prng = np.random.RandomState(1234567891)
    x = prng.rand(10000, 1)
    # x = np.random.rand(10000, 1)
    y = x

    print(f"minimum = {min(x)}")
    time.sleep(1)

    def create_model():
        # dropout_nodes = 0.1
        dropout_nodes = 0.0
        # intermediary_activation = 'linear'
        intermediary_activation = 'relu'
        final_activation = 'linear'

        # initialize sequential model
        model = tf.keras.models.Sequential()

        layer_nodes = [16, 8, 4, 2]
        for i, layer_node in enumerate(layer_nodes):
            if i==0:
                # first layer
                model.add(tf.keras.layers.Dense(layer_node, input_dim=1))
                model.add(tf.keras.layers.Activation(intermediary_activation))
                model.add(tf.keras.layers.Dropout(dropout_nodes))
                # model.add(tf.keras.layers.BatchNormalization()) #we can re-normalize the data after each layer
            else:
                # other layers
                model.add(tf.keras.layers.Dense(layer_node))
                model.add(tf.keras.layers.Activation(intermediary_activation))
                model.add(tf.keras.layers.Dropout(dropout_nodes))
                # model.add(tf.keras.layers.BatchNormalization()) #we can re-normalize the data after each layer
        model.add(tf.keras.layers.Dense(1))
        # model.add(tf.keras.layers.Activation('relu'))
        model.add(tf.keras.layers.Activation(final_activation))

        loss = 'mse'
        metric = ["mae", "mape"]
        opt = tf.keras.optimizers.SGD(learning_rate=1e-2)
        # opt = tf.keras.optimizers.Adam(learning_rate=1e-3)

        model.compile(loss=loss, optimizer=opt, metrics=[metric])

        return model

    model = create_model()

    history = model.fit(x=x, y=y,
                        validation_split=0.1, shuffle=False,
                        epochs=20,
                        batch_size=32,
                        verbose=1, )

    pred = model.predict(x)

    df = pd.DataFrame(x, columns=["x"])
    df['y'] = y
    df['pred'] = pred
    model_evaluation = model.evaluate(x, y, verbose=2)
    dict_model_evaluation = {k.name: model_evaluation[i] for i, k in enumerate(model.metrics)}
    print(dict_model_evaluation)