_split), c(1, 3))
    one_split = .find_one_column_split(data, "b", response, sum_of_squares)
    expect_equal(one_split$split_column_name, "b")
    expect_equal(one_split$criterion_value, 67.46669, tolerance = .0001)
    expect_equal(one_split$split_value, 3.35)
    expect_type(one_split$split_column_name, "character")
    expect_type(one_split$criterion_value, "double")
    expect_type(one_split$split_value, "double")
    expect_equal(dim(one_split), c(1, 3))
    one_split = .find_one_column_split(data, "c", response, sum_of_squares)
    expect_equal(one_split$split_column_name, "c")
    expect_equal(one_split$criterion_value, 18.4066)
    expect_equal(one_split$split_value, 2.45)
    expect_type(one_split$split_column_name, "character")
    expect_type(one_split$criterion_value, "double")
    expect_type(one_split$split_value, "double")
    expect_equal(dim(one_split), c(1, 3))
})

test_that("Single column split is calculated correctly when column has no variation", {
    dummy_data = data.frame(a = rep(3.4, length(response)))
    one_split = .find_one_column_split(dummy_data, "a", response, sum_of_squares)
    expect_equal(one_split$split_column_name, "a")
    expect_equal(one_split$criterion_value, NA)
    expect_equal(one_split$split_value, 3.4)
    expect_type(one_split$split_column_name, "character")
    expect_type(one_split$criterion_value, "logical")
    expect_type(one_split$split_value, "double")
    expect_equal(dim(one_split), c(1, 3))
})

test_that("Single tree training is correct", {
    one_tree = create_tree(data, response, evaluation_criterion = sum_of_squares, min_obs = 5, max_depth = 8)
    # dput(one_tree)
    expected_tree = structure(list(split_column = "c", criterion_value = 18.4066,
                split_value = 2.45, left = structure(list(split_column = "a",
                    criterion_value = 0.4575, split_value = 4.95, left = structure(list(
                        split_column_name = "b", criterion_value = 0.0578947368421053,
                        split_value = 2.6, prediction = 0.195, count = 20L), .Names = c("split_column_name",
                    "criterion_value", "split_value", "prediction", "count"
                    ), row.names = 2L, class = "data.frame"), right = structure(list(
                        split_column = "c", criterion_value = 0.314603174603175,
                        split_value = 1.55, left = structure(list(split_column_name = "b",
                            criterion_value = 0.128, split_value = 4.3, prediction = 0.247619047619048,
                            count = 21L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction", "count"
                        ), row.names = 2L, class = "data.frame"), right = structure(list(
                            split_column_name = "b", criterion_value = 0.135,
                            split_value = 3.15, prediction = 0.355555555555556,
                            count = 9L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction", "count"
                        ), row.names = 2L, class = "data.frame")), .Names = c("split_column",
                    "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
                "criterion_value", "split_value", "left", "right")), right = structure(list(
                    split_column = "c", criterion_value = 6.29527272727273,
                    split_value = 4.75, left = structure(list(split_column = "c",
                        criterion_value = 0.80582995951417, split_value = 4.15,
                        left = structure(list(split_column = "b", criterion_value = 0.246309523809524,
                            split_value = 2.65, left = structure(list(split_column_name = "c",
                              criterion_value = 0.07875, split_value = 3.95,
                              prediction = 1.09166666666667, count = 12L), .Names = c("split_column_name",
                            "criterion_value", "split_value", "prediction",
                            "count"), row.names = 3L, class = "data.frame"),
                            right = structure(list(split_column_name = "a",
                              criterion_value = 0.0541666666666667, split_value = 5.75,
                              prediction = 1.25714285714286, count = 7L), .Names = c("split_column_name",
                            "criterion_value", "split_value", "prediction",
                            "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                        "criterion_value", "split_value", "left", "right"
                        )), right = structure(list(split_column = "c", criterion_value = 0.3135,
                            split_value = 4.45, left = structure(list(split_column_name = "a",
                              criterion_value = 0.0433333333333333, split_value = 5.8,
                              prediction = 1.32, count = 10L), .Names = c("split_column_name",
                            "criterion_value", "split_value", "prediction",
                            "count"), row.names = 1L, class = "data.frame"),
                            right = structure(list(split_column_name = "a",
                              criterion_value = 0.177333333333333, split_value = 5.15,
                              prediction = 1.4625, count = 16L), .Names = c("split_column_name",
                            "criterion_value", "split_value", "prediction",
                            "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                        "criterion_value", "split_value", "left", "right"
                        ))), .Names = c("split_column", "criterion_value",
                    "split_value", "left", "right")), right = structure(list(
                        split_column = "c", criterion_value = 3.68673992673993,
                        split_value = 5.05, left = structure(list(split_column_name = "a",
                            criterion_value = 0.281363636363636, split_value = 6.75,
                            prediction = 1.73076923076923, count = 13L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction", "count"
                        ), row.names = 1L, class = "data.frame"), right = structure(list(
                            split_column = "b", criterion_value = 2.47298823529412,
                            split_value = 3.05, left = structure(list(split_column = "a",
                              criterion_value = 1.34404411764706, split_value = 6.35,
                              left = structure(list(split_column_name = "a",
                                criterion_value = 0.294666666666667, split_value = 5.85,
                                prediction = 1.7875, count = 8L), .Names = c("split_column_name",
                              "criterion_value", "split_value", "prediction",
                              "count"), row.names = 1L, class = "data.frame"),
                              right = structure(list(split_column_name = "a",
                                criterion_value = 0.564423076923077, split_value = 7.5,
                                prediction = 2.02941176470588, count = 17L), .Names = c("split_column_name",
                              "criterion_value", "split_value", "prediction",
                              "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                            "criterion_value", "split_value", "left", "right"
                            )), right = structure(list(split_column = "b",
                              criterion_value = 0.690972222222222, split_value = 3.25,
                              left = structure(list(split_column_name = "a",
                                criterion_value = 0.28875, split_value = 7.05,
                                prediction = 2.14444444444444, count = 9L), .Names = c("split_column_name",
                              "criterion_value", "split_value", "prediction",
                              "count"), row.names = 1L, class = "data.frame"),
                              right = structure(list(split_column_name = "a",
                                criterion_value = 0.148333333333333, split_value = 7.45,
                                prediction = 2.3125, count = 8L), .Names = c("split_column_name",
                              "criterion_value", "split_value", "prediction",
                              "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                            "criterion_value", "split_value", "left", "right"
                            ))), .Names = c("split_column", "criterion_value",
                        "split_value", "left", "right"))), .Names = c("split_column",
                    "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
                "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
            "criterion_value", "split_value", "left", "right"), class = c("aml_tree",
            "list"))
    expect_equal(one_tree, expected_tree)

    one_tree = create_tree(data, response, evaluation_criterion = sum_of_squares, min_obs = 20, max_depth = 20)
    # dput(one_tree)
    expected_tree = structure(list(split_column = "c", criterion_value = 18.4066,
            split_value = 2.45, left = structure(list(split_column_name = "a",
                criterion_value = 0.4575, split_value = 4.95, prediction = 0.246,
                count = 50L), .Names = c("split_column_name", "criterion_value",
            "split_value", "prediction", "count"), row.names = 1L, class = "data.frame"),
            right = structure(list(split_column = "c", criterion_value = 6.29527272727273,
                split_value = 4.75, left = structure(list(split_column_name = "c",
                    criterion_value = 0.80582995951417, split_value = 4.15,
                    prediction = 1.3, count = 45L), .Names = c("split_column_name",
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 3L, class = "data.frame"), right = structure(list(
                    split_column_name = "c", criterion_value = 3.68673992673993,
                    split_value = 5.05, prediction = 1.98363636363636,
                    count = 55L), .Names = c("split_column_name", "criterion_value",
                "split_value", "prediction", "count"), row.names = 3L, class = "data.frame")), .Names = c("split_column",
            "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
        "criterion_value", "split_value", "left", "right"), class = c("aml_tree",
        "list"))
    expect_equal(one_tree, expected_tree)

    one_tree = create_tree(data, response, evaluation_criterion = sum_of_squares, min_obs = 5, max_depth = 20)
    expected_tree = structure(list(split_column = "c", criterion_value = 18.4066,
            split_value = 2.45, left = structure(list(split_column = "a",
                criterion_value = 0.4575, split_value = 4.95, left = structure(list(
                    split_column_name = "b", criterion_value = 0.0578947368421053,
                    split_value = 2.6, prediction = 0.195, count = 20L), .Names = c("split_column_name",
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 2L, class = "data.frame"), right = structure(list(
                    split_column = "c", criterion_value = 0.314603174603175,
                    split_value = 1.55, left = structure(list(split_column_name = "b",
                        criterion_value = 0.128, split_value = 4.3, prediction = 0.247619047619048,
                        count = 21L), .Names = c("split_column_name",
                    "criterion_value", "split_value", "prediction", "count"
                    ), row.names = 2L, class = "data.frame"), right = structure(list(
                        split_column_name = "b", criterion_value = 0.135,
                        split_value = 3.15, prediction = 0.355555555555556,
                        count = 9L), .Names = c("split_column_name",
                    "criterion_value", "split_value", "prediction", "count"
                    ), row.names = 2L, class = "data.frame")), .Names = c("split_column",
                "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
            "criterion_value", "split_value", "left", "right")), right = structure(list(
                split_column = "c", criterion_value = 6.29527272727273,
                split_value = 4.75, left = structure(list(split_column = "c",
                    criterion_value = 0.80582995951417, split_value = 4.15,
                    left = structure(list(split_column = "b", criterion_value = 0.246309523809524,
                        split_value = 2.65, left = structure(list(split_column_name = "c",
                          criterion_value = 0.07875, split_value = 3.95,
                          prediction = 1.09166666666667, count = 12L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction",
                        "count"), row.names = 3L, class = "data.frame"),
                        right = structure(list(split_column_name = "a",
                          criterion_value = 0.0541666666666667, split_value = 5.75,
                          prediction = 1.25714285714286, count = 7L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction",
                        "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                    "criterion_value", "split_value", "left", "right"
                    )), right = structure(list(split_column = "c", criterion_value = 0.3135,
                        split_value = 4.45, left = structure(list(split_column_name = "a",
                          criterion_value = 0.0433333333333333, split_value = 5.8,
                          prediction = 1.32, count = 10L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction",
                        "count"), row.names = 1L, class = "data.frame"),
                        right = structure(list(split_column_name = "a",
                          criterion_value = 0.177333333333333, split_value = 5.15,
                          prediction = 1.4625, count = 16L), .Names = c("split_column_name",
                        "criterion_value", "split_value", "prediction",
                        "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                    "criterion_value", "split_value", "left", "right"
                    ))), .Names = c("split_column", "criterion_value",
                "split_value", "left", "right")), right = structure(list(
                    split_column = "c", criterion_value = 3.68673992673993,
                    split_value = 5.05, left = structure(list(split_column_name = "a",
                        criterion_value = 0.281363636363636, split_value = 6.75,
                        prediction = 1.73076923076923, count = 13L), .Names = c("split_column_name",
                    "criterion_value", "split_value", "prediction", "count"
                    ), row.names = 1L, class = "data.frame"), right = structure(list(
                        split_column = "b", criterion_value = 2.47298823529412,
                        split_value = 3.05, left = structure(list(split_column = "a",
                          criterion_value = 1.34404411764706, split_value = 6.35,
                          left = structure(list(split_column_name = "a",
                            criterion_value = 0.294666666666667, split_value = 5.85,
                            prediction = 1.7875, count = 8L), .Names = c("split_column_name",
                          "criterion_value", "split_value", "prediction",
                          "count"), row.names = 1L, class = "data.frame"),
                          right = structure(list(split_column_name = "a",
                            criterion_value = 0.564423076923077, split_value = 7.5,
                            prediction = 2.02941176470588, count = 17L), .Names = c("split_column_name",
                          "criterion_value", "split_value", "prediction",
                          "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                        "criterion_value", "split_value", "left", "right"
                        )), right = structure(list(split_column = "b",
                          criterion_value = 0.690972222222222, split_value = 3.25,
                          left = structure(list(split_column_name = "a",
                            criterion_value = 0.28875, split_value = 7.05,
                            prediction = 2.14444444444444, count = 9L), .Names = c("split_column_name",
                          "criterion_value", "split_value", "prediction",
                          "count"), row.names = 1L, class = "data.frame"),
                          right = structure(list(split_column_name = "a",
                            criterion_value = 0.148333333333333, split_value = 7.45,
                            prediction = 2.3125, count = 8L), .Names = c("split_column_name",
                          "criterion_value", "split_value", "prediction",
                          "count"), row.names = 1L, class = "data.frame")), .Names = c("split_column",
                        "criterion_value", "split_value", "left", "right"
                        ))), .Names = c("split_column", "criterion_value",
                    "split_value", "left", "right"))), .Names = c("split_column",
                "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
            "criterion_value", "split_value", "left", "right"))), .Names = c("split_column",
        "criterion_value", "split_value", "left", "right"), class = c("aml_tree",
        "list"))
    expect_equal(one_tree, expected_tree)
})

test_that("single tree prediction works correctly", {
    one_tree = create_tree(data, response, evaluation_criterion = sum_of_squares, min_obs = 20, max_depth = 20)
    expect_error(predict(one_tree, data.frame(beans=1, pizza=2)), "ERROR: Split column not provided in prediction data row")
    expect_error(predict(one_tree, data.frame(a=rnorm(10), b=rnorm(10), c = rnorm(10))), "ERROR: data must be a data.frame of dimension 1 x p")
    expect_error(predict(one_tree, c(1, 2, 3)), "ERROR: data must be a data.frame")

    expected_predictions = c(0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,0.246000,1.300000,1.300000,1.983636,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.983636,1.300000,1.983636,1.300000,1.300000,1.300000,1.983636,1.983636,1.300000,1.300000,1.300000,1.300000,1.300000,1.983636,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.300000,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.300000,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636,1.983636)
    predictions = sapply(1:nrow(data), function(i){predict(one_tree, data[i,])})
    expect_equal(expected_predictions, predictions, tolerance = .00001)

    expect_equal(predict(one_tree, data.frame(c=1)), .246, tolerance = .00001)
    expect_equal(predict(one_tree, data.frame(c=3)), 1.3, tolerance = .00001) 
    expect_equal(predict(one_tree, data.frame(c=10)), 1.983636, tolerance = .00001) 

})

test_that("random forest prediction works correctly", {
    set.seed(1337)
    forest = aml_random_forest(data, response, evaluation_criterion = sum_of_squares, b = 25, m = 2, min_obs = 20, max_depth = 20)
    expect_error(predict(forest, data.frame(beans=1, pizza=2)), "ERROR: Split column not provided in prediction data row")
    expect_error(predict(forest, data.frame(a=rnorm(10), b=rnorm(10), c = rnorm(10))), "ERROR: data must be a data.frame of dimension 1 x p")
    expect_error(predict(forest, c(1, 2, 3)), "ERROR: data must be a data.frame")

    expected_predictions = c(0.302354120762067, 0.290477871864219, 0.290477871864219, 0.293961742831961, 0.29461251422046, 0.305837991729809, 0.290477871864219, 0.298096385188202, 0.290477871864219, 0.293961742831961, 0.305837991729809, 0.293961742831961, 0.290477871864219, 0.290477871864219, 0.577327158467041, 0.533238711341917, 0.302354120762067, 0.302354120762067, 0.533238711341917, 0.305837991729809, 0.305837991729809, 0.305837991729809, 0.290477871864219, 0.305837991729809, 0.293961742831961, 0.298096385188202, 0.298096385188202, 0.305837991729809, 0.302354120762067, 0.293961742831961, 0.293961742831961, 0.305837991729809, 0.305837991729809, 0.302354120762067, 0.293961742831961, 0.29461251422046, 0.302354120762067, 0.290477871864219, 0.290477871864219, 0.305837991729809, 0.29461251422046, 0.290477871864219, 0.290477871864219, 0.298096385188202, 0.305837991729809, 0.290477871864219, 0.305837991729809, 0.290477871864219, 0.305837991729809, 0.29461251422046, 1.47450315339333, 1.47450315339333, 1.86984880426984, 1.07835265698102, 1.45830025484261, 1.35842601367282, 1.47450315339333, 0.960267890280962, 1.45830025484261, 1.07835265698102, 0.960267890280962, 1.36459309395339, 1.35332569468599, 1.40599833176569, 1.26681337659312, 1.43309791558104, 1.35842601367282, 1.35332569468599, 1.45830025484261, 1.30575337659312, 1.71687844534765, 1.35332569468599, 1.85364590571911, 1.40599833176569, 1.41689501703031, 1.41689501703031, 1.76918036842457, 1.85364590571911, 1.40599833176569, 1.18766860989307, 1.07835265698102, 1.03941265698102, 1.35332569468599, 1.85110294526614, 1.13102529406071, 1.40599833176569, 1.47450315339333, 1.41689501703031, 1.30575337659312, 1.07835265698102, 1.08962005624841, 1.40599833176569, 1.35332569468599, 0.960267890280962, 1.31702077586052, 1.31702077586052, 1.31702077586052, 1.41689501703031, 0.960267890280962, 1.30575337659312, 1.99010540973436, 1.85110294526614, 1.96176172443416, 1.96176172443416, 1.96176172443416, 1.96176172443416, 1.13102529406071, 1.96176172443416, 1.96176172443416, 1.99010540973436, 1.93174855364327, 1.95005482788243, 1.95005482788243, 1.75377166454932, 1.85110294526614, 1.97839851318264, 1.95005482788243, 1.99010540973436, 1.96176172443416, 1.80134398264219, 1.99010540973436, 1.75377166454932, 1.96176172443416, 1.85364590571911, 1.99010540973436, 1.99010540973436, 1.76918036842457, 1.80134398264219, 1.96176172443416, 1.96176172443416, 1.96176172443416, 1.99010540973436, 1.96176172443416, 1.90340486834306, 1.90945980135723, 1.96176172443416, 1.99010540973436, 1.97839851318264, 1.71687844534765, 1.97839851318264, 1.99010540973436, 1.93174855364327, 1.85110294526614, 1.99010540973436, 1.99010540973436, 1.95005482788243, 1.85364590571911, 1.95005482788243, 1.97839851318264, 1.85110294526614)
    predictions = sapply(1:nrow(data), function(i){predict(forest, data[i,])})
    expect_equal(expected_predictions, predictions, tolerance = .00001)

    set.seed(8675309)
    forest = aml_random_forest(data, response, evaluation_criterion = sum_of_squares, b = 2, m = 2, min_obs = 20, max_depth = 20)

    expect_equal(predict(forest, data.frame(a=1, b=1, c=1)), mean(c(0.2375, 0.2410714)), tolerance = .00001)
    expect_equal(predict(forest, data.frame(a=1, b=10, c=2.5)), mean(c(0.2375, 1.3)), tolerance = .00001)

    expect_equal(predict(forest, data.frame(a=10, b=1, c=10)), mean(c(1.973333, 1.998039)), tolerance = .00001)
    expect_equal(predict(forest, data.frame(a=10, b=10, c=4)), mean(c(1.352381, 1.3)), tolerance = .00001)
})


context("gbm testing")


# Code used to generate and save the ablone data
# aburl = 'http://archive.ics.uci.edu/ml/machine-learning-databases/abalone/abalone.data'
# abnames = c('sex','length','diameter','height','weight.w','weight.s','weight.v','weight.sh','rings')
# abalone = read.table(aburl, header = F , sep = ',', col.names = abnames)
# abalone$sex = as.numeric(abalone$sex)
# response = abalone$rings
# data = abalone
# data$rings = NULL
# abalone_data = list(data=data, response=response)
# saveRDS(abalone_data, 'abalone_data.RDS')
abalone_data_file = system.file("external_data", "abalone_data.RDS", package="ArtisanalMachineLearning", mustWork=TRUE)
abalone_data = readRDS(abalone_data_file)
gbm = aml_gbm(abalone_data$data, abalone_data$response, learning_rate = .25, n_trees = 3, evaluation_criterion = sum_of_squares, min_obs = 10, max_depth = 4, verbose = FALSE)
gbm_predictions = predict_all(gbm, abalone_data$data, n_trees = 3)




test_that('small gbm is trained correctly', {
    expected_gbm = structure(list(structure(list(tree = structure(list(split_column = "weight.sh", 
        criterion_value = 31161.2633751672, split_value = 0.16775, 
        left = structure(list(split_column = "weight.sh", criterion_value = 4835.3511353183, 
            split_value = 0.05875, left = structure(list(split_column = "weight.sh", 
                criterion_value = 578.695543000628, split_value = 0.0265, 
                left = structure(list(split_column_name = "weight.w", 
                    criterion_value = 96.44, split_value = 0.02325, 
                    prediction = -5.47605734388885, count = 118L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 2L, class = "data.frame"), right = structure(list(
                    split_column_name = "diameter", criterion_value = 410.878787878788, 
                    split_value = 0.2225, prediction = -3.64973384524897, 
                    count = 243L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 4L, class = "data.frame")), .Names = c("split_column", 
            "criterion_value", "split_value", "left", "right")), 
            right = structure(list(split_column = "weight.sh", criterion_value = 3596.30728417012, 
                split_value = 0.11175, left = structure(list(split_column_name = "sex", 
                    criterion_value = 1202.2196748096, split_value = 2.5, 
                    prediction = -2.38250336017071, count = 508L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 3L, class = "data.frame"), right = structure(list(
                    split_column_name = "weight.s", criterion_value = 2093.97582783856, 
                    split_value = 0.23225, prediction = -1.1630751435365, 
                    count = 558L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 7L, class = "data.frame")), .Names = c("split_column", 
            "criterion_value", "split_value", "left", "right"))), .Names = c("split_column", 
        "criterion_value", "split_value", "left", "right")), right = structure(list(
            split_column = "weight.sh", criterion_value = 22278.8532695375, 
            split_value = 0.37475, left = structure(list(split_column = "weight.sh", 
                criterion_value = 13872.600952381, split_value = 0.24925, 
                left = structure(list(split_column_name = "weight.s", 
                    criterion_value = 4219.47619047619, split_value = 0.24325, 
                    prediction = 0.0210774422289866, count = 840L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 7L, class = "data.frame"), right = structure(list(
                    split_column_name = "weight.s", criterion_value = 7924.81474455454, 
                    split_value = 0.44375, prediction = 1.17831553746708, 
                    count = 1250L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 7L, class = "data.frame")), .Names = c("split_column", 
            "criterion_value", "split_value", "left", "right")), 
            right = structure(list(split_column = "weight.s", criterion_value = 6823.78381607936, 
                split_value = 0.53525, left = structure(list(split_column_name = "weight.sh", 
                    criterion_value = 2245.10869565217, split_value = 0.5075, 
                    prediction = 4.94830311510683, count = 161L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 1L, class = "data.frame"), right = structure(list(
                    split_column_name = "weight.sh", criterion_value = 3700.06811594203, 
                    split_value = 0.56875, prediction = 2.21461213065345, 
                    count = 499L), .Names = c("split_column_name", 
                "criterion_value", "split_value", "prediction", "count"
                ), row.names = 1L, class = "data.frame")), .Names = c("split_column", 
            "criterion_value", "split_value", "left", "right"))), .Names = c("split_column", 
        "criterion_value", "split_value", "left", "right"))), .Names = c("split_column", 
    "criterion_value", "split_value", "left", "right"), class = c("aml_tree", 
    "list")), tree_predictions = c(-1.1630751435365, -2.38250336017071, 
    0.0210774422289866, -1.1630751435365, -3.64973384524897, -1.1630751435365, 
    1.17831553746708, 1.17831553746708, -1.1630751435365, 1.17831553746708, 
    0.0210774422289866, -1.1630751435365, 0.0210774422289866, 0.0210774422289866, 
    0.0210774422289866, 0.0210774422289866, -1.1630751435365, -1.1630751435365, 
    -2.38250336017071, -1.1630751435365, -2.38250336017071, -2.38250336017071, 
    1.17831553746708, 0.0210774422289866, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 0.0210774422289866, 
    1.17831553746708, 2.21461213065345, 1.17831553746708, 2.21461213065345, 
    2.21461213065345, -1.1630751435365, 1.17831553746708, -1.1630751435365, 
    1.17831553746708, -2.38250336017071, -1.1630751435365, 1.17831553746708, 
    -5.47605734388885, -5.47605734388885, -5.47605734388885, -2.38250336017071, 
    -1.1630751435365, -1.1630751435365, -3.64973384524897, 0.0210774422289866, 
    0.0210774422289866, -2.38250336017071, -1.1630751435365, -1.1630751435365, 
    -2.38250336017071, 0.0210774422289866, -1.1630751435365, 0.0210774422289866, 
    -5.47605734388885, 0.0210774422289866, -1.1630751435365, 0.0210774422289866, 
    0.0210774422289866, -2.38250336017071, 0.0210774422289866, -1.1630751435365, 
    1.17831553746708, 4.94830311510683, 0.0210774422289866, -3.64973384524897, 
    1.17831553746708, -2.38250336017071, 4.94830311510683, 4.94830311510683, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 4.94830311510683, 
    1.17831553746708, 4.94830311510683, 1.17831553746708, 4.94830311510683, 
    4.94830311510683, 1.17831553746708, -1.1630751435365, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 4.94830311510683, 4.94830311510683, 
    2.21461213065345, 2.21461213065345, 1.17831553746708, -1.1630751435365, 
    -1.1630751435365, -1.1630751435365, -2.38250336017071, 1.17831553746708, 
    1.17831553746708, 0.0210774422289866, 1.17831553746708, 0.0210774422289866, 
    1.17831553746708, 0.0210774422289866, 0.0210774422289866, -1.1630751435365, 
    -1.1630751435365, 0.0210774422289866, -2.38250336017071, -1.1630751435365, 
    0.0210774422289866, 0.0210774422289866, 0.0210774422289866, -1.1630751435365, 
    1.17831553746708, -2.38250336017071, -1.1630751435365, -2.38250336017071, 
    1.17831553746708, -2.38250336017071, -2.38250336017071, -3.64973384524897, 
    -2.38250336017071, -2.38250336017071, 2.21461213065345, 2.21461213065345, 
    4.94830311510683, -1.1630751435365, -2.38250336017071, -2.38250336017071, 
    -3.64973384524897, -1.1630751435365, -3.64973384524897, -2.38250336017071, 
    -1.1630751435365, -2.38250336017071, 0.0210774422289866, 1.17831553746708, 
    4.94830311510683, 0.0210774422289866, 0.0210774422289866, 0.0210774422289866, 
    -1.1630751435365, -3.64973384524897, -5.47605734388885, -5.47605734388885, 
    1.17831553746708, 1.17831553746708, 4.94830311510683, 1.17831553746708, 
    1.17831553746708, 0.0210774422289866, 1.17831553746708, 2.21461213065345, 
    1.17831553746708, 4.94830311510683, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 2.21461213065345, 2.21461213065345, 2.21461213065345, 
    2.21461213065345, 2.21461213065345, 2.21461213065345, 4.94830311510683, 
    2.21461213065345, 1.17831553746708, 1.17831553746708, 0.0210774422289866, 
    -5.47605734388885, -2.38250336017071, -3.64973384524897, -3.64973384524897, 
    -5.47605734388885, 1.17831553746708, 1.17831553746708, 4.94830311510683, 
    1.17831553746708, 1.17831553746708, 2.21461213065345, 1.17831553746708, 
    1.17831553746708, 2.21461213065345, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, -1.1630751435365, 
    0.0210774422289866, 0.0210774422289866, 0.0210774422289866, 4.94830311510683, 
    1.17831553746708, 1.17831553746708, -1.1630751435365, 1.17831553746708, 
    0.0210774422289866, 1.17831553746708, -1.1630751435365, -1.1630751435365, 
    -1.1630751435365, -1.1630751435365, 1.17831553746708, -2.38250336017071, 
    0.0210774422289866, -2.38250336017071, -1.1630751435365, 0.0210774422289866, 
    0.0210774422289866, 1.17831553746708, -1.1630751435365, -2.38250336017071, 
    -1.1630751435365, -2.38250336017071, -1.1630751435365, 0.0210774422289866, 
    0.0210774422289866, -1.1630751435365, -2.38250336017071, -1.1630751435365, 
    -2.38250336017071, -2.38250336017071, 1.17831553746708, 0.0210774422289866, 
    1.17831553746708, 1.17831553746708, 4.94830311510683, -3.64973384524897, 
    -1.1630751435365, -3.64973384524897, -5.47605734388885, -5.47605734388885, 
    -5.47605734388885, -5.47605734388885, 1.17831553746708, -3.64973384524897, 
    -5.47605734388885, -3.64973384524897, -2.38250336017071, -2.38250336017071, 
    -3.64973384524897, -2.38250336017071, -3.64973384524897, -2.38250336017071, 
    -2.38250336017071, 1.17831553746708, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 4.94830311510683, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 1.17831553746708, 
    0.0210774422289866, -5.47605734388885, -3.64973384524897, -1.1630751435365, 
    0.0210774422289866, -2.38250336017071, 1.17831553746708, 0.0210774422289866, 
    4.94830311510683, 1.17831553746708, 4.94830311510683, 2.21461213065345, 
    4.94830311510683, 2.21461213065345, 4.94830311510683, 4.94830311510683, 
    2.21461213065345, 1.17831553746708, 1.17831553746708, -2.38250336017071, 
    -1.1630751435365, 0.0210774422289866, 1.17831553746708, 1.17831553746708, 
    0.0210774422289866, 0.0210774422289866, 0.0210774422289866, 0.0210774422289866, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 1.17831553746708, 
    4.94830311510683, -3.64973384524897, -3.64973384524897, -3.64973384524897, 
    -1.1630751435365, -2.38250336017071, -2.38250336017071, 1.17831553746708, 
    -2.38250336017071, -2.38250336017071, -1.1630751435365, -5.47605734388885, 
    -5.47605734388885, 4.94830311510683, 0.0210774422289866, 1.17831553746708, 
    4.94830311510683, 1.17831553746708, 1.17831553746708, 4.94830311510683, 
    4.94830311510683, -1.1630751435365, 2.21461213065345, -1.1630751435365, 
    1.17831553746708, -2.38250336017071, -3.64973384524897, -5.47605734388885, 
    -2.38250336017071, -3.64973384524897, -2.38250336017071, -2.38250336017071, 
    -2.38250336017071, 0.0210774422289866, -2.38250336017071, -2.38250336017071, 
    0.0210774422289866, -2.38250336017071, -3.64973384524897, -5.47605734388885, 
    2.21461213065345, 1.17831553746708, 1.17831553746708, 4.94830311510683, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 4.94830311510683, 
    1.17831553746708, 0.0210774422289866, 0.0210774422289866, 0.0210774422289866, 
    1.17831553746708, -3.64973384524897, -2.38250336017071, 1.17831553746708, 
    0.0210774422289866, 1.17831553746708, 0.0210774422289866, 0.0210774422289866, 
    1.17831553746708, 2.21461213065345, 2.21461213065345, 2.21461213065345, 
    2.21461213065345, 2.21461213065345, 1.17831553746708, 1.17831553746708, 
    2.21461213065345, 1.17831553746708, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 2.21461213065345, 
    2.21461213065345, 2.21461213065345, 2.21461213065345, 4.94830311510683, 
    4.94830311510683, 2.21461213065345, 1.17831553746708, 1.17831553746708, 
    1.17831553746708, 1.17831553746708, 4.94830311510683, 1.17831553746708, 
    0.0210774422289866, 0.0210774422289866, 0.0210774422289866, -1.1630751435365, 
    0.0210774422289866, -1.1630751435365, 0.0210774422289866, -1.1630751435365, 
    -2.38250336017071, 0.0210774422289866, 0.0210774422289866, -2.38250336017071, 
    -2.38250336017071, -1.1630751435365, 0.0210774422289866, 0.0210774422289866, 
    1.17831553746708, 1.17831553746708, 0.0210774422289866, 0.0210774422289866, 
    -1.1630751435365, 0.0210774422289866, -2.38250336017071, 0.0210774422289866, 
    -1.1630751435365, 1.17831553746708, 1.17831553746708, 0.0210774422289866, 
    1.17831553746708, 1.17831553746708, 1.17831553746708, 0.0210774422289866, 
    4.94830311510683, 1.17831553746708, 2.21461213065345, 4.94830311510683, 
    1.17831553746708, 0.0210774422289866, 4.94830311510683, -1.1630751435365, 
    0.0210774422289866, -3.64973384524897, -3.64973384524897, 1.17831553746708, 
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    -0.551181102362205, 2.888, -1.5511811023622, -1.5511811023622, 
    -1.28395061728395, -1.5511811023622, 0.448818897637795, 6.85170340681363, 
    5.85170340681363, 2.11801242236025, 0.229390681003584, -0.551181102362205, 
    -0.551181102362205, 0.716049382716049, -0.770609318996416, 0.716049382716049, 
    1.4488188976378, 0.229390681003584, 1.4488188976378, 0.0452380952380952, 
    -1.112, 1.11801242236025, 1.0452380952381, 0.0452380952380952, 
    0.0452380952380952, 1.22939068100358, 2.71604938271605, 0.542372881355933, 
    -0.457627118644067, 3.888, -2.112, -4.88198757763975, -1.112, 
    0.888, 0.0452380952380952, 1.888, 3.85170340681363, 1.888, -1.88198757763975, 
    1.888, 1.888, 0.888, 5.85170340681363, 3.85170340681363, 1.85170340681363, 
    7.85170340681363, 7.85170340681363, 1.85170340681363, -2.88198757763975, 
    1.85170340681363, -4.112, -3.112, -1.9547619047619, 0.542372881355933, 
    -0.551181102362205, -1.28395061728395, 1.71604938271605, -0.457627118644067, 
    -0.112, 2.888, 6.11801242236025, -1.112, -1.112, -0.148296593186373, 
    1.888, 0.888, -2.14829659318637, -0.112, -2.112, 1.888, 0.888, 
    2.888, -0.770609318996416, 0.0452380952380952, 2.0452380952381, 
    1.0452380952381, 1.11801242236025, 3.888, -1.112, 0.229390681003584, 
    1.888, 2.0452380952381, 1.888, -0.770609318996416, 0.229390681003584, 
    0.229390681003584, -0.770609318996416, 1.888, -0.551181102362205, 
    0.0452380952380952, -0.551181102362205, 3.22939068100358, -0.954761904761905, 
    4.0452380952381, -1.112, -0.770609318996416, -0.551181102362205, 
    1.22939068100358, 0.448818897637795, 0.229390681003584, 1.0452380952381, 
    -0.954761904761905, 2.22939068100358, 2.4488188976378, 0.229390681003584, 
    -0.551181102362205, -0.551181102362205, -0.112, 5.0452380952381, 
    1.888, 2.888, 7.11801242236025, 0.716049382716049, 3.22939068100358, 
    2.71604938271605, -3.45762711864407, -1.45762711864407, -1.45762711864407, 
    0.542372881355933, 5.888, -1.28395061728395, 0.542372881355933, 
    1.71604938271605, 0.448818897637795, 2.4488188976378, 6.71604938271605, 
    1.4488188976378, 0.716049382716049, -0.551181102362205, -0.551181102362205, 
    1.888, 0.888, 3.888, 3.888, 3.888, 4.11801242236025, -1.112, 
    3.888, 1.888, -0.112, 0.888, 1.0452380952381, -0.457627118644067, 
    -0.283950617283951, 2.22939068100358, 4.0452380952381, 0.448818897637795, 
    -2.112, 3.0452380952381, 7.11801242236025, 4.888, -0.881987577639752, 
    2.85170340681363, -1.88198757763975, 9.85170340681363, -2.88198757763975, 
    3.11801242236025, 7.85170340681363, -0.112, 3.888, -0.551181102362205, 
    0.229390681003584, 4.0452380952381, 2.888, -1.112, 0.0452380952380952, 
    7.0452380952381, -0.954761904761905, 0.0452380952380952, 5.888, 
    0.888, 3.888, 7.888, 11.1180124223603, -0.283950617283951, -0.283950617283951, 
    -2.28395061728395, 2.22939068100358, 1.4488188976378, 1.4488188976378, 
    1.888, 0.448818897637795, -1.5511811023622, 1.22939068100358, 
    -0.457627118644067, -1.45762711864407, -1.88198757763975, 4.0452380952381, 
    -1.112, 6.11801242236025, 2.888, 7.888, 8.11801242236025, 8.11801242236025, 
    -0.770609318996416, 1.85170340681363, 1.22939068100358, 6.888, 
    -1.5511811023622, -1.28395061728395, -0.457627118644067, 3.4488188976378, 
    -1.28395061728395, -0.551181102362205, -0.551181102362205, -0.551181102362205, 
    2.0452380952381, 0.448818897637795, 0.448818897637795, 2.0452380952381, 
    0.448818897637795, -1.28395061728395, 0.542372881355933, 3.85170340681363, 
    -0.112, 2.888, 1.11801242236025, 1.888, 3.888, 2.888, -0.881987577639752, 
    0.888, 2.0452380952381, -1.9547619047619, 3.0452380952381, -2.112, 
    -0.283950617283951, 0.448818897637795, 2.888, -1.9547619047619, 
    10.888, 2.0452380952381, -0.954761904761905, 4.888, 7.85170340681363, 
    0.851703406813627, 5.85170340681363, 4.85170340681363, 3.85170340681363, 
    6.888, 0.888, 7.85170340681363, 4.888, 0.888, 7.888, -0.112, 
    -1.112, 0.888, 4.85170340681363, 3.85170340681363, 3.85170340681363, 
    6.85170340681363, -0.881987577639752, -1.88198757763975, 7.85170340681363, 
    -0.112, -1.112, 3.888, 0.888, 0.118012422360248, -1.112, 0.0452380952380952, 
    2.0452380952381, 0.0452380952380952, 0.229390681003584, 2.0452380952381, 
    1.22939068100358, 4.0452380952381, 0.229390681003584, 2.4488188976378, 
    0.0452380952380952, 0.0452380952380952, 1.4488188976378, -1.5511811023622, 
    2.22939068100358, 0.0452380952380952, -1.9547619047619, 0.888, 
    -0.112, -0.954761904761905, -0.954761904761905, -1.77060931899642, 
    0.0452380952380952, -0.551181102362205, 2.0452380952381, -0.770609318996416, 
    4.888, -0.112, -1.9547619047619, 3.888, 2.888, -0.112, 2.0452380952381, 
    -0.881987577639752, 3.888, 7.85170340681363, 5.11801242236025, 
    4.888, 3.0452380952381, -0.881987577639752, 2.22939068100358, 
    3.0452380952381, 1.71604938271605, -0.283950617283951, 1.888, 
    6.888, 7.888, 6.11801242236025, 3.11801242236025, 6.888, 8.888, 
    6.888, 10.888, 4.22939068100358, 1.0452380952381, -0.551181102362205, 
    6.4488188976378, 1.4488188976378, 1.888, 2.4488188976378, 0.448818897637795, 
    7.888, 2.4488188976378, 1.22939068100358, -2.112, -1.88198757763975, 
    1.11801242236025, -2.88198757763975, 6.888, 3.85170340681363, 
    3.85170340681363, 5.888, -0.112, 2.888, 1.0452380952381, 0.118012422360248, 
    1.4488188976378, 2.4488188976378, 1.0452380952381, 3.4488188976378, 
    0.888, 1.54237288135593, 0.542372881355933, 1.54237288135593, 
    0.542372881355933, -0.148296593186373, 0.851703406813627, 4.85170340681363, 
    8.85170340681363, -0.954761904761905, 0.0452380952380952, 1.4488188976378, 
    1.0452380952381, -1.112, 5.888, 0.229390681003584, 2.11801242236025, 
    8.85170340681363, 1.11801242236025, 16.8517034068136, 5.888, 
    5.0452380952381, 7.888, 0.888, 1.888, -0.112, 3.888, 1.0452380952381, 
    2.888, 2.888, 1.888, -3.88198757763975, 0.118012422360248, 5.888, 
    3.888, -2.88198757763975, 7.888, -0.112, -1.112, 2.0452380952381, 
    8.11801242236025, 3.888, 1.888, 2.11801242236025, 3.888, 0.888, 
    3.888, -0.112, 4.888, -1.112, 1.22939068100358, 0.0452380952380952, 
    -0.283950617283951, 0.542372881355933, -0.283950617283951, 1.4488188976378, 
    -1.28395061728395, -2.28395061728395, -0.283950617283951, -1.45762711864407, 
    -1.28395061728395, 1.4488188976378, 0.542372881355933, -0.457627118644067, 
    -0.457627118644067, -1.45762711864407, 4.0452380952381, 0.888, 
    1.4488188976378, 10.0452380952381, 4.22939068100358, 3.22939068100358, 
    1.4488188976378, 1.22939068100358, 2.22939068100358, 1.0452380952381, 
    0.716049382716049, -1.28395061728395, 2.4488188976378, 5.0452380952381, 
    2.22939068100358, 6.22939068100358, -0.770609318996416, 2.4488188976378, 
    4.71604938271605, 1.71604938271605, 2.54237288135593, 2.0452380952381, 
    -0.112, 5.888, 1.888, 0.888, 4.22939068100358, 0.229390681003584, 
    1.22939068100358, 2.888, 0.888, -1.88198757763975, 3.0452380952381, 
    -0.770609318996416, 3.0452380952381, 2.22939068100358, 1.0452380952381, 
    4.0452380952381, 2.4488188976378, 2.0452380952381, 4.4488188976378, 
    0.716049382716049, 3.4488188976378, 7.22939068100358, 5.22939068100358, 
    5.11801242236025, 5.888, -1.112, -0.112, -1.112, -1.112, -0.112, 
    2.11801242236025, -0.112, 4.0452380952381, 6.85170340681363, 
    4.22939068100358, 3.4488188976378, 1.0452380952381, 0.0452380952380952, 
    1.888, 5.22939068100358, 5.4488188976378, 3.0452380952381, 1.4488188976378, 
    8.0452380952381, 4.11801242236025, 2.0452380952381, 1.888, -0.954761904761905, 
    1.888, 0.888, 4.888, 5.888, 2.4488188976378, 5.4488188976378, 
    2.22939068100358, 2.0452380952381, 4.22939068100358, 1.4488188976378, 
    1.22939068100358, 2.4488188976378, 4.4488188976378, 3.22939068100358, 
    -0.457627118644067, 1.4488188976378, 8.0452380952381, 6.22939068100358, 
    4.22939068100358, 3.22939068100358, 0.716049382716049, 2.71604938271605, 
    2.54237288135593, 3.71604938271605, 8.0452380952381, 2.0452380952381, 
    7.0452380952381, 6.22939068100358, 2.0452380952381, 1.22939068100358, 
    0.448818897637795, 9.888, 2.4488188976378, 0.229390681003584, 
    -1.77060931899642, 1.22939068100358, 0.229390681003584, 1.4488188976378, 
    0.448818897637795, -0.551181102362205, -0.283950617283951, 5.22939068100358, 
    3.0452380952381, 0.716049382716049, -1.88198757763975, 7.888, 
    -0.551181102362205, 1.4488188976378, 3.4488188976378, -0.283950617283951, 
    -0.954761904761905, 2.22939068100358, 0.229390681003584, 0.542372881355933, 
    -1.5511811023622, 2.22939068100358, 0.716049382716049, 2.4488188976378, 
    0.716049382716049, 5.888, 1.11801242236025, 3.11801242236025, 
    -0.112, 5.85170340681363, -0.112, 1.22939068100358, 4.4488188976378, 
    10.2293906810036, 2.4488188976378, 2.22939068100358, 5.0452380952381, 
    1.888, 3.0452380952381, 4.0452380952381, 7.0452380952381, 9.0452380952381, 
    11.0452380952381, 13.0452380952381, 12.0452380952381, 2.0452380952381, 
    1.0452380952381, 11.888, 0.448818897637795, -0.551181102362205, 
    0.0452380952380952, -1.77060931899642, 4.888, 0.0452380952380952, 
    3.888, 3.0452380952381, 4.888, 1.0452380952381, -0.112, 0.0452380952380952, 
    0.542372881355933, 3.4488188976378, 1.4488188976378, -0.457627118644067, 
    0.716049382716049, -0.457627118644067, -1.28395061728395, 4.22939068100358, 
    7.22939068100358, 4.4488188976378, 4.0452380952381, 0.229390681003584, 
    4.4488188976378, 0.229390681003584, 1.22939068100358, 3.4488188976378, 
    2.4488188976378, 2.4488188976378, 0.716049382716049, -0.551181102362205, 
    3.4488188976378, 0.716049382716049, 0.448818897637795, 1.4488188976378, 
    0.716049382716049, 1.71604938271605, 1.54237288135593, -0.457627118644067, 
    -2.45762711864407, -1.45762711864407, 1.888, 0.118012422360248, 
    3.888, 2.22939068100358, 7.0452380952381, 2.4488188976378, 3.22939068100358, 
    1.888, 6.22939068100358, -0.112, 3.0452380952381, 3.888, 3.0452380952381, 
    6.888, 0.0452380952380952, 2.0452380952381, 2.0452380952381, 
    2.888, 1.22939068100358, 4.0452380952381, 0.448818897637795, 
    4.0452380952381, 5.888, 8.888, 5.888, 4.85170340681363, 0.229390681003584, 
    2.888, 2.85170340681363, 3.0452380952381, 1.22939068100358, 1.888, 
    1.888, 5.11801242236025, 1.888, 8.888, 0.118012422360248, 1.888, 
    3.888, 3.888, 4.888, 5.888, 1.85170340681363, 2.888, -0.112, 
    1.888, 1.4488188976378, 1.0452380952381, 5.888, -0.112, -1.9547619047619, 
    0.448818897637795, 0.229390681003584, 0.0452380952380952, -0.112, 
    5.0452380952381, 3.0452380952381, 5.0452380952381, 5.0452380952381, 
    1.888, 2.0452380952381, -1.112, -1.5511811023622, 0.542372881355933, 
    3.888, -0.954761904761905, 0.888, 0.229390681003584, 0.888, -1.112, 
    0.0452380952380952, 0.229390681003584, 0.888, 0.888, 5.0452380952381, 
    1.0452380952381, 0.229390681003584, -0.112, 2.22939068100358, 
    0.0452380952380952, 1.22939068100358, 0.229390681003584, -0.551181102362205, 
    1.22939068100358, -0.551181102362205, -0.283950617283951, 5.0452380952381, 
    1.22939068100358, 2.0452380952381, 0.888, 11.0452380952381, 1.54237288135593, 
    0.542372881355933, 0.716049382716049, 0.716049382716049, -0.283950617283951, 
    -1.5511811023622, -0.283950617283951, -0.551181102362205, -0.551181102362205, 
    -1.5511811023622, -0.551181102362205, -1.5511811023622, -0.551181102362205, 
    -0.551181102362205, -1.5511811023622, -1.5511811023622, -1.5511811023622, 
    -0.551181102362205, -1.5511811023622, -1.5511811023622, 0.229390681003584, 
    -0.551181102362205, -0.551181102362205, -0.770609318996416, -1.9547619047619, 
    -0.954761904761905, -1.9547619047619, 0.229390681003584, -1.9547619047619, 
    -0.954761904761905, 0.229390681003584, -1.9547619047619, -1.9547619047619, 
    -0.954761904761905, 1.0452380952381, 0.0452380952380952, -3.112, 
    -1.112, -1.112, -0.954761904761905, -1.112, -2.112, 0.0452380952380952, 
    -2.112, -2.112, 0.888, -1.112, -3.112, -5.112, 0.888, -0.112, 
    -1.112, -0.112, -2.14829659318637, -2.112, 0.888, -1.112, -2.112, 
    -2.88198757763975, -0.112, -2.112, -3.88198757763975, -1.14829659318637, 
    -0.881987577639752, -3.14829659318637, -1.112, -2.112, -3.112, 
    -1.14829659318637, -3.14829659318637, 4.85170340681363, 2.85170340681363, 
    -2.14829659318637, -2.14829659318637, -0.148296593186373, -3.14829659318637, 
    -1.14829659318637, -1.14829659318637, -1.14829659318637, 4.85170340681363, 
    1.54237288135593, 0.542372881355933, -1.45762711864407, -0.283950617283951, 
    -0.457627118644067, 1.54237288135593, -2.28395061728395, -1.28395061728395, 
    -2.28395061728395, -0.283950617283951, -1.28395061728395, -0.283950617283951, 
    1.71604938271605, -1.28395061728395, -0.283950617283951, -0.283950617283951, 
    0.716049382716049, 0.716049382716049, -1.28395061728395, 0.716049382716049, 
    -0.551181102362205, -1.5511811023622, -0.551181102362205, -0.283950617283951, 
    -1.5511811023622, -0.551181102362205, -0.551181102362205, -1.5511811023622, 
    -1.5511811023622, -2.5511811023622, -1.5511811023622, -1.5511811023622, 
    -1.5511811023622, -0.551181102362205, -0.551181102362205, -0.770609318996416, 
    -2.77060931899642, -2.77060931899642, -0.551181102362205, -2.77060931899642, 
    -1.77060931899642, -1.77060931899642, -0.770609318996416, -1.77060931899642, 
    -1.77060931899642, -1.77060931899642, -2.77060931899642, -1.77060931899642, 
    -1.77060931899642, -1.77060931899642, -1.77060931899642, -1.77060931899642, 
    -1.5511811023622, -0.770609318996416, -0.770609318996416, 0.229390681003584, 
    -2.77060931899642, -3.9547619047619, -2.77060931899642, -0.770609318996416, 
    -1.77060931899642, -1.77060931899642, -1.9547619047619, -0.770609318996416, 
    -1.77060931899642, -2.77060931899642, -0.770609318996416, -1.77060931899642, 
    -2.9547619047619, -0.954761904761905, -0.770609318996416, 0.229390681003584, 
    -1.9547619047619, -1.9547619047619, -2.9547619047619, -2.9547619047619, 
    -1.9547619047619, -1.9547619047619, -1.9547619047619, -1.77060931899642, 
    -1.9547619047619, 1.0452380952381, -1.9547619047619, -1.9547619047619, 
    -2.9547619047619, -1.9547619047619, -1.9547619047619, -1.9547619047619, 
    -0.954761904761905, -2.112, -2.112, -1.9547619047619, -1.112, 
    -1.112, -3.112, -1.9547619047619, -2.9547619047619, -2.112, -0.954761904761905, 
    -4.112, -3.112, -1.112, -3.112, -0.954761904761905, -0.112, -3.112, 
    -3.112, 2.22939068100358, -0.112, -2.112, -2.112, -2.112, -2.112, 
    -2.112, -0.112, -0.112, -1.112, -3.112, -1.14829659318637, -1.112, 
    -2.14829659318637, -1.112, -2.112, -3.14829659318637, -3.112, 
    -0.112, -3.112, -1.14829659318637, -1.112, -1.112, -1.14829659318637, 
    -4.88198757763975, -1.112, -1.14829659318637, -4.14829659318637, 
    -3.112, -0.112, -1.112, -4.88198757763975, -2.112, -1.14829659318637, 
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    -1.112, -1.112, 0.0452380952380952, -0.954761904761905, 0.0452380952380952, 
    -0.112, -0.112, -1.112, -0.112, -1.112, -2.112, -1.112, -3.112, 
    -1.112, -3.112, -0.112, -0.112, -2.112, 0.888, -2.14829659318637, 
    -0.112, -2.112, -0.112, 2.85170340681363, -2.112, 0.888, -0.112, 
    -2.112, -1.112, -0.112, -3.88198757763975, -0.112, -2.112, -0.112, 
    -3.88198757763975, -0.112, 0.888, 0.888, -1.112, -0.112, -1.112, 
    -4.88198757763975, -1.112, -2.112, -0.112, -0.148296593186373, 
    -0.112, 3.85170340681363, -1.112, 1.888, -4.88198757763975, -1.14829659318637, 
    -2.14829659318637, -2.112, -2.14829659318637, -0.112, -1.112, 
    -2.88198757763975, -0.148296593186373, -0.148296593186373, -1.14829659318637, 
    -1.14829659318637, -0.148296593186373, -2.14829659318637, -2.14829659318637, 
    -1.14829659318637, 0.851703406813627, 0.851703406813627, -0.148296593186373, 
    0.851703406813627, -2.14829659318637, -0.148296593186373, -1.14829659318637, 
    -1.14829659318637, -1.14829659318637, 0.851703406813627, -0.457627118644067, 
    -0.457627118644067, 0.542372881355933, -0.283950617283951, 0.716049382716049, 
    -0.283950617283951, -1.28395061728395, -0.283950617283951, -0.283950617283951, 
    -0.283950617283951, 0.716049382716049, -0.283950617283951, 0.716049382716049, 
    -0.283950617283951, 1.4488188976378, -1.5511811023622, 0.716049382716049, 
    -1.5511811023622, -0.551181102362205, -0.551181102362205, -0.551181102362205, 
    0.448818897637795, -0.551181102362205, 0.448818897637795, -0.551181102362205, 
    -0.770609318996416, -1.77060931899642, 1.22939068100358, 1.22939068100358, 
    -0.770609318996416, 0.229390681003584, 2.0452380952381, 1.22939068100358, 
    -0.954761904761905, -0.954761904761905, -0.954761904761905, -0.954761904761905, 
    -0.954761904761905, 1.0452380952381, -1.112, -2.112, -0.954761904761905, 
    0.0452380952380952, -2.112, -1.112, 0.0452380952380952, 0.888, 
    -1.112, -0.881987577639752, -3.14829659318637, 0.542372881355933, 
    -1.28395061728395, -1.28395061728395, -0.283950617283951, 1.71604938271605, 
    1.71604938271605, 0.448818897637795, -0.551181102362205, -0.551181102362205, 
    0.448818897637795, -0.551181102362205, -1.5511811023622, 1.4488188976378, 
    -0.770609318996416, -0.770609318996416, -0.770609318996416, -0.770609318996416, 
    -1.77060931899642, -1.77060931899642, 0.229390681003584, -2.9547619047619, 
    -0.770609318996416, -0.770609318996416, -0.770609318996416, -0.954761904761905, 
    -1.9547619047619, -1.77060931899642, -0.770609318996416, -1.9547619047619, 
    -1.9547619047619, 0.0452380952380952, -0.954761904761905, -0.954761904761905, 
    -0.954761904761905, 1.0452380952381, -0.954761904761905, -3.112, 
    -2.9547619047619, -0.112, -2.112, -1.112, -1.9547619047619, -3.112, 
    -2.112, -2.112, -3.112, -2.14829659318637, -1.14829659318637, 
    -0.148296593186373, -2.14829659318637, -1.112, -1.14829659318637, 
    -0.148296593186373, -2.14829659318637, 4.85170340681363, -1.9547619047619, 
    0.0452380952380952, 1.0452380952381, -0.551181102362205, -0.551181102362205, 
    1.0452380952381, -1.77060931899642, -1.9547619047619, 1.22939068100358, 
    2.4488188976378, 9.0452380952381, 1.4488188976378, 1.4488188976378, 
    2.22939068100358, -1.112, 2.888, 2.85170340681363, 14.8517034068136, 
    1.888, -1.28395061728395, 0.229390681003584, -1.9547619047619, 
    -0.551181102362205, -0.457627118644067, -1.45762711864407, -0.283950617283951, 
    -0.551181102362205, -1.9547619047619, 0.229390681003584, -0.551181102362205, 
    0.229390681003584, 2.22939068100358, -0.283950617283951, -0.551181102362205, 
    -0.770609318996416, 0.0452380952380952, -0.551181102362205, -2.88198757763975, 
    2.0452380952381, -2.112, -0.283950617283951, 0.0452380952380952, 
    0.229390681003584, -0.770609318996416, 2.0452380952381, -2.112, 
    -1.112, 4.888, 1.85170340681363, 1.22939068100358, 0.716049382716049, 
    0.229390681003584, 1.22939068100358, 0.229390681003584, 1.4488188976378, 
    1.0452380952381, 2.0452380952381, -0.770609318996416, 0.716049382716049, 
    1.22939068100358, 5.85170340681363, 0.448818897637795, -1.28395061728395, 
    -1.112, 1.11801242236025, -2.88198757763975, 4.85170340681363, 
    2.888, -0.148296593186373, 6.85170340681363, 4.85170340681363, 
    -1.14829659318637, -2.112, -2.5511811023622, -2.112, -1.5511811023622, 
    -2.5511811023622, -0.283950617283951, -0.457627118644067, 0.716049382716049, 
    1.54237288135593, 0.542372881355933, 0.0452380952380952, 1.888, 
    0.888, 5.11801242236025, -0.881987577639752, 3.888, -0.881987577639752, 
    6.11801242236025, 4.888, 1.888, -5.112, -0.283950617283951, 0.229390681003584, 
    -0.954761904761905, 2.888, 2.0452380952381, 0.0452380952380952, 
    -0.112, 0.118012422360248, 2.888, 1.54237288135593, 4.22939068100358, 
    -1.28395061728395, 3.4488188976378, 1.22939068100358, -0.283950617283951, 
    6.11801242236025, -1.88198757763975, 10.1180124223602, 7.888, 
    3.11801242236025, -1.77060931899642, -0.283950617283951, -1.28395061728395, 
    -0.770609318996416, 1.11801242236025, 12.1180124223603, 3.11801242236025, 
    5.888, -1.88198757763975, 4.85170340681363, -0.770609318996416, 
    0.0452380952380952, -0.551181102362205, 1.888, 2.888, 3.0452380952381, 
    -1.9547619047619, 2.11801242236025, -1.88198757763975, -0.881987577639752, 
    -2.112, 1.888, -0.551181102362205, 0.716049382716049, 2.0452380952381, 
    -0.551181102362205, 1.888, -2.112, -2.112, 5.888, 2.888, -1.88198757763975, 
    3.888, 2.11801242236025, 0.448818897637795, -0.770609318996416, 
    3.22939068100358, 2.22939068100358, -2.9547619047619, 1.22939068100358, 
    3.4488188976378, -0.954761904761905, 2.4488188976378, 0.229390681003584, 
    -1.5511811023622, 0.888, -1.14829659318637, -1.88198757763975, 
    -0.881987577639752, -0.112, 1.85170340681363, 2.0452380952381, 
    -1.9547619047619, 1.888, -0.770609318996416, 1.888, -1.112, -0.112, 
    5.888, 1.888, 2.888, 0.851703406813627, 2.888, 0.118012422360248, 
    1.888, 0.888, 6.888, 2.888, 2.85170340681363, 1.888, 2.85170340681363, 
    5.11801242236025, 2.888, 4.11801242236025, -0.954761904761905, 
    0.0452380952380952, 0.229390681003584, -1.9547619047619, 0.0452380952380952, 
    -1.77060931899642, 1.4488188976378, 1.4488188976378, -0.954761904761905, 
    -0.551181102362205, -1.5511811023622, -1.112, -1.5511811023622, 
    0.0452380952380952, 1.4488188976378, -0.283950617283951, 2.0452380952381, 
    -1.112, 1.888, -1.9547619047619, -1.77060931899642, -0.770609318996416, 
    0.0452380952380952, 0.0452380952380952, -0.954761904761905, -0.112, 
    -0.112, 11.888, 0.888, 6.0452380952381, 1.0452380952381, 3.0452380952381, 
    4.22939068100358, -0.551181102362205, 1.71604938271605, 4.888, 
    2.888, 5.888, 1.888, 1.888, 2.0452380952381, 5.0452380952381, 
    2.4488188976378, 4.0452380952381, 2.0452380952381, 0.448818897637795, 
    4.85170340681363, 2.4488188976378, 2.22939068100358, 3.0452380952381, 
    5.0452380952381, 3.888, 0.229390681003584, 3.888, -0.954761904761905, 
    0.851703406813627, 10.8517034068136, 11.888, 6.888, 1.0452380952381, 
    4.85170340681363, 4.85170340681363, -0.112, 0.716049382716049, 
    1.54237288135593, 1.54237288135593, 6.11801242236025, 4.85170340681363, 
    1.888, 1.0452380952381, 4.888, 0.229390681003584, 2.0452380952381, 
    7.888, 5.85170340681363, 4.85170340681363, -0.112, 1.888, -1.88198757763975, 
    5.888, 5.11801242236025, 0.851703406813627, -0.112, 0.888, 3.11801242236025, 
    6.888, 3.888, 0.888, 6.85170340681363, 0.118012422360248, 3.85170340681363, 
    0.888, 0.448818897637795, -1.45762711864407, 4.4488188976378, 
    2.0452380952381, 3.22939068100358, 2.4488188976378, 0.448818897637795, 
    2.0452380952381, 4.4488188976378, 2.4488188976378, 0.542372881355933, 
    0.542372881355933, 1.0452380952381, 6.0452380952381, 2.22939068100358, 
    3.22939068100358, 4.0452380952381, 2.22939068100358, 0.0452380952380952, 
    2.22939068100358, 7.22939068100358, 2.4488188976378, 2.4488188976378, 
    0.716049382716049, 1.85170340681363, 2.888, 2.888, 4.85170340681363, 
    4.0452380952381, 7.0452380952381, 3.0452380952381, 2.0452380952381, 
    7.22939068100358, 3.71604938271605, 3.888, 3.888, -1.112, -0.148296593186373, 
    3.888, -3.112, 1.22939068100358, -0.954761904761905, 0.716049382716049, 
    2.0452380952381, 1.4488188976378, 1.22939068100358, 9.22939068100358, 
    4.71604938271605, 9.22939068100358, 1.22939068100358, 5.4488188976378, 
    3.888, 3.22939068100358, 2.4488188976378, -0.283950617283951, 
    1.888, 2.888, -0.283950617283951, 0.0452380952380952, 1.4488188976378, 
    1.0452380952381, 3.11801242236025, -3.88198757763975, 3.85170340681363, 
    3.85170340681363, 4.0452380952381, 11.888, 2.71604938271605, 
    4.888, 1.4488188976378, 4.22939068100358, -1.112, 0.229390681003584, 
    2.22939068100358, 0.229390681003584, 2.0452380952381, 2.888, 
    -0.283950617283951, -0.551181102362205, 1.4488188976378, 1.22939068100358, 
    2.4488188976378, 1.4488188976378, 1.71604938271605, -1.28395061728395, 
    1.54237288135593, 0.542372881355933, 0.542372881355933, -0.457627118644067, 
    8.888, 4.0452380952381, 1.888, -0.770609318996416, 5.888, 1.0452380952381, 
    1.0452380952381, 1.4488188976378, 6.0452380952381, 0.448818897637795, 
    3.0452380952381, 1.0452380952381, 5.11801242236025, 1.85170340681363, 
    2.888, 2.888, 0.888, 5.85170340681363, 1.888, -0.770609318996416, 
    4.0452380952381, 3.0452380952381, 0.448818897637795, 2.0452380952381, 
    2.888, 4.0452380952381, 0.448818897637795, 1.888, -0.112, 4.0452380952381, 
    5.0452380952381, -1.77060931899642, -1.112, 1.0452380952381, 
    0.448818897637795, 1.4488188976378, 2.0452380952381, 5.0452380952381, 
    0.888, 3.888, 7.888, 2.0452380952381, 1.4488188976378, -1.28395061728395, 
    -0.283950617283951, -1.5511811023622, -0.283950617283951, 0.716049382716049, 
    -1.77060931899642, -1.5511811023622, -1.5511811023622, 0.448818897637795, 
    -1.5511811023622, -0.770609318996416, -1.9547619047619, -0.770609318996416, 
    -0.770609318996416, 1.22939068100358, -1.77060931899642, -1.9547619047619, 
    -2.9547619047619, -0.954761904761905, -0.954761904761905, -0.112, 
    -0.954761904761905, -0.112, -2.112, -2.112, -1.112, -2.112, -3.112, 
    -2.112, -1.112, -1.112, -2.14829659318637, -0.148296593186373, 
    -1.14829659318637, -0.148296593186373, -1.14829659318637, 2.85170340681363, 
    0.851703406813627, 0.851703406813627, -3.14829659318637, 1.85170340681363, 
    -2.14829659318637, -2.14829659318637, -0.457627118644067, -0.457627118644067, 
    0.542372881355933, -0.457627118644067, -1.28395061728395, -1.28395061728395, 
    -0.283950617283951, -0.283950617283951, 0.716049382716049, -0.551181102362205, 
    -1.5511811023622, -1.5511811023622, -0.551181102362205, -1.5511811023622, 
    -0.551181102362205, -0.551181102362205, -2.77060931899642, -1.5511811023622, 
    -1.77060931899642, -2.77060931899642, -0.770609318996416, -1.77060931899642, 
    -2.77060931899642, -0.551181102362205, -1.5511811023622, -1.77060931899642, 
    0.229390681003584, -1.77060931899642, -0.770609318996416, -0.770609318996416, 
    -1.77060931899642, -1.77060931899642, -2.9547619047619, -0.954761904761905, 
    -2.9547619047619, -1.9547619047619, -2.77060931899642, -3.9547619047619, 
    -1.9547619047619, -0.954761904761905, -1.9547619047619, -2.9547619047619, 
    -2.112, -1.9547619047619, -4.112, -1.9547619047619, -1.9547619047619, 
    -4.112, -2.112, -2.112, -0.112, -1.9547619047619, -3.112, -2.112, 
    -3.112, -1.112, -1.112, -3.112, -2.112, -1.112, -2.112, -1.112, 
    -2.112, -3.112, -1.14829659318637, -2.112, -3.112, -0.112, -0.112, 
    -2.112, -0.148296593186373, -2.112, -3.14829659318637, 0.851703406813627, 
    -4.14829659318637, -2.14829659318637, -0.148296593186373, 0.851703406813627, 
    -2.14829659318637, -0.148296593186373, -2.14829659318637, -0.457627118644067, 
    -1.28395061728395, -1.28395061728395, -0.283950617283951, -1.5511811023622, 
    -1.5511811023622, 0.448818897637795, -1.5511811023622, -0.551181102362205, 
    -0.551181102362205, -0.551181102362205, -1.77060931899642, -1.77060931899642, 
    -2.77060931899642, -1.77060931899642, -1.77060931899642, -1.77060931899642, 
    -0.770609318996416, -0.770609318996416, -0.770609318996416, -1.77060931899642, 
    -0.770609318996416, 0.229390681003584, -2.9547619047619, -0.770609318996416, 
    -1.9547619047619, -0.954761904761905, -0.954761904761905, -0.954761904761905, 
    -2.9547619047619, -2.9547619047619, -0.954761904761905, -1.9547619047619, 
    -1.9547619047619, -1.9547619047619, -0.954761904761905, -2.112, 
    -2.112, -0.954761904761905, -1.9547619047619, -1.9547619047619, 
    -2.9547619047619, -1.9547619047619, -1.9547619047619, -2.112, 
    -3.112, -3.112, -2.112, -0.954761904761905, -2.14829659318637, 
    -1.112, -0.954761904761905, -4.112, -0.954761904761905, -1.112, 
    -2.112, -1.112, -0.112, -2.112, -1.112, -0.112, -2.14829659318637, 
    -1.9547619047619, -2.112, -2.112, -2.112, -2.112, -2.112, -1.112, 
    -2.112, -2.112, -2.14829659318637, -2.112, -0.112, 0.851703406813627, 
    0.851703406813627, -1.14829659318637, -1.14829659318637, -2.14829659318637, 
    0.851703406813627, -1.14829659318637, -3.14829659318637, -1.14829659318637, 
    -0.148296593186373, -1.14829659318637, -1.45762711864407, -0.457627118644067, 
    -0.457627118644067, -1.28395061728395, -0.283950617283951, -0.283950617283951, 
    -1.5511811023622, 0.716049382716049, -2.5511811023622, 0.716049382716049, 
    0.448818897637795, -0.551181102362205, -0.551181102362205, 0.448818897637795, 
    0.448818897637795, -0.551181102362205, -0.551181102362205, 0.448818897637795, 
    -0.551181102362205, -1.5511811023622, 0.448818897637795, 0.448818897637795, 
    -0.551181102362205, 0.448818897637795, 0.448818897637795, -0.551181102362205, 
    0.229390681003584, -0.770609318996416, -1.77060931899642, -0.770609318996416, 
    -0.770609318996416, 0.448818897637795, -1.77060931899642, 1.0452380952381, 
    -0.770609318996416, -1.9547619047619, 1.22939068100358, -0.954761904761905, 
    0.229390681003584, -1.9547619047619, 0.229390681003584, -2.9547619047619, 
    -0.770609318996416, -1.9547619047619, 0.0452380952380952, -1.9547619047619, 
    -0.954761904761905, 0.0452380952380952, -3.112, 0.0452380952380952, 
    0.0452380952380952, -0.954761904761905, 0.0452380952380952, -0.954761904761905, 
    1.0452380952381, -3.112, 0.0452380952380952, -0.112, -0.112, 
    -1.112, -0.954761904761905, -1.112, -0.112, -2.112, -1.112, -1.112, 
    -0.954761904761905, -1.9547619047619, -2.112, -1.112, -1.112, 
    -3.112, -0.112, -0.954761904761905, -2.112, -1.112, -0.112, -1.112, 
    -2.112, -1.112, -1.112, -1.112, 0.888, -1.112, 0.888, -4.88198757763975, 
    -0.112, -1.112, -1.112, -0.112, 0.0452380952380952, -2.112, -0.148296593186373, 
    -2.112, -1.14829659318637, -3.14829659318637, 0.851703406813627, 
    -3.14829659318637, -1.14829659318637, -2.14829659318637, -3.14829659318637, 
    0.542372881355933, -0.457627118644067, -0.457627118644067, 0.716049382716049, 
    -0.283950617283951, 0.716049382716049, 1.71604938271605, -1.28395061728395, 
    -1.5511811023622, -0.551181102362205, -0.551181102362205, -0.551181102362205, 
    -1.77060931899642, -0.770609318996416, 0.229390681003584, -0.770609318996416, 
    -0.954761904761905, -2.9547619047619, -0.954761904761905, -2.9547619047619, 
    -0.954761904761905, -0.954761904761905, -1.9547619047619, -3.112, 
    -2.112, -1.9547619047619, -2.112, -1.112, -2.112, -2.112, -2.112, 
    -1.112, -1.112, -1.112, -1.112, -3.112, -2.112, -1.112, -1.112, 
    -2.88198757763975, -2.112, -3.112, -1.14829659318637, -3.88198757763975, 
    -0.112, -0.112, -1.14829659318637, -1.14829659318637, -2.14829659318637, 
    -0.148296593186373, -2.14829659318637, -1.14829659318637, -0.283950617283951, 
    -2.28395061728395, -1.28395061728395, -0.283950617283951, 0.716049382716049, 
    -1.28395061728395, -0.551181102362205, -0.551181102362205, 0.448818897637795, 
    -1.5511811023622, -0.770609318996416, -1.77060931899642, -0.551181102362205, 
    0.229390681003584, -0.770609318996416, -1.9547619047619, -0.770609318996416, 
    -0.770609318996416, -0.954761904761905, -0.770609318996416, -0.954761904761905, 
    -1.9547619047619, -0.770609318996416, -0.954761904761905, -1.9547619047619, 
    -0.770609318996416, -3.112, -1.9547619047619, -1.112, -1.9547619047619, 
    1.0452380952381, 0.0452380952380952, -1.9547619047619, 0.0452380952380952, 
    -1.9547619047619, -1.9547619047619, -0.954761904761905, -1.9547619047619, 
    -0.954761904761905, -1.9547619047619, -0.954761904761905, -1.9547619047619, 
    -3.112, -1.112, -0.954761904761905, -2.112, -0.112, 1.0452380952381, 
    -2.112, -2.112, -0.954761904761905, -1.112, -1.112, -1.112, -2.112, 
    -1.112, -1.112, -2.112, -0.112, 1.888, -2.112, -1.112, -0.112, 
    -2.88198757763975, -0.112, -0.112, -0.112, -2.112, -1.112, -1.112, 
    -2.112, -1.112, -0.112, -1.112, -0.112, -1.112, 0.0452380952380952, 
    -2.14829659318637, -2.112, -1.112, -4.112, -1.14829659318637, 
    -0.112, -1.112, -3.112, -0.112, -0.112, -1.14829659318637, 0.888, 
    -0.112, -0.148296593186373, 2.85170340681363, -0.148296593186373, 
    -1.14829659318637, -0.148296593186373, -1.88198757763975, -1.112, 
    -1.112, -3.14829659318637, -0.148296593186373, -3.14829659318637, 
    -3.14829659318637, -1.112, -0.112, 0.888, -2.14829659318637, 
    1.888, -1.14829659318637, 0.851703406813627, -0.148296593186373, 
    -0.148296593186373, -1.5511811023622, 0.448818897637795, -1.5511811023622, 
    -3.112, -3.112, -1.77060931899642, -0.770609318996416, -2.112, 
    -1.9547619047619, -1.112, -1.9547619047619, 1.888, -2.14829659318637, 
    -0.954761904761905, -0.954761904761905, -2.112, -3.112, -3.112, 
    -1.14829659318637, -2.112, -2.112, -1.112, -2.112, -2.112, -0.112, 
    -2.112, -0.112, -2.14829659318637, -1.112, -0.112, 0.851703406813627, 
    -0.112, 1.85170340681363, -0.148296593186373, -0.457627118644067, 
    -1.5511811023622, 0.448818897637795, -0.551181102362205, 0.448818897637795, 
    -1.5511811023622, -1.5511811023622, -1.77060931899642, -0.770609318996416, 
    0.229390681003584, -0.770609318996416, -0.770609318996416, 0.229390681003584, 
    -0.770609318996416, -0.770609318996416, 0.229390681003584, -1.77060931899642, 
    -0.770609318996416, -1.9547619047619, -1.77060931899642, 1.0452380952381, 
    1.0452380952381, -1.9547619047619, -0.954761904761905, -0.770609318996416, 
    -4.88198757763975, 0.0452380952380952, -0.112, -2.112, -0.954761904761905, 
    -1.112, 0.0452380952380952, -2.112, -1.9547619047619, 0.0452380952380952, 
    -0.954761904761905, 0.0452380952380952, -0.112, -0.954761904761905, 
    -3.112, -0.954761904761905, -2.88198757763975, -2.112, -2.112, 
    -0.112, 0.888, -3.88198757763975, -0.112, 1.888, -0.112, -0.112, 
    -0.112, -4.88198757763975, -1.14829659318637, -2.112, -5.88198757763975, 
    -0.112, -2.112, -1.14829659318637, 0.888, -1.14829659318637, 
    -2.112, -0.112, -2.14829659318637, -4.88198757763975, -1.14829659318637, 
    -1.14829659318637, -1.14829659318637, -2.14829659318637, -1.14829659318637, 
    -1.14829659318637, 0.851703406813627, 1.85170340681363, -1.14829659318637, 
    -0.457627118644067, 0.542372881355933, 1.54237288135593, -0.551181102362205, 
    -0.551181102362205, 0.448818897637795, -0.770609318996416, 0.0452380952380952, 
    1.22939068100358, 1.0452380952381, 1.0452380952381, -0.954761904761905, 
    0.229390681003584, 0.229390681003584, -0.112, -1.9547619047619, 
    -2.112, 1.22939068100358, -0.112, -3.112, -1.14829659318637, 
    -2.14829659318637, -1.28395061728395, -1.28395061728395, -2.5511811023622, 
    -0.551181102362205, -0.551181102362205, 0.448818897637795, 0.448818897637795, 
    -0.551181102362205, -1.77060931899642, -0.551181102362205, -2.77060931899642, 
    1.22939068100358, -0.770609318996416, -1.9547619047619, 0.0452380952380952, 
    -0.954761904761905, -2.9547619047619, -1.9547619047619, -0.954761904761905, 
    0.0452380952380952, -1.112, -0.112, -2.112, 1.22939068100358, 
    -1.112, -0.112, -1.14829659318637, -1.112, -0.954761904761905, 
    -1.9547619047619, -0.954761904761905, -0.112, 0.0452380952380952, 
    0.0452380952380952, 3.4488188976378, 5.11801242236025, 0.542372881355933, 
    0.542372881355933, -0.457627118644067, -2.112, 3.0452380952381, 
    2.888, 1.888, -0.148296593186373, 11.8517034068136, -2.14829659318637, 
    8.85170340681363, 2.22939068100358, 0.229390681003584, -2.9547619047619, 
    -0.954761904761905, -1.112, 0.229390681003584, -0.954761904761905, 
    -0.283950617283951, 0.716049382716049, -0.283950617283951, 0.118012422360248, 
    -0.954761904761905, -1.88198757763975, -0.954761904761905, 5.85170340681363, 
    3.888, 3.888, -1.112, 2.888, 1.888, 1.0452380952381, -1.5511811023622, 
    0.229390681003584, 1.0452380952381, 3.22939068100358, 5.0452380952381, 
    0.448818897637795, 1.71604938271605, -0.551181102362205, 1.0452380952381, 
    -4.88198757763975, -0.112, 0.851703406813627, 1.0452380952381, 
    -2.77060931899642, -1.9547619047619, 3.85170340681363, -2.9547619047619, 
    0.542372881355933, 0.851703406813627, 4.0452380952381, 8.888, 
    0.888, 3.11801242236025, -1.28395061728395, 0.716049382716049, 
    2.22939068100358, -0.954761904761905, 0.0452380952380952, -1.5511811023622, 
    2.11801242236025, 2.11801242236025, 0.118012422360248, 1.4488188976378, 
    1.71604938271605, 5.0452380952381, 1.4488188976378, 5.22939068100358, 
    0.888, -1.112, 2.888, 3.0452380952381, 2.888, -0.112, 1.11801242236025, 
    1.22939068100358, 2.888, 1.11801242236025, 1.0452380952381, 1.4488188976378, 
    6.888, -3.112, 1.11801242236025, 0.229390681003584, 1.22939068100358, 
    4.22939068100358, 0.229390681003584, -2.88198757763975, -0.112, 
    3.22939068100358, 1.888, 0.888, -1.88198757763975, 1.85170340681363, 
    0.448818897637795, 6.888, 1.85170340681363, 2.85170340681363, 
    3.888, 1.85170340681363, 2.85170340681363, 2.888, 6.85170340681363, 
    0.851703406813627, 1.888, 3.888, -0.112, -0.283950617283951, 
    0.229390681003584, -1.9547619047619, 2.0452380952381, -1.5511811023622, 
    -1.77060931899642, -1.28395061728395, 0.888, -0.954761904761905, 
    -1.77060931899642, 5.85170340681363, 1.888, 0.888, 2.888, 5.888, 
    0.888, 5.22939068100358, 1.0452380952381, 1.22939068100358, 2.22939068100358, 
    0.888, 3.0452380952381, 5.888, 2.22939068100358, 3.0452380952381, 
    6.888, 3.22939068100358, 2.0452380952381, 5.0452380952381, 2.0452380952381, 
    3.11801242236025, 9.11801242236025, 1.0452380952381, 1.888, -0.112, 
    -0.112, 0.851703406813627, 2.888, 2.0452380952381, 3.888, 5.0452380952381, 
    2.0452380952381, -0.954761904761905, 1.0452380952381, 1.888, 
    2.888, 4.0452380952381, 2.888, 2.11801242236025, -1.88198757763975, 
    1.11801242236025, 1.11801242236025, -1.14829659318637, 2.85170340681363, 
    0.888, 6.0452380952381, 4.888, 2.4488188976378, 1.4488188976378, 
    -1.28395061728395, 0.229390681003584, 1.888, 3.22939068100358, 
    7.0452380952381, 3.4488188976378, 2.22939068100358, 1.4488188976378, 
    6.0452380952381, 0.716049382716049, -0.457627118644067, 4.11801242236025, 
    4.888, 1.0452380952381, 6.22939068100358, 4.4488188976378, 4.4488188976378, 
    3.71604938271605, 0.888, 3.85170340681363, 1.888, 0.0452380952380952, 
    2.4488188976378, 1.0452380952381, 3.0452380952381, 3.22939068100358, 
    0.448818897637795, 3.22939068100358, 2.22939068100358, 2.85170340681363, 
    3.85170340681363, 0.888, 5.888, 2.0452380952381, 5.22939068100358, 
    4.22939068100358, 3.0452380952381, 2.0452380952381, 4.0452380952381, 
    3.4488188976378, 4.22939068100358, 0.0452380952380952, 1.0452380952381, 
    3.0452380952381, 5.0452380952381, -0.770609318996416, 1.22939068100358, 
    1.22939068100358, -1.5511811023622, 0.448818897637795, -1.28395061728395, 
    8.888, 7.888, 1.4488188976378, 1.4488188976378, 0.0452380952380952, 
    4.71604938271605, 2.22939068100358, -1.28395061728395, 2.11801242236025, 
    1.888, 5.888, 3.22939068100358, 3.71604938271605, 6.0452380952381, 
    7.888, 1.22939068100358, 1.22939068100358, -0.283950617283951, 
    -1.28395061728395, 1.71604938271605, 1.71604938271605, 0.542372881355933, 
    7.888, 5.0452380952381, 4.0452380952381, 0.716049382716049, 4.22939068100358, 
    1.888, 6.888, 1.888, 4.888, -1.112, 1.888, 6.85170340681363, 
    -1.112, 1.888, -1.88198757763975, 6.888, 2.0452380952381, 1.4488188976378, 
    -0.770609318996416, -1.112, 6.888, 3.0452380952381, 1.4488188976378, 
    0.448818897637795, 0.716049382716049, 0.448818897637795, -0.283950617283951, 
    -0.551181102362205, -0.551181102362205, -1.5511811023622, -0.551181102362205, 
    -1.9547619047619, -0.954761904761905, -1.77060931899642, -2.112, 
    -2.9547619047619, -2.112, -3.112, -3.112, -1.112, -0.112, -2.112, 
    -0.112, -2.14829659318637, -2.14829659318637, 0.851703406813627, 
    0.851703406813627, -0.457627118644067, -0.283950617283951, -0.283950617283951, 
    -2.5511811023622, -1.5511811023622, -1.5511811023622, -1.5511811023622, 
    -0.551181102362205, -1.5511811023622, 0.448818897637795, -1.5511811023622, 
    -0.770609318996416, -1.77060931899642, -1.77060931899642, -0.770609318996416, 
    -1.77060931899642, 0.229390681003584, -0.770609318996416, -0.770609318996416, 
    -0.770609318996416, -1.77060931899642, -2.9547619047619, -2.9547619047619, 
    -3.112, -1.9547619047619, -1.9547619047619, -3.112, -2.112, 0.888, 
    -1.112, -3.112, -3.112, -2.112, -0.112, -4.88198757763975, -1.14829659318637, 
    -1.112, -2.112, -2.112, -1.112, -1.14829659318637, -2.14829659318637, 
    -1.14829659318637, -3.14829659318637, -1.45762711864407, -0.457627118644067, 
    -1.5511811023622, -1.5511811023622, -0.551181102362205, -1.5511811023622, 
    -0.551181102362205, -0.551181102362205, -0.770609318996416, -1.5511811023622, 
    -1.77060931899642, -1.77060931899642, -1.9547619047619, -1.77060931899642, 
    -3.112, -0.770609318996416, -0.770609318996416, -1.9547619047619, 
    0.0452380952380952, -3.112, -1.9547619047619, -1.9547619047619, 
    -0.954761904761905, -1.9547619047619, -1.9547619047619, -0.954761904761905, 
    -1.112, -2.112, -3.112, 0.888, -1.112, -0.112, -1.112, -1.112, 
    -2.112, -0.112, -2.112, -1.112, -3.14829659318637, -0.112, -1.14829659318637, 
    -3.14829659318637, -2.14829659318637, -0.148296593186373, -1.14829659318637, 
    -1.14829659318637, -1.14829659318637, -2.14829659318637, -1.14829659318637, 
    -1.45762711864407, -0.457627118644067, -2.28395061728395, -0.283950617283951, 
    -0.283950617283951, -0.283950617283951, 0.716049382716049, -0.283950617283951, 
    -0.283950617283951, 0.716049382716049, -0.551181102362205, -0.551181102362205, 
    -1.5511811023622, -1.5511811023622, 1.4488188976378, 0.448818897637795, 
    -1.5511811023622, -1.77060931899642, -0.770609318996416, -0.770609318996416, 
    -0.770609318996416, -0.770609318996416, 0.448818897637795, 0.229390681003584, 
    -0.770609318996416, -1.77060931899642, 0.229390681003584, -1.77060931899642, 
    0.229390681003584, -0.770609318996416, -0.954761904761905, -0.770609318996416, 
    -0.954761904761905, -1.9547619047619, -1.9547619047619, -0.954761904761905, 
    -1.9547619047619, 0.0452380952380952, -1.112, -1.112, -0.954761904761905, 
    -1.9547619047619, -3.112, -0.954761904761905, -2.112, -2.112, 
    -1.112, 0.0452380952380952, 1.0452380952381, -2.112, -2.112, 
    -2.112, 0.0452380952380952, -2.112, -3.112, -3.88198757763975, 
    -0.112, -1.112, -0.954761904761905, -1.112, -2.112, -1.112, -2.112, 
    -3.88198757763975, -2.112, -0.112, -1.112, 0.888, -1.14829659318637, 
    -1.14829659318637, -2.112, -1.14829659318637, -4.14829659318637, 
    0.888, -1.14829659318637, -1.112, -1.14829659318637, -0.148296593186373, 
    -0.148296593186373, -0.457627118644067, 0.448818897637795, -2.5511811023622, 
    -0.551181102362205, -0.770609318996416, -0.770609318996416, -1.77060931899642, 
    -0.770609318996416, -2.9547619047619, -0.954761904761905, -0.954761904761905, 
    -1.112, -1.112, -0.112, -0.112, -2.112, 2.888, -0.954761904761905, 
    -1.14829659318637, 0.888, -2.112, -3.112, -1.112, -2.14829659318637, 
    -2.112, -2.14829659318637, -2.14829659318637, -2.14829659318637, 
    0.851703406813627, -0.283950617283951, 0.716049382716049, -1.28395061728395, 
    -1.28395061728395, -1.28395061728395, -0.283950617283951, -1.5511811023622, 
    0.448818897637795, -1.5511811023622, -0.770609318996416, 0.448818897637795, 
    -1.77060931899642, 0.229390681003584, -0.770609318996416, -0.770609318996416, 
    -1.77060931899642, 0.229390681003584, 0.229390681003584, -0.770609318996416, 
    -0.954761904761905, -0.954761904761905, -1.9547619047619, 0.0452380952380952, 
    0.0452380952380952, -0.954761904761905, -0.954761904761905, -0.954761904761905, 
    1.0452380952381, -2.9547619047619, -1.112, -0.954761904761905, 
    0.0452380952380952, 0.0452380952380952, -1.9547619047619, -0.954761904761905, 
    -0.954761904761905, -0.954761904761905, -1.9547619047619, -0.112, 
    -1.112, -2.112, -3.112, -1.112, -1.112, -1.112, 0.888, -1.112, 
    -1.112, -0.112, -1.112, -1.112, -2.112, -0.112, -0.112, -1.112, 
    -0.112, -1.112, 2.888, -0.112, -0.112, -5.88198757763975, -1.88198757763975, 
    -0.148296593186373, -0.112, -1.14829659318637, -1.112, -2.14829659318637, 
    0.851703406813627, -2.88198757763975, -2.14829659318637, -1.14829659318637, 
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    0.129583584181737, -0.0972222222222223, -0.335137713209722, -7.66119828907915, 
    -1.35105393104627, -1.03424630977671, -1.60880354934535, -0.913660603503905, 
    -1.91366060350391, 0.0863393964960946, -2.17128624024365, -0.467324386685025, 
    -0.835942269178833, -0.50235401034485, 1.20833646584563, 0.799660041203293, 
    -1.79166353415437, -0.50235401034485, -0.791663534154374, -1.79166353415437, 
    -3.20033995879671, 0.208336465845626, 0.49764598965515, -2.20033995879671, 
    1.86355635808197, -3.20033995879671, -1.20033995879671, -0.870416415818263, 
    -1.87041641581826, -0.870416415818263, 0.208281412130307, -1.03424630977671, 
    -0.0342463097767067, -0.35105393104627, -1.35105393104627, 0.391196450654647, 
    -0.608803549345353, -0.608803549345353, 0.391196450654647, -1.13644364191803, 
    -0.467324386685025, -2.13644364191803, 0.532675613314975, -1.83594226917883, 
    0.164057730821167, -0.166823013945825, 1.16405773082117, 2.20833646584563, 
    0.49764598965515, 0.49764598965515, -1.79166353415437, 0.164057730821167, 
    -2.20033995879671, -0.456132537755349, 1.20833646584563, 1.79966004120329, 
    -2.20033995879671, -2.20033995879671, -1.20033995879671, 1.79966004120329, 
    -1.20033995879671, -1.20033995879671, -2.20033995879671, -1.47948124006068, 
    -0.870416415818263, -1.87041641581826, -0.993719655853504, -1.13644364191803, 
    -0.125251792988357, -2.20033995879671, -0.200339958796707, -2.20033995879671, 
    -1.60880354934535, -0.608803549345353, -1.60880354934535, -0.608803549345353, 
    0.0863393964960946, -0.913660603503905, 0.0863393964960946, 0.0863393964960946, 
    -2.16682301394582, -2.46732438668502, -1.83594226917883, -3.45613253775535, 
    -0.835942269178833, 0.49764598965515, -1.83594226917883, -1.83594226917883, 
    1.20833646584563, -2.20033995879671, -1.20033995879671, -1.20033995879671, 
    -0.200339958796707, -1.83594226917883, 0.208336465845626, -4.32761003024516, 
    -0.791663534154374, -0.200339958796707, 0.799660041203293, -0.4594141070933, 
    -0.200339958796707, 1.79966004120329, -0.200339958796707, 0.5405858929067, 
    -2.20033995879671, -2.20033995879671, -2.4594141070933, -2.20033995879671, 
    -1.14283685320664, -0.870416415818263, -1.87041641581826, -0.870416415818263, 
    -2.87041641581826, -0.870416415818263, -0.608803549345353, -0.913660603503905, 
    -0.993719655853504, -2.4594141070933, -1.13644364191803, -2.87041641581826, 
    -1.50235401034485, -0.50235401034485, 0.208336465845626, -0.791663534154374, 
    -2.20033995879671, -2.4594141070933, -1.79171858786969, -1.68886260169495, 
    1.08633939649609, 0.0863393964960946, -2.46732438668502, -2.17128624024365, 
    -0.136443641918033, 0.874748207011643, -0.125251792988357, -1.79166353415437, 
    0.164057730821167, -0.125251792988357, 0.874748207011643, -3.66119828907915, 
    1.20833646584563, -1.12525179298836, -0.200339958796707, -2.20033995879671, 
    -0.200339958796707, -0.200339958796707, -1.20033995879671, -3.16290398617403, 
    -1.47948124006068, 1.79966004120329, 1.5405858929067, -0.870416415818263, 
    -0.870416415818263, -1.4594141070933, -0.870416415818263, -0.200339958796707, 
    0.208281412130307, 0.862703716109491, -0.137296283890509, -0.35105393104627, 
    0.391196450654647, -1.60880354934535, -1.91366060350391, -0.993719655853504, 
    -2.17128624024365, 0.0863393964960946, -1.12525179298836, -0.200339958796707, 
    1.20833646584563, -0.688862601694951, -0.608803549345353, -0.608803549345353, 
    -0.608803549345353, -0.171286240243653, 0.00628034414649642, 
    -2.78235992878372, 0.863556358081967, 0.164057730821167, -1.50235401034485, 
    1.16405773082117, 0.208336465845626, -2.20033995879671, -1.20033995879671, 
    0.129583584181737)), .Names = c("tree", "tree_predictions", "tree_residuals"
    )), learning_rate = 0.25, n_trees = 3, mean_value = 9.93368446253292), .Names = c("", 
    "", "", "learning_rate", "n_trees", "mean_value"), class = c("aml_gbm", 
    "list"))
    expect_equal(gbm, expected_gbm)
    expect_equal(gbm[["learning_rate"]], .25)
    expect_equal(gbm[["n_trees"]], 3)
    expect_true(gbm[["mean_value"]] - 9.93 < .009)
    expect_is(gbm, "aml_gbm")
    expect_length(gbm, 6)
})

test_that("small gbm predictions are equivalent", {
    expected_gbm_predictions = c(8.36374221308446, 7.14431399645024, 10.5417850722083, 8.65813385918199, 
        5.34931912998551, 8.09372744999706, 12.2502896052773, 11.6990231674464, 
        8.65813385918199, 12.2502896052773, 10.5417850722083, 8.36374221308446, 
        10.5417850722083, 10.5417850722083, 10.1573219870462, 10.5417850722083, 
        8.09372744999706, 8.40876299209575, 7.14431399645024, 8.36374221308446, 
        7.14431399645024, 6.87429923336285, 11.0327147224206, 10.2090648860165, 
        11.3848838285812, 12.2502896052773, 11.3663029812546, 11.3663029812546, 
        12.2502896052773, 10.2090648860165, 12.2502896052773, 12.8321827304926, 
        11.3848838285812, 12.8321827304926, 12.8321827304926, 8.36374221308446, 
        11.3848838285812, 8.40876299209575, 11.3663029812546, 7.14431399645024, 
        8.40876299209575, 11.3663029812546, 2.95318042885326, 2.64370155610638, 
        2.64370155610638, 6.87429923336285, 8.36374221308446, 8.40876299209575, 
        5.12508162351396, 10.2090648860165, 10.5417850722083, 7.14431399645024, 
        8.65813385918199, 8.40876299209575, 7.14431399645024, 10.5417850722083, 
        8.36374221308446, 9.84228644494748, 2.95318042885326, 10.1573219870462, 
        8.36374221308446, 9.50956625875573, 10.5417850722083, 7.14431399645024, 
        9.84228644494748, 8.36374221308446, 12.2502896052773, 16.7067560570505, 
        10.1573219870462, 5.12508162351396, 11.6990231674464, 7.18933477546154, 
        16.1749385391884, 15.154871406221, 11.3848838285812, 11.0327147224206, 
        12.2502896052773, 12.2502896052773, 11.6990231674464, 11.3848838285812, 
        11.3663029812546, 16.1749385391884, 12.2502896052773, 16.7067560570505, 
        12.2502896052773, 16.7067560570505, 15.154871406221, 11.3663029812546, 
        8.97316940128069, 12.2502896052773, 11.3663029812546, 11.3663029812546, 
        15.6866889240831, 15.154871406221, 13.441247554735, 13.441247554735, 
        11.6990231674464, 8.36374221308446, 8.65813385918199, 8.97316940128069, 
        6.87429923336285, 11.3663029812546, 12.2502896052773, 10.2090648860165, 
        11.3848838285812, 10.5417850722083, 11.6990231674464, 10.5417850722083, 
        10.5417850722083, 8.40876299209575, 8.65813385918199, 9.84228644494748, 
        6.87429923336285, 8.65813385918199, 10.5417850722083, 10.1573219870462, 
        10.5417850722083, 8.65813385918199, 12.2502896052773, 7.14431399645024, 
        8.40876299209575, 6.87429923336285, 11.3663029812546, 7.14431399645024, 
        6.87429923336285, 4.77950392749314, 6.87429923336285, 6.87429923336285, 
        12.8321827304926, 12.8321827304926, 16.1749385391884, 8.40876299209575, 
        6.61654961506376, 6.87429923336285, 4.77950392749314, 8.40876299209575, 
        5.34931912998551, 6.88656437815116, 8.40876299209575, 7.14431399645024, 
        10.2090648860165, 11.6990231674464, 16.1749385391884, 10.2090648860165, 
        9.84228644494748, 10.1573219870462, 8.65813385918199, 4.77950392749314, 
        2.64370155610638, 2.64370155610638, 11.3848838285812, 11.3848838285812, 
        16.1749385391884, 12.2502896052773, 12.2502896052773, 10.2090648860165, 
        12.2502896052773, 13.441247554735, 11.3663029812546, 16.7067560570505, 
        11.9167013464433, 11.0327147224206, 11.3848838285812, 12.8321827304926, 
        13.441247554735, 12.8321827304926, 12.8321827304926, 12.8321827304926, 
        12.8321827304926, 16.1749385391884, 12.8321827304926, 11.3663029812546, 
        11.0327147224206, 10.2090648860165, 2.64370155610638, 6.87429923336285, 
        4.77950392749314, 5.34931912998551, 2.64370155610638, 12.2502896052773, 
        12.2502896052773, 16.1749385391884, 11.9167013464433, 11.9167013464433, 
        12.8321827304926, 11.3848838285812, 11.3663029812546, 12.4211804217676, 
        11.3848838285812, 11.3663029812546, 11.3848838285812, 11.9167013464433, 
        12.2502896052773, 8.09372744999706, 9.87547662718255, 10.2090648860165, 
        10.5417850722083, 16.1749385391884, 11.0327147224206, 11.3663029812546, 
        8.40876299209575, 11.6990231674464, 10.5417850722083, 11.6990231674464, 
        8.36374221308446, 8.97316940128069, 8.09372744999706, 8.09372744999706, 
        12.2502896052773, 6.87429923336285, 10.5417850722083, 6.88656437815116, 
        8.40876299209575, 10.5417850722083, 10.5417850722083, 11.6990231674464, 
        8.36374221308446, 6.87429923336285, 8.65813385918199, 7.18933477546154, 
        8.40876299209575, 10.1573219870462, 10.5417850722083, 8.97316940128069, 
        6.87429923336285, 8.97316940128069, 7.18933477546154, 6.87429923336285, 
        11.9167013464433, 10.5417850722083, 11.3663029812546, 12.2502896052773, 
        16.1749385391884, 4.77950392749314, 8.09372744999706, 5.12508162351396, 
        2.64370155610638, 2.64370155610638, 2.64370155610638, 2.64370155610638, 
        11.3663029812546, 4.77950392749314, 2.95318042885326, 5.12508162351396, 
        6.61654961506376, 6.61654961506376, 5.34931912998551, 6.87429923336285, 
        5.12508162351396, 6.87429923336285, 6.61654961506376, 11.9167013464433, 
        11.3848838285812, 11.3848838285812, 11.3848838285812, 12.2502896052773, 
        16.7067560570505, 12.2502896052773, 11.3848838285812, 11.3848838285812, 
        11.3663029812546, 11.3663029812546, 10.2090648860165, 2.95318042885326, 
        4.77950392749314, 8.97316940128069, 10.2090648860165, 7.14431399645024, 
        11.6990231674464, 10.1573219870462, 16.1749385391884, 11.9167013464433, 
        16.0202771829171, 13.441247554735, 16.7067560570505, 12.8321827304926, 
        16.1749385391884, 16.1749385391884, 13.441247554735, 11.6990231674464, 
        12.2502896052773, 6.87429923336285, 8.40876299209575, 10.5417850722083, 
        12.2502896052773, 11.6990231674464, 10.5417850722083, 10.5417850722083, 
        10.5417850722083, 10.2090648860165, 12.2502896052773, 11.3848838285812, 
        11.9167013464433, 12.2502896052773, 16.0202771829171, 4.77950392749314, 
        4.77950392749314, 4.77950392749314, 8.36374221308446, 7.14431399645024, 
        7.18933477546154, 12.2502896052773, 7.14431399645024, 7.14431399645024, 
        8.40876299209575, 2.64370155610638, 2.64370155610638, 16.1749385391884, 
        10.5417850722083, 11.3663029812546, 15.154871406221, 11.0327147224206, 
        11.3848838285812, 16.7067560570505, 16.7067560570505, 8.09372744999706, 
        12.4211804217676, 8.36374221308446, 12.2502896052773, 6.61654961506376, 
        4.77950392749314, 2.64370155610638, 7.14431399645024, 4.77950392749314, 
        7.14431399645024, 6.87429923336285, 6.61654961506376, 10.5417850722083, 
        7.14431399645024, 6.87429923336285, 10.5417850722083, 7.18933477546154, 
        4.77950392749314, 2.95318042885326, 13.441247554735, 11.3848838285812, 
        11.9167013464433, 16.1749385391884, 11.3848838285812, 11.0327147224206, 
        11.3848838285812, 16.1749385391884, 11.3848838285812, 10.1573219870462, 
        10.5417850722083, 9.84228644494748, 11.6990231674464, 5.34931912998551, 
        6.87429923336285, 11.0327147224206, 9.87547662718255, 11.3663029812546, 
        9.87547662718255, 9.87547662718255, 11.3848838285812, 12.8321827304926, 
        12.4211804217676, 12.4211804217676, 12.8321827304926, 12.8321827304926, 
        11.3848838285812, 12.2502896052773, 12.8321827304926, 11.9167013464433, 
        11.3848838285812, 11.9167013464433, 11.0327147224206, 11.0327147224206, 
        11.3848838285812, 12.8321827304926, 12.8321827304926, 12.8321827304926, 
        13.441247554735, 16.1749385391884, 15.154871406221, 12.8321827304926, 
        11.0327147224206, 11.0327147224206, 12.2502896052773, 12.2502896052773, 
        16.0202771829171, 11.3663029812546, 10.2090648860165, 10.5417850722083, 
        10.2090648860165, 8.40876299209575, 10.2090648860165, 8.36374221308446, 
        10.5417850722083, 8.09372744999706, 6.87429923336285, 9.84228644494748, 
        10.1573219870462, 6.87429923336285, 6.87429923336285, 8.09372744999706, 
        10.2090648860165, 9.84228644494748, 11.6990231674464, 11.9167013464433, 
        10.1573219870462, 10.5417850722083, 8.97316940128069, 10.2090648860165, 
        6.87429923336285, 10.2090648860165, 8.36374221308446, 11.3663029812546, 
        11.0327147224206, 10.2090648860165, 11.3848838285812, 11.0327147224206, 
        11.0327147224206, 10.2090648860165, 15.154871406221, 12.2502896052773, 
        12.4211804217676, 16.1749385391884, 12.2502896052773, 10.5417850722083, 
        16.1749385391884, 8.65813385918199, 10.5417850722083, 5.12508162351396, 
        4.77950392749314, 11.9167013464433, 12.2502896052773, 12.2502896052773, 
        16.0202771829171, 16.0202771829171, 12.2502896052773, 11.9167013464433, 
        12.2502896052773, 11.6990231674464, 8.09372744999706, 10.5417850722083, 
        6.87429923336285, 6.87429923336285, 7.14431399645024, 11.6990231674464, 
        6.87429923336285, 6.87429923336285, 11.6990231674464, 6.87429923336285, 
        8.40876299209575, 11.6990231674464, 16.0202771829171, 16.0202771829171, 
        15.154871406221, 11.3663029812546, 12.8321827304926, 13.441247554735, 
        11.3848838285812, 11.0327147224206, 11.3848838285812, 10.2090648860165, 
        15.154871406221, 6.87429923336285, 6.87429923336285, 10.5417850722083, 
        7.14431399645024, 11.3663029812546, 2.95318042885326, 2.95318042885326, 
        2.95318042885326, 2.64370155610638, 12.4211804217676, 13.441247554735, 
        13.441247554735, 13.441247554735, 10.2090648860165, 10.1573219870462, 
        6.87429923336285, 10.1573219870462, 11.6990231674464, 11.6990231674464, 
        8.40876299209575, 16.1749385391884, 12.8321827304926, 16.1749385391884, 
        12.8321827304926, 12.2502896052773, 10.2090648860165, 11.0327147224206, 
        11.9167013464433, 12.2502896052773, 11.3663029812546, 11.3848838285812, 
        10.2090648860165, 11.0327147224206, 11.0327147224206, 11.3663029812546, 
        16.1749385391884, 16.1749385391884, 11.3848838285812, 12.2502896052773, 
        16.7067560570505, 11.9167013464433, 11.9167013464433, 12.2502896052773, 
        10.2090648860165, 16.0202771829171, 12.2502896052773, 11.9167013464433, 
        16.7067560570505, 11.3848838285812, 12.2502896052773, 12.2502896052773, 
        11.3663029812546, 11.6990231674464, 11.3848838285812, 8.40876299209575, 
        10.5417850722083, 4.77950392749314, 2.95318042885326, 4.77950392749314, 
        7.14431399645024, 4.77950392749314, 5.12508162351396, 5.34931912998551, 
        2.64370155610638, 5.34931912998551, 6.87429923336285, 2.64370155610638, 
        2.64370155610638, 2.64370155610638, 2.64370155610638, 10.5417850722083, 
        11.3663029812546, 7.14431399645024, 10.5417850722083, 8.40876299209575, 
        8.65813385918199, 7.18933477546154, 8.09372744999706, 8.65813385918199, 
        9.84228644494748, 5.12508162351396, 4.77950392749314, 7.18933477546154, 
        10.1573219870462, 8.40876299209575, 8.36374221308446, 8.36374221308446, 
        7.18933477546154, 5.61933389307291, 4.77950392749314, 2.64370155610638, 
        10.2090648860165, 11.3663029812546, 11.3848838285812, 11.9167013464433, 
        11.3663029812546, 8.65813385918199, 8.09372744999706, 8.65813385918199, 
        11.3663029812546, 11.3848838285812, 16.1749385391884, 10.5417850722083, 
        8.40876299209575, 9.84228644494748, 8.97316940128069, 10.5417850722083, 
        10.1573219870462, 6.88656437815116, 9.84228644494748, 6.87429923336285, 
        4.77950392749314, 7.18933477546154, 8.09372744999706, 8.09372744999706, 
        16.7067560570505, 12.2502896052773, 11.9167013464433, 11.3848838285812, 
        11.0327147224206, 11.0327147224206, 11.3663029812546, 16.1749385391884, 
        11.3848838285812, 10.2090648860165, 12.8321827304926, 8.09372744999706, 
        7.18933477546154, 10.5417850722083, 10.5417850722083, 11.3663029812546, 
        8.36374221308446, 7.18933477546154, 10.5417850722083, 7.18933477546154, 
        10.2090648860165, 16.1749385391884, 10.5417850722083, 12.2502896052773, 
        10.5417850722083, 12.2502896052773, 12.2502896052773, 12.2502896052773, 
        11.3663029812546, 7.18933477546154, 7.18933477546154, 8.65813385918199, 
        10.5417850722083, 8.65813385918199, 6.88656437815116, 8.09372744999706, 
        7.14431399645024, 7.14431399645024, 8.40876299209575, 2.64370155610638, 
        6.88656437815116, 9.84228644494748, 8.65813385918199, 8.36374221308446, 
        8.40876299209575, 5.61933389307291, 5.12508162351396, 2.95318042885326, 
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        11.3848838285812, 11.3848838285812, 11.3848838285812, 12.8321827304926, 
        11.3848838285812, 12.8321827304926, 12.8321827304926, 11.3848838285812, 
        12.8321827304926, 12.8321827304926, 2.64370155610638, 2.95318042885326, 
        12.2502896052773, 6.61654961506376, 5.34931912998551, 6.87429923336285, 
        8.09372744999706, 8.09372744999706, 8.09372744999706, 8.65813385918199, 
        9.84228644494748, 10.2090648860165, 9.87547662718255, 11.0327147224206, 
        11.3848838285812, 11.0327147224206, 9.87547662718255, 11.0327147224206, 
        11.0327147224206, 11.3848838285812, 11.0327147224206, 9.87547662718255, 
        11.3848838285812, 9.50956625875573, 11.3848838285812, 11.3848838285812, 
        12.8321827304926, 12.8321827304926, 12.8321827304926, 4.77950392749314, 
        5.34931912998551, 5.34931912998551, 6.61654961506376, 6.61654961506376, 
        6.87429923336285, 6.87429923336285, 6.87429923336285, 6.87429923336285, 
        9.50956625875573, 9.84228644494748, 9.50956625875573, 9.84228644494748, 
        10.2090648860165, 10.2090648860165, 10.5417850722083, 10.2090648860165, 
        11.0327147224206, 9.87547662718255, 9.87547662718255, 11.0327147224206, 
        10.2090648860165, 11.3848838285812, 11.6990231674464, 11.0327147224206, 
        11.3848838285812, 11.3848838285812, 11.3848838285812, 11.3848838285812, 
        11.3848838285812, 11.3848838285812, 11.3848838285812, 11.3848838285812, 
        13.441247554735, 12.8321827304926, 12.8321827304926, 8.36374221308446, 
        9.50956625875573, 11.3663029812546, 11.3848838285812, 11.3848838285812, 
        11.3848838285812, 6.87429923336285, 6.87429923336285, 6.87429923336285, 
        6.87429923336285, 8.09372744999706, 8.09372744999706, 8.09372744999706, 
        8.09372744999706, 10.5417850722083, 9.84228644494748, 10.2090648860165, 
        11.6990231674464, 10.2090648860165, 9.87547662718255, 10.2090648860165, 
        10.2090648860165, 11.0327147224206, 11.3848838285812, 11.3848838285812, 
        11.3848838285812, 11.3848838285812, 10.2090648860165, 11.0327147224206, 
        11.9167013464433, 11.0327147224206, 11.3848838285812, 11.3848838285812, 
        12.4211804217676, 11.3848838285812, 11.3848838285812, 11.3848838285812, 
        12.4211804217676, 11.3848838285812, 11.3848838285812, 12.4211804217676, 
        11.3848838285812, 15.154871406221, 12.8321827304926, 12.8321827304926, 
        12.8321827304926, 12.8321827304926, 12.8321827304926, 6.87429923336285, 
        8.09372744999706, 8.36374221308446, 12.4211804217676, 9.50956625875573, 
        12.8321827304926, 9.87547662718255, 9.87547662718255, 11.0327147224206, 
        11.0327147224206, 11.3848838285812, 12.4211804217676, 4.77950392749314, 
        7.14431399645024, 8.09372744999706, 8.09372744999706, 9.84228644494748, 
        8.65813385918199, 9.50956625875573, 11.3663029812546, 11.3663029812546, 
        11.0327147224206, 10.2090648860165, 11.3663029812546, 11.3663029812546, 
        12.2502896052773, 11.0327147224206, 11.3663029812546, 11.3848838285812, 
        11.3848838285812, 11.3848838285812, 11.3848838285812, 11.3848838285812, 
        16.1749385391884, 13.441247554735, 11.3848838285812, 12.4211804217676, 
        12.8321827304926, 12.8321827304926, 12.4211804217676, 12.8321827304926, 
        11.3848838285812, 4.77950392749314, 5.12508162351396, 5.12508162351396, 
        6.61654961506376, 6.87429923336285, 6.87429923336285, 8.09372744999706, 
        8.36374221308446, 8.65813385918199, 8.09372744999706, 11.3663029812546, 
        11.3848838285812, 11.0327147224206, 7.14431399645024, 6.87429923336285, 
        6.87429923336285, 6.87429923336285, 8.65813385918199, 8.36374221308446, 
        10.1573219870462, 9.50956625875573, 10.2090648860165, 9.87547662718255, 
        10.2090648860165, 11.0327147224206, 11.3848838285812, 11.3848838285812, 
        12.8321827304926)
    expect_equal(gbm_predictions, expected_gbm_predictions)
    expect_length(gbm_predictions, 4177)
})