├── .Python ├── .gitattributes ├── .gitignore ├── LSTM_basic.py ├── LSTM_sequence.py ├── LSTM_tree.py ├── NN.py ├── README.md ├── data ├── allowed_d2.p ├── allowed_d3.p ├── allowed_d4.p ├── desired_equation_components_d2.txt ├── desired_equation_components_d3.txt ├── desired_equation_components_d4.txt ├── encoded_states_d2.txt ├── encoded_states_d3.txt ├── encoded_states_d4.txt ├── equation_trees_d2.p ├── equation_trees_d3.p └── equation_trees_d4.p ├── data_loader.py ├── encoder.py ├── equation_tree.py ├── fitter.py ├── generate_examples.py ├── generate_examples_helper.py └── plot_data ├── tree_saveLosses_d0.txt └── tree_saveLosses_d1.txt /.Python: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/twhughes/Symbolic-Regression/b96d1026b8b89607d835304bd518ca4fa0f8a2c4/.Python -------------------------------------------------------------------------------- /.gitattributes: -------------------------------------------------------------------------------- 1 | *.p linguist-language=Python 2 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Byte-compiled / optimized / DLL files 2 | __pycache__/ 3 | *.py[cod] 4 | *$py.class 5 | 6 | # C extensions 7 | *.so 8 | 9 | # Distribution / packaging 10 | .Python 11 | build/ 12 | develop-eggs/ 13 | dist/ 14 | downloads/ 15 | eggs/ 16 | .eggs/ 17 | lib/ 18 | lib64/ 19 | parts/ 20 | sdist/ 21 | var/ 22 | wheels/ 23 | *.egg-info/ 24 | .installed.cfg 25 | *.egg 26 | MANIFEST 27 | 28 | # PyInstaller 29 | # Usually these files are written by a python script from a template 30 | # before PyInstaller builds the exe, so as to inject date/other infos into it. 31 | *.manifest 32 | *.spec 33 | 34 | # Installer logs 35 | pip-log.txt 36 | pip-delete-this-directory.txt 37 | 38 | # Unit test / coverage reports 39 | htmlcov/ 40 | .tox/ 41 | .coverage 42 | .coverage.* 43 | .cache 44 | nosetests.xml 45 | coverage.xml 46 | *.cover 47 | .hypothesis/ 48 | .pytest_cache/ 49 | 50 | # Translations 51 | *.mo 52 | *.pot 53 | 54 | # Django stuff: 55 | *.log 56 | local_settings.py 57 | db.sqlite3 58 | 59 | # Flask stuff: 60 | instance/ 61 | .webassets-cache 62 | 63 | # Scrapy stuff: 64 | .scrapy 65 | 66 | # Sphinx documentation 67 | docs/_build/ 68 | 69 | # PyBuilder 70 | target/ 71 | 72 | # Jupyter Notebook 73 | .ipynb_checkpoints 74 | 75 | # pyenv 76 | .python-version 77 | 78 | # celery beat schedule file 79 | celerybeat-schedule 80 | 81 | # SageMath parsed files 82 | *.sage.py 83 | 84 | # Environments 85 | .env 86 | .venv 87 | env/ 88 | venv/ 89 | ENV/ 90 | env.bak/ 91 | venv.bak/ 92 | 93 | # Spyder project settings 94 | .spyderproject 95 | .spyproject 96 | 97 | # Rope project settings 98 | .ropeproject 99 | 100 | # mkdocs documentation 101 | /site 102 | 103 | # mypy 104 | .mypy_cache/ 105 | -------------------------------------------------------------------------------- /LSTM_basic.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Accelerating Symbolic Regression with Deep Learning 3 | By Tyler Hughes, Siddharth Buddhiraju and Rituraj 4 | For CS 221, Fall 2017-2018 5 | 6 | This file does simple tests on LSTMs with one or two, user-defined 7 | datasets. Used for debugging and testing generalization of the model. 8 | ''' 9 | 10 | import numpy as np 11 | import tensorflow as tf 12 | import sys 13 | 14 | # set up training data 15 | feature_vector_arr = [[1,0], 16 | [0,1]] 17 | 18 | equation_strings_arr = [['sin','(','x',')',''], 19 | ['x','+','c','']] # correct equation labels 20 | #feature_vector_arr = [[1,0]] # single input to LSTM 21 | #equation_strings_arr = [['sin','(','x','+','c',')']] # correct equation labels 22 | 23 | N_feature = len(feature_vector_arr[0]) 24 | eq_dict = {'(':0,')':1,'x':2,'c':3,'sin':4,'+':5,'cos':6,'':7} # id the equation components 25 | reverse_dict = {a:b for b,a in eq_dict.iteritems()} 26 | 27 | N_vocab = len(eq_dict) 28 | N_train = len(equation_strings_arr) 29 | N_steps = max([len(e) for e in equation_strings_arr]) 30 | LSTM_size = 10 31 | 32 | # turn the equation into a one-hot representation 33 | def get_one_hot(eq_string): 34 | one_hot_list = [] 35 | for i in range(N_steps): 36 | one_hot = np.zeros((N_vocab,1)) 37 | if len(eq_string) > i: 38 | s = eq_string[i] 39 | one_hot[eq_dict[s],0] = 1 40 | one_hot_list.append(one_hot) 41 | return one_hot_list 42 | 43 | 44 | # turn the equation into a one-hot representation and reshape for TF 45 | features = [np.reshape(np.array(f),(1,N_feature)) for f in feature_vector_arr] 46 | eq_one_hot = [np.reshape(np.array(get_one_hot(e)),(1,N_steps,N_vocab)) for e in equation_strings_arr] 47 | 48 | # input to the first LSTM cell (the feature vector) 49 | feature = tf.placeholder(tf.float32,[1,N_feature]) 50 | # target out values from each LSTM cell 51 | target = tf.placeholder(tf.float32,[1,N_steps,N_vocab]) 52 | 53 | # output weights and biases (to softmax) 54 | Wo = tf.Variable(tf.random_normal([N_vocab,LSTM_size])) 55 | bo = tf.Variable(tf.zeros([N_vocab,1])) 56 | # output weights and biases (to softmax) 57 | Wi = tf.Variable(tf.random_normal([LSTM_size,N_vocab])) 58 | bi = tf.Variable(tf.zeros([LSTM_size,1])) 59 | # output weights and biases (to softmax) 60 | Wf = tf.Variable(tf.random_normal([N_feature,LSTM_size])) 61 | bf = tf.Variable(tf.zeros([1,LSTM_size])) 62 | 63 | # define the basic lstm cell 64 | lstm_cell = tf.contrib.rnn.BasicLSTMCell(LSTM_size) 65 | def predict(feature, lstm_cell): 66 | # first output from feeding the feature vector 67 | feature = tf.add(tf.matmul(feature,Wf),bf) 68 | out, _ = tf.contrib.rnn.static_rnn(lstm_cell,[feature], dtype=tf.float32) 69 | # apply first connected layer to output 70 | out = tf.reshape(out,[LSTM_size,-1]) 71 | out = tf.add(tf.matmul(Wo,out),bo) 72 | # apply softmax and get max entry 73 | out = tf.nn.softmax(out,dim=0) 74 | predict1 = tf.argmax(out) 75 | out_list = [out] 76 | for i in range(N_steps-1): 77 | in_state = tf.add(tf.matmul(Wi,out),bi) 78 | in_state = tf.reshape(in_state,[1,LSTM_size]) 79 | out, state = tf.contrib.rnn.static_rnn(lstm_cell,[in_state], dtype=tf.float32) 80 | # apply first connected layer to output 81 | out = tf.reshape(out,[LSTM_size,-1]) 82 | out = tf.add(tf.matmul(Wo,out),bo) 83 | # apply softmax and get max entry 84 | out = tf.nn.softmax(out,dim=0) 85 | predict = tf.argmax(out) 86 | out_list.append(out) 87 | return out_list 88 | 89 | def one_hot_to_eq_str(one_hot_list): 90 | one_hot_list = one_hot_list[0] # need to get 0th element since only one training example in practice 91 | N = len(one_hot_list) 92 | equation = '' 93 | for i in range(N): 94 | prediction = np.argmax(one_hot_list[i]) 95 | eq_el = reverse_dict[prediction] 96 | equation += eq_el 97 | if eq_el == '': 98 | return equation 99 | return equation 100 | 101 | loss = tf.constant(0.0) 102 | out_list = tf.reshape(predict(feature, lstm_cell),[1,N_steps,N_vocab]) 103 | loss = loss + tf.reduce_sum(tf.square(tf.abs(tf.subtract(out_list,target)))) 104 | 105 | optimizer = tf.train.RMSPropOptimizer(learning_rate=0.01).minimize(loss) 106 | N_epoch = 1000 107 | 108 | with tf.Session() as sess: 109 | sess.run(tf.global_variables_initializer()) 110 | losses = [] 111 | for i in range(N_epoch): 112 | epoch_loss = 0.0 113 | for m in range(N_train): 114 | 115 | _, loss_calc, out_list_calc = sess.run([optimizer, loss, out_list], \ 116 | feed_dict={ feature:features[m], 117 | target:eq_one_hot[m]}) 118 | epoch_loss += loss_calc 119 | losses.append(epoch_loss) 120 | sys.stdout.write("\repoch %s of %s. loss: %s" % (i,N_epoch,epoch_loss)) 121 | sys.stdout.flush() 122 | 123 | print("\n") 124 | 125 | def test_prediction(index): 126 | p = sess.run(out_list,feed_dict={feature:features[index]}) 127 | eq_pred = one_hot_to_eq_str(p) 128 | print("supplied feature vector for : %s" % (''.join(equation_strings_arr[index]))) 129 | print("predicted equation of : %s" % (eq_pred)) 130 | 131 | test_prediction(0) 132 | test_prediction(1) 133 | 134 | -------------------------------------------------------------------------------- /LSTM_sequence.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Accelerating Symbolic Regression with Deep Learning 3 | By Tyler Hughes, Siddharth Buddhiraju and Rituraj 4 | For CS 221, Fall 2017-2018 5 | 6 | This file reads examples generated from generate_examples.py, and trains a 7 | decoder(LSTM) to minimize L2 loss 8 | on the generated equation against the correct equation. 9 | Then, it predicts on the test dataset and returns statistics. 10 | ''' 11 | 12 | import numpy as np 13 | import tensorflow as tf 14 | import sys 15 | from data_loader import load_data 16 | 17 | #============Read examples from file ======================== 18 | max_depth = 2 19 | 20 | fname_phi = './data/encoded_states_d'+str(max_depth)+'.txt' 21 | fname_eq = './data/desired_equation_components_d'+str(max_depth)+'.txt' 22 | 23 | feature_vector_arr, equation_strings_arr, one_hot_list, eq_dict,\ 24 | reverse_dict = load_data(fname_phi,fname_eq) 25 | 26 | #========Separating training and testing data======== 27 | feature_vector_full = feature_vector_arr 28 | equation_strings_full = equation_strings_arr 29 | train_ratio = 0.95 30 | N_total = len(feature_vector_arr) 31 | feature_vector_test = feature_vector_arr[int(N_total*train_ratio):N_total] 32 | equation_strings_test = equation_strings_arr[int(N_total*train_ratio):N_total] 33 | feature_vector_train = feature_vector_arr[0:int(N_total*train_ratio)] 34 | equation_strings_train = equation_strings_arr[0:int(N_total*train_ratio)] 35 | 36 | #=================Setting up LSTM parameters========== 37 | N_feature = len(feature_vector_train[0]) 38 | N_vocab = len(eq_dict) 39 | N_train = len(equation_strings_train) 40 | N_steps = max([len(e) for e in equation_strings_train]) 41 | LSTM_size = 20 42 | N_epoch = 300 43 | 44 | print('working on %s examples' % N_train) 45 | print(' number of equation elements : %s' % N_vocab) 46 | print(' maximum equation length : %s' % N_steps) 47 | print(' length of feature vector : %s' % N_feature) 48 | print(' size of LSTM states : %s' % LSTM_size) 49 | 50 | #===========Functions================================ 51 | # turn the equation into a one-hot representation 52 | def get_one_hot(eq_string): 53 | one_hot_list = [] 54 | for i in range(N_steps): 55 | one_hot = np.zeros((N_vocab,1)) 56 | if i < len(eq_string): 57 | s = eq_string[i] 58 | one_hot[eq_dict[s],0] = 1 59 | else: 60 | s = '' 61 | one_hot[eq_dict[s],0] = 1 62 | one_hot_list.append(one_hot) 63 | return one_hot_list 64 | 65 | def predictTraintime(feature, target, lstm_cell): 66 | 67 | 68 | feature = tf.add(tf.matmul(feature,Wf),bf) 69 | out, state = tf.contrib.rnn.static_rnn(lstm_cell,[feature], dtype=tf.float32) 70 | 71 | #cell = tf.contrib.rnn.DropoutWrapper(lstm_cell, output_keep_prob=0.8) <- Tried but did not improve results 72 | #out, state = tf.contrib.rnn.static_rnn(cell,[feature], dtype=tf.float32) 73 | 74 | out = tf.reshape(out,[LSTM_size,-1]) 75 | out = tf.add(tf.matmul(Wo,out),bo) 76 | 77 | 78 | out = tf.nn.softmax(out,dim=0) 79 | out_list = [out] #out_list shifted above softmax for cross entropy 80 | 81 | for i in range(N_steps-1): 82 | 83 | in_prev = tf.reshape(target[0,i,:],[N_vocab,1]) 84 | input_element = tf.add(tf.matmul(Wi,in_prev),bi) 85 | input_element = tf.reshape(input_element,[1,LSTM_size]) 86 | #out, state = tf.contrib.rnn.static_rnn(cell,[input_element], initial_state=state, dtype=tf.float32) 87 | out, state = tf.contrib.rnn.static_rnn(lstm_cell,[input_element], initial_state=state, dtype=tf.float32) 88 | 89 | out = tf.reshape(out,[LSTM_size,-1]) 90 | out = tf.add(tf.matmul(Wo,out),bo) 91 | 92 | out = tf.nn.softmax(out,dim=0) 93 | out_list.append(out) #out_list shifted above softmax for cross entropy 94 | 95 | return out_list 96 | 97 | def predictTesttime(feature, lstm_cell): 98 | 99 | 100 | feature = tf.add(tf.matmul(feature,Wf),bf) 101 | out, state = tf.contrib.rnn.static_rnn(lstm_cell,[feature], dtype=tf.float32) 102 | 103 | out = tf.reshape(out,[LSTM_size,-1]) 104 | out = tf.add(tf.matmul(Wo,out),bo) 105 | 106 | out = tf.nn.softmax(out,dim=0) 107 | out_list = [out] 108 | 109 | for i in range(N_steps-1): 110 | 111 | input_element = tf.add(tf.matmul(Wi,out),bi) 112 | input_element = tf.reshape(input_element,[1,LSTM_size]) 113 | out, state = tf.contrib.rnn.static_rnn(lstm_cell,[input_element], initial_state=state, dtype=tf.float32) 114 | 115 | out = tf.reshape(out,[LSTM_size,-1]) 116 | out = tf.add(tf.matmul(Wo,out),bo) 117 | out = tf.nn.softmax(out,dim=0) 118 | 119 | out_list.append(out) 120 | 121 | return out_list 122 | 123 | def one_hot_to_eq_str(one_hot_list): 124 | one_hot_list = one_hot_list[0] # need to get 0th element since only one training example in practice 125 | N = len(one_hot_list) 126 | equation = '' 127 | eq_el = '' 128 | for i in range(N): 129 | one_hot_allowed = one_hot_list[i] 130 | prediction = np.argmax(one_hot_allowed) 131 | eq_el = reverse_dict[prediction] 132 | equation += eq_el 133 | 134 | return equation 135 | 136 | #===========Setting up objects for LSTM========== 137 | # turn the equation into a one-hot representation and reshape for TF 138 | features = [np.reshape(np.array(f),(1,N_feature)) for f in feature_vector_train] 139 | eq_one_hot = [np.reshape(np.array(get_one_hot(e)),(1,N_steps,N_vocab)) for e in equation_strings_train] 140 | 141 | # input to the first LSTM cell (the feature vector) 142 | feature = tf.placeholder(tf.float32,[1,N_feature]) 143 | # desired out values from each LSTM cell 144 | target = tf.placeholder(tf.float32,[1,N_steps,N_vocab]) 145 | 146 | # output weights and biases (to softmax) 147 | Wo = tf.Variable(tf.random_normal([N_vocab,LSTM_size])) 148 | bo = tf.Variable(tf.zeros([N_vocab,1])) 149 | # output weights and biases (to softmax) 150 | Wi = tf.Variable(tf.random_normal([LSTM_size,N_vocab])) 151 | bi = tf.Variable(tf.zeros([LSTM_size,1])) 152 | # output weights and biases (to softmax) 153 | Wf = tf.Variable(tf.random_normal([N_feature,LSTM_size])) 154 | bf = tf.Variable(tf.zeros([1,LSTM_size])) 155 | 156 | # define the basic lstm cell 157 | lstm_cell = tf.contrib.rnn.BasicLSTMCell(LSTM_size) 158 | #================================================== 159 | 160 | loss = tf.constant(0.0) 161 | 162 | #=========Outlists at training and testing time===== 163 | out_list = predictTraintime(feature, target, lstm_cell) 164 | out_list_tensor = tf.reshape(out_list,[1,N_steps,N_vocab]) 165 | 166 | out_list_run = predictTesttime(feature, lstm_cell) 167 | out_list_run_tensor = tf.reshape(out_list_run,[1,N_steps,N_vocab]) 168 | 169 | #======L2 Loss====== 170 | loss = loss + tf.reduce_sum(tf.square(tf.subtract(out_list_tensor,target))) 171 | #======Cross entropy with Logits====== 172 | #loss = loss + tf.reduce_sum(tf.nn.softmax_cross_entropy_with_logits(labels=target,logits=\ 173 | #out_list_tensor)) 174 | 175 | optimizer = tf.train.AdamOptimizer(learning_rate=0.001).minimize(loss) 176 | 177 | # turn the equation into a one-hot representation and reshape for TF 178 | features_train = [np.reshape(np.array(f),(1,N_feature)) for f in\ 179 | feature_vector_train] 180 | features_test = [np.reshape(np.array(f),(1,N_feature)) for f in\ 181 | feature_vector_test] 182 | eq_one_hot_train = [np.reshape(np.array(get_one_hot(e)),(1,N_steps,N_vocab))\ 183 | for e in equation_strings_train] 184 | 185 | with tf.Session() as sess: 186 | 187 | #======Training the NN+LSTM on training data====== 188 | sess.run(tf.global_variables_initializer()) 189 | losses = [] 190 | for i in range(N_epoch): 191 | epoch_loss = 0.0 192 | for m in range(N_train): 193 | _, loss_calc, out_list_calc = sess.run([optimizer, loss, \ 194 | out_list_tensor], feed_dict={ feature:features_train[m],\ 195 | target:eq_one_hot_train[m]}) 196 | 197 | epoch_loss += loss_calc 198 | 199 | losses.append(epoch_loss) 200 | sys.stdout.write("\repoch %s of %s. loss: %s" % (i,N_epoch,epoch_loss)) 201 | sys.stdout.flush() 202 | 203 | print("\n") 204 | #======Test error on the training (seen) data====== 205 | def trainError(index): 206 | p = sess.run(out_list_run_tensor,feed_dict=\ 207 | {feature:features_train[index]}) 208 | eq_pred = one_hot_to_eq_str(p) 209 | suppliedString = ''.join(equation_strings_train[index]).replace('','') 210 | predictedString = eq_pred.replace('','') 211 | #print '--' 212 | #print("supplied feature vector for : %s" % (suppliedString)) 213 | #print("predicted equation of : %s" % (predictedString)) 214 | 215 | if (suppliedString == 'x') and (predictedString=='x'): 216 | return (0,1) 217 | elif (suppliedString == 'c') and (predictedString=='c'): 218 | return (0,1) 219 | elif predictedString==suppliedString: 220 | return (1,0) 221 | 222 | return (0,0) 223 | #======Test error on the test (unseen) data====== 224 | def testError(index): 225 | p = sess.run(out_list_run_tensor,feed_dict={feature:features_test[index]}) 226 | eq_pred = one_hot_to_eq_str(p) 227 | suppliedString = ''.join(equation_strings_test[index]).replace('','') 228 | predictedString = eq_pred.replace('','') 229 | print '--' 230 | print("supplied feature vector for : %s" % (suppliedString)) 231 | print("predicted equation of : %s" % (predictedString)) 232 | 233 | if (suppliedString == 'x') and (predictedString=='x'): 234 | return (0,1) 235 | elif (suppliedString == 'c') and (predictedString=='c'): 236 | return (0,1) 237 | elif predictedString==suppliedString: 238 | return (1,0) 239 | 240 | return (0,0) 241 | 242 | #==================Console output======================== 243 | print 'Testing on test data:' 244 | correctPreds = 0 245 | correctPredsX = 0 246 | for j in range(len(features_test)): 247 | output = testError(j) 248 | correctPreds += output[0] 249 | correctPredsX += output[1] 250 | print 'Number of correct "x/c" predictions: %d' %correctPredsX 251 | print 'Number of correct predictions excluding "x/c": %d' %correctPreds 252 | print 'Total %d out of %d' %(correctPreds+correctPredsX,\ 253 | len(feature_vector_test)) 254 | 255 | print ("\n") 256 | print 'Now on original training data:' 257 | 258 | correctPreds = 0 259 | for j in range(len(features_train)): 260 | output = trainError(j) 261 | correctPreds += output[0] 262 | correctPredsX += output[1] 263 | print 'Number of correct "x/c" predictions: %d' %correctPredsX 264 | print 'Number of correct predictions excluding "x/c": %d' %correctPreds 265 | print 'Total %d out of %d' %(correctPreds+correctPredsX,len(feature_vector_train)) 266 | 267 | new_examples = [''.join(ex).replace(''] = 'const' #HACK 58 | 59 | #========Compute and print important information for the next steps======== 60 | 61 | """ 62 | def compute_max_depth(trees): 63 | def recurse(node,depth): 64 | if node == None: 65 | return depth 66 | else: 67 | return max([recurse(node.nextL,depth+1),recurse(node.nextR,depth+1)]) 68 | max_depth = 0 69 | for t in trees: 70 | depth = recurse(t.head,0) 71 | if depth > max_depth: 72 | max_depth = depth 73 | return max_depth 74 | 75 | depth_buffer = 0 76 | max_depth = compute_max_depth(equation_trees_full) + depth_buffer 77 | """ 78 | depth_buffer = 0 79 | num_elements = sum([2**i for i in range(max_depth)]) 80 | N_feature = len(feature_vector_full[0]) 81 | N_vocab = len(eq_dict) 82 | N_train = len(equation_strings_train) 83 | N_test = len(equation_strings_test) 84 | N_steps = num_elements 85 | LSTM_size = 20 86 | 87 | print('working on %s total examples' % N_total) 88 | print(' number of training examples : %s' % N_train) 89 | print(' number of test examples : %s' % N_test) 90 | print(' considering a max depth of : %s' % (max_depth + depth_buffer)) 91 | print(' number of equation elements : %s' % N_vocab) 92 | print(' maximum # equation elements : %s' % N_steps) 93 | print(' length of feature vector : %s' % N_feature) 94 | print(' size of LSTM states : %s' % LSTM_size) 95 | 96 | #========Get one-hot representations and prep data for training======== 97 | 98 | def eq_tree_to_one_hot(eq_tree, depth): 99 | one_hot_list = [] 100 | def recurse(node,depth): 101 | if depth > 0: 102 | one_hot = np.zeros((N_vocab,1)) 103 | if node is None: 104 | node = Node() 105 | one_hot[eq_dict[''],0] = 1 106 | node.name = '' 107 | node.eq_class = 'const' 108 | else: 109 | s = node.name 110 | one_hot[eq_dict[s],0] = 1 111 | one_hot_list.append(one_hot) 112 | node.one_hot = one_hot 113 | if node is None: 114 | recurse(None,depth-1) 115 | recurse(None,depth-1) 116 | elif node.eq_class == 'op': 117 | recurse(node.nextL,depth-1) 118 | recurse(node.nextR,depth-1) 119 | elif node.eq_class == 'fn': 120 | recurse(node.nextR,depth-1) 121 | recurse(None,depth-1) 122 | else: 123 | recurse(None,depth-1) 124 | recurse(None,depth-1) 125 | recurse(eq_tree.head, depth) 126 | return one_hot_list 127 | 128 | features_train = [np.reshape(np.array(f),(1,N_feature)) for f in feature_vector_train] 129 | features_test = [np.reshape(np.array(f),(1,N_feature)) for f in feature_vector_test] 130 | features_full = [np.reshape(np.array(f),(1,N_feature)) for f in feature_vector_full] 131 | true_one_hot_train = [np.reshape(eq_tree_to_one_hot(eq_tree,max_depth),(1,-1,N_vocab)) for eq_tree in equation_trees_train] 132 | true_one_hot_test = [np.reshape(eq_tree_to_one_hot(eq_tree,max_depth),(1,-1,N_vocab)) for eq_tree in equation_trees_test] 133 | true_one_hot_full = [np.reshape(eq_tree_to_one_hot(eq_tree,max_depth),(1,-1,N_vocab)) for eq_tree in equation_trees_full] 134 | 135 | #========Define placeholders and variables for tensorflow graph======== 136 | 137 | # input to the first LSTM cell (the feature vector) 138 | feature = tf.placeholder(tf.float32,[1,N_feature]) 139 | # target out values from each LSTM cell 140 | target = tf.placeholder(tf.float32,[1,N_steps,N_vocab]) 141 | 142 | # weights and biases from LSTM to softmax 143 | Wo = tf.Variable(tf.random_normal([N_vocab,LSTM_size])) 144 | bo = tf.Variable(tf.zeros([N_vocab,1])) 145 | # from softmax to next LSTM input 146 | Wo_R = tf.Variable(tf.random_normal([N_vocab,N_vocab])) 147 | bo_R = tf.Variable(tf.zeros([N_vocab,1])) 148 | Wo_L = tf.Variable(tf.random_normal([N_vocab,N_vocab])) 149 | bo_L = tf.Variable(tf.zeros([N_vocab,1])) 150 | # weights and biases from input to LSTM 151 | Wi = tf.Variable(tf.random_normal([LSTM_size,N_vocab])) 152 | bi = tf.Variable(tf.zeros([LSTM_size,1])) 153 | # vector input weights and biases from feature vector to input 154 | Wf = tf.Variable(tf.random_normal([N_feature,N_vocab])) 155 | bf = tf.Variable(tf.zeros([1,N_vocab])) 156 | Wf2 = tf.Variable(tf.random_normal([N_vocab,N_vocab])) 157 | bf2 = tf.Variable(tf.zeros([N_vocab,1])) 158 | # define the basic lstm cell 159 | lstm_cell = tf.contrib.rnn.BasicLSTMCell(LSTM_size) 160 | 161 | #========Function to create the computational graph and compute loss======== 162 | 163 | def predict_train(input_to_LSTM, out_list, init_state, depth): 164 | # reformat inputs to LSTM 165 | input_to_LSTM = tf.add(tf.matmul(Wi,input_to_LSTM),bi) 166 | input_to_LSTM = tf.reshape(input_to_LSTM,[1,1,LSTM_size]) 167 | # get outputs and states 168 | out, state = tf.nn.dynamic_rnn(lstm_cell,input_to_LSTM,initial_state=init_state,dtype=tf.float32) 169 | # get encoded outputs 170 | out = tf.reshape(out,[LSTM_size,-1]) 171 | out = tf.add(tf.matmul(Wo,out),bo) 172 | #out = tf.nn.softmax(out,dim=0) 173 | out_list.append(out) 174 | if depth > 0: 175 | # create new inputs to right and left LSTMS 176 | out_R = tf.add(tf.matmul(Wo_R,out),bo_R) 177 | out_L = tf.add(tf.matmul(Wo_L,out),bo_L) 178 | predict_train(out_L, out_list, state, depth-1) 179 | predict_train(out_R, out_list, state, depth-1) 180 | 181 | #========Function to predict an equation tree given a feature vector======== 182 | def predict_test(input_to_LSTM, init_state, node, pred_out, depth): 183 | # reformat inputs to LSTM 184 | input_to_LSTM = tf.add(tf.matmul(Wi,input_to_LSTM),bi) 185 | input_to_LSTM = tf.reshape(input_to_LSTM,[1,1,LSTM_size]) 186 | # get outputs and states 187 | out, state = tf.nn.dynamic_rnn(lstm_cell,input_to_LSTM,initial_state=init_state,dtype=tf.float32) 188 | # get encoded outputs 189 | out = tf.reshape(out,[LSTM_size,-1]) 190 | out = tf.add(tf.matmul(Wo,out),bo) 191 | out = tf.nn.softmax(out,dim=0) 192 | node.one_hot = out 193 | pred_out.append(out) 194 | if depth > 0: 195 | # create new inputs to right and left LSTMS 196 | out_R = tf.add(tf.matmul(Wo_R,out),bo_R) 197 | out_L = tf.add(tf.matmul(Wo_L,out),bo_L) 198 | node.nextL = Node() 199 | node.nextR = Node() 200 | predict_test(out_L, state, node.nextL, pred_out, depth-1) 201 | predict_test(out_R, state, node.nextR, pred_out, depth-1) 202 | 203 | #========Define loss and optimizer======== 204 | 205 | print("building computational graph...") 206 | loss = tf.constant(0.0) 207 | input_to_LSTM = tf.reshape(tf.add(tf.matmul(feature,Wf),bf),[N_vocab,1]) 208 | #input_to_LSTM = tf.nn.relu(input_to_LSTM) 209 | #input_to_LSTM = tf.reshape(tf.add(tf.matmul(Wf2,input_to_LSTM),bf2),[N_vocab,1]) 210 | #input_to_LSTM = tf.nn.sigmoid(input_to_LSTM) 211 | 212 | predict_tree = EquationTree() 213 | out_list = [] 214 | predict_train(input_to_LSTM, out_list, None, max_depth-1) 215 | out_list = tf.reshape(out_list,[1,-1,N_vocab]) 216 | loss = tf.reduce_sum(tf.square(tf.abs(out_list-target))) 217 | #loss = tf.losses.softmax_cross_entropy(target,out_list) 218 | optimizer = tf.train.AdamOptimizer(learning_rate=0.001).minimize(loss) 219 | N_epoch = 300 220 | 221 | with tf.Session() as sess: 222 | print("") 223 | print("initializing tensorflow variables...") 224 | sess.run(tf.global_variables_initializer()) 225 | print("") 226 | 227 | losses = [] 228 | for i in range(N_epoch): 229 | epoch_loss = 0.0 230 | for m in range(N_train): 231 | _, loss_calc = sess.run([optimizer, loss], feed_dict={ 232 | feature:features_train[m], 233 | target:true_one_hot_train[m]}) 234 | epoch_loss += loss_calc 235 | if i == 0: 236 | print("first epoch_loss = %s" % epoch_loss) 237 | losses.append(epoch_loss) 238 | sys.stdout.write("\repoch %s of %s. loss: %s" % (i,N_epoch,epoch_loss)) 239 | sys.stdout.flush() 240 | 241 | print("\n") 242 | print("predicting trees with max depth of %s..."%(max_depth-1)) 243 | pred_list = [] 244 | matches_train = 0 245 | matches_test = 0 246 | 247 | input_to_LSTM = tf.reshape(tf.add(tf.matmul(feature,Wf),bf),[N_vocab,1]) 248 | eq_tree_predict = EquationTree() 249 | 250 | pred_out = [] 251 | predict_test(input_to_LSTM, None, eq_tree_predict.head, pred_out, max_depth) 252 | 253 | for m in range(N_total): 254 | 255 | print("working on %sth test example..."%(m)) 256 | 257 | predicted_one_hots = sess.run(pred_out,feed_dict={feature:features_full[m]}) 258 | 259 | def load_one_hots_into_tree(node, one_hots, index_list, depth): 260 | index = index_list[0] 261 | one_hot = one_hots[index] 262 | node.one_hot = one_hot 263 | if depth > 0: 264 | node.nextL = Node() 265 | node.nextR = Node() 266 | load_one_hots_into_tree(node.nextL, one_hots, [index_list[0]+1], depth-1) 267 | load_one_hots_into_tree(node.nextR, one_hots, [index_list[0]+1], depth-1) 268 | 269 | pred_tree = EquationTree() 270 | load_one_hots_into_tree(pred_tree.head,predicted_one_hots,[0],max_depth-1) 271 | 272 | def print_one_hot_tree(node): 273 | if node is not None: 274 | print(node.one_hot) 275 | print_one_hot_tree(node.nextR) 276 | print_one_hot_tree(node.nextL) 277 | #uncomment for debugging 278 | print_one_hot_tree(pred_tree.head) 279 | 280 | def recurse_and_prune(node, depth): 281 | one_hot = node.one_hot 282 | predict = np.argmax(one_hot) 283 | index = int(predict) 284 | symbol = reverse_dict[index] 285 | node.name = symbol 286 | eq_class = class_dict[symbol] 287 | node.eq_class = eq_class 288 | if depth > 0: 289 | if eq_class == 'op': 290 | recurse_and_prune(node.nextL, depth-1) 291 | recurse_and_prune(node.nextR, depth-1) 292 | elif eq_class == 'fn': 293 | recurse_and_prune(node.nextR, depth-1) 294 | node.nextL = None 295 | else: 296 | node.nextR = None 297 | node.nextL = None 298 | 299 | recurse_and_prune(pred_tree.head, max_depth-1) 300 | 301 | eq_string = pred_tree.flatten() 302 | eq_string = ''.join(eq_string) 303 | 304 | original_equation = ''.join(equation_strings_full[m][:-1]) 305 | print(" original equation : %s"%(original_equation)) 306 | print(" predicted equation : %s"%(eq_string)) 307 | if eq_string == original_equation and m < N_train: 308 | matches_train += 1 309 | if eq_string == original_equation and m >= N_train: 310 | matches_test += 1 311 | 312 | print("done.") 313 | print("Matched train = %s/%s equations for an accuracy of %s percent" % (matches_train,N_train,int(float(matches_train)/N_train*1000)/10)) 314 | print("Matched test = %s/%s equations for an accuracy of %s percent" % (matches_test,N_test,int(float(matches_test)/N_test*1000)/10)) 315 | print("Matched total = %s/%s equations for an accuracy of %s percent" % ((matches_train+matches_test),N_total,int(float(matches_train+matches_test)/N_total*1000)/10)) 316 | 317 | fname = './plot_data/tree_saveLosses_d'+str(max_depth-1)+'.txt' 318 | losses_str = [str(l) for l in losses] 319 | losses_str = ','.join(losses_str) 320 | 321 | f = open(fname,'w') 322 | f.write(losses_str) 323 | 324 | # save the model? 325 | 326 | 327 | -------------------------------------------------------------------------------- /NN.py: -------------------------------------------------------------------------------- 1 | import numpy as np 2 | 3 | # activation function dictionary 4 | # relu and linear don't work as expected, stick to tanh and sigmoid 5 | possible_activations = { 6 | 'tanh' : lambda z : np.tanh(z), 7 | 'relu' : lambda z : np.maximum(z,0), 8 | 'sigmoid' : lambda z : 1./(1+np.exp(-z)), 9 | 'linear' : lambda z : z 10 | } 11 | # activation function derivative dictionary 12 | # note: defined in terms of the activations (a) for speed up in computation 13 | possible_activation_derivatives = { 14 | 'tanh' : lambda a : 1-np.power(a,2), 15 | 'relu' : lambda a : 1.*(a>0), 16 | 'sigmoid' : lambda a : a*(1-a), 17 | 'linear' : lambda a : 1.0 18 | } 19 | 20 | class NN: 21 | 22 | def __init__(self, layer_sizes, activations): 23 | # initialization method: 24 | # INPUTS: 25 | # layer_sizes = list of integers [input layer size, hidden layer 1 size, hidden layer 2 size, ... output layer size] 26 | # activations = list of strings [activation 1, activation 2, ... activation N] 27 | # COMPUTES: 28 | # creates random initial weights and biases 29 | # stores activation functions and their derivatives 30 | # RETURNS: 31 | # neural network class 32 | assert (len(layer_sizes) == len(activations) + 1), "number of layers must be one greater than number of activations" 33 | self.weights = {} 34 | self.biases = {} 35 | self.layer_sizes = layer_sizes 36 | self.N_layers = len(layer_sizes) 37 | self.activations = {} 38 | self.activation_derivatives = {} 39 | self.cache = {} 40 | self.grads = {} 41 | np.random.seed(1) 42 | for l in range(self.N_layers-1): 43 | self.weights['W'+str(l+1)] = 2.*np.random.rand(layer_sizes[l+1],layer_sizes[l])-1. 44 | self.biases['b'+str(l+1)] = np.zeros((layer_sizes[l+1],1),dtype=np.float32) 45 | self.activations['a'+str(l+1)] = possible_activations[activations[l]] 46 | self.activation_derivatives['a'+str(l+1)] = possible_activation_derivatives[activations[l]] 47 | np.random.seed(None) 48 | 49 | def forward_prop(self, input_vec): 50 | # forward propagation method: 51 | # INPUTS: 52 | # input_vec = np array of size (N_inputs, m) where m is the number of training examples to compute 53 | # COMPUTES: 54 | # performs forward propagation in the netowrk 55 | # saves Z[l] = W[l]a[l-1]+b[l] and activations a[l] in the cache for backpropagation later 56 | # RETURNS: 57 | # output layer output 58 | m = (input_vec.shape)[1] 59 | assert (input_vec.shape[0]==self.layer_sizes[0]) 60 | a_prev = input_vec 61 | self.cache['a0'] = input_vec 62 | for l in range(1,self.N_layers): 63 | zl = np.dot(self.weights['W'+str(l)],a_prev) + self.biases['b'+str(l)] 64 | self.cache['z'+str(l)] = zl 65 | al = self.activations['a'+str(l)](zl) 66 | self.cache['a'+str(l)] = al 67 | a_prev = al 68 | return al 69 | 70 | 71 | def back_prop(self, dZ_end): 72 | # backward propagation method: 73 | # INPUTS: 74 | # dZ_end = np array of size (N_output, m) which is the derivative of the loss function with respect to the last Z[l] output 75 | # COMPUTES: 76 | # performs backpropagation on the netowrk 77 | # saves gradients in the self.grads{} cache 78 | # RETURNS: 79 | # None 80 | m = dZ_end.shape[1] 81 | assert (dZ_end.shape[0]==self.layer_sizes[self.N_layers-1]) 82 | dZ = dZ_end 83 | for l in range(self.N_layers-1,1,-1): 84 | dWl = 1./m*np.dot(dZ,self.cache['a'+str(l-1)].T) 85 | dbl = 1./m*np.sum(dZ,axis=1,keepdims=True) 86 | self.grads['dW'+str(l)] = dWl 87 | self.grads['db'+str(l)] = dbl 88 | dZ = np.multiply(np.dot(self.weights['W'+str(l)].T, dZ), self.activation_derivatives['a'+str(l-1)](self.cache['a'+str(l-1)])) 89 | dW1 = 1./m*np.dot(dZ,self.cache['a0'].T) 90 | db1 = 1./m*np.sum(dZ,axis=1,keepdims=True) 91 | self.grads['dW1'] = dW1 92 | self.grads['db1'] = db1 93 | 94 | def update_weights(self, learning_rate=0.01, lambda_reg=0): 95 | # weight update method: 96 | # INPUTS: 97 | # learning_rate = float, amount to increment weights 98 | # COMPUTES: 99 | # takes gradient cache and updates each weight and bias according to learning_rate 100 | # RETURNS: 101 | # None 102 | # note: expand to incorporate other learning algorithms later 103 | for l in range(1,self.N_layers): 104 | self.weights['W'+str(l)] = self.weights['W'+str(l)] + learning_rate*self.grads['dW'+str(l)] - lambda_reg*self.weights['W'+str(l)] 105 | self.biases[ 'b'+str(l)] = self.biases[ 'b'+str(l)] + learning_rate*self.grads['db'+str(l)] - lambda_reg*self.biases[ 'b'+str(l)] 106 | 107 | def derivative_check(self, m=5, epsilon=1e-4, verbose=False): 108 | # numerical derivative checking method: use to make sure it is working correctly 109 | # INPUTS: 110 | # m = integer, number of training examples to simulate 111 | # epsilon = float, amount to perturb weights 112 | # verbose = boolean, whether to print out all of the derivatives 113 | # COMPUTES: 114 | # takes numerical derivative of loss function with respect to each weight and bias 115 | # compares numerical calculation with backprop result 116 | # gives errors if they are different (this function used mainly for debugging purposes, don't do it every time) 117 | # RETURNS: 118 | # {True/False} if numerical derivatives {match/do not match} backprop results 119 | input_vec = np.random.rand((self.weights['W1'].shape)[1],m) 120 | y = np.random.rand((self.weights['W'+str(self.N_layers-1)].shape)[0],m) 121 | output_vec = self.forward_prop(input_vec) 122 | self.back_prop(output_vec-y) 123 | correct = True 124 | for l in range(1,self.N_layers): 125 | Wl = self.weights['W'+str(l)] 126 | nx,ny = Wl.shape 127 | for i in range(nx): 128 | for j in range(ny): 129 | self.weights['W'+str(l)][i,j] += epsilon 130 | out_plus = self.forward_prop(input_vec) 131 | loss_plus = -(y*np.log(out_plus)+(1-y)*np.log(1-out_plus))/m 132 | self.weights['W'+str(l)][i,j] -= 2*epsilon 133 | out_minus = self.forward_prop(input_vec) 134 | loss_minus = -(y*np.log(out_minus)+(1-y)*np.log(1-out_minus))/m 135 | self.weights['W'+str(l)][i,j] += epsilon 136 | deriv_numerical = np.sum((loss_plus-loss_minus)/2./epsilon) 137 | deriv_back_prop = self.grads['dW'+str(l)][i][j] 138 | if verbose: 139 | print('layer : '+str(l)+' inedeces : ('+str(i)+','+str(j)+')') 140 | print(' numerical : '+str(deriv_numerical)) 141 | print(' analytical : '+str(deriv_back_prop)) 142 | if (np.abs(deriv_numerical - deriv_back_prop) > 1e-5): 143 | correct = False 144 | if correct: 145 | print('success: backpropagation matches numerical derivatives.') 146 | else: 147 | print('WARNING: backpropagation does not match numerical derivatives, please check') 148 | return correct 149 | 150 | def flatten_parameters(self): 151 | # gets all of the parameters in the network, stick them into a vector and return them (this is our feature vector) 152 | feature_vec = [] 153 | for l in range(1,self.N_layers): 154 | W_array = self.weights['W'+str(l)] 155 | b_array = self.biases[ 'b'+str(l)] 156 | Nx,Ny = W_array.shape 157 | for i in range(Nx): 158 | for j in range(Ny): 159 | feature_vec.append(W_array[i,j]) 160 | feature_vec.append(b_array[i,0]) 161 | return feature_vec 162 | 163 | 164 | 165 | 166 | 167 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | 2 | # Accelerating Symbolic Regression with Deep Learning 3 | 4 | by Tyler Hughes, Siddharth Buddhiraju, and Rituraj 5 | 6 | ## Introduction 7 | 8 | The goal of symbolic regression is to generate a function that describes a given set of datapoints. This function can, generally, include undetermined constants that may be fit later. Typical approaches to symbolic regression involve global optimization techniques based on genetic algorithms [1,2,3], that search a subset of the entire space of possible equations to find the best fit. This approach is cumbersome and does not utilize any of the features or structure inherent in the original data. 9 | 10 | In this work, we approach symbolic as a modified machine translation problem, where our goal is to translate the original dataset into an equation using a mixture of machine learning techniques. We first train a neural network to extract features from the dataset by performing a fit and stripping out the learned parameters from the network. We then train a recurrent neural network model (using LSTMs) to decode this feature vector into an equation. Further processing of this equation can be performed to fit constants and evaluate accuracy vs. simplicity. 11 | 12 | This work presents a fresh approach to the problem of symbolic regression and may allow for potential increases in predictive power, reliability, and speed compared to previous solutions. 13 | 14 | ## Paper 15 | This work was performed as the final project for [Stanford CS 221, Artificial Intelligence: Principles and Techniques](http://web.stanford.edu/class/cs221/). The final writeup is linked [here](https://twhughes.github.io/pdfs/cs221_final.pdf). 16 | ## Code 17 | 18 | ### Generating the Dataset 19 | 20 | The data is generated by running the ``` generate_examples.py ``` script. One must specify the maximum equation tree depth allowable by setting the ```tree_depth``` variable. For a number of training examples, this script generates a random equation up to this maximum depth, sets the constants randomly, and then generates a set of (x,y) pairs. Then, a neural network in ```NN.py``` fits to this dataset and returns a feature vector for this training example. All of this data is stored in ```./data/``` directory and is separated by the maximum allowed tree depth. 1500 examples of depths 1, 2, and 3 have been pre-generated and are in ```./data/```. Therefore, for purposes of training, this section can be skipped. 21 | 22 | ### Decoding and Equation Prediction 23 | 24 | The files ```LSTM_basic.py```, ```LSTM_sequence.py```, and ```LSTM_tree.py``` are each separate implementations of the LSTM network used to decode the feature vector into equations. 25 | 26 | ```LSTM_basic.py``` allows for user-defined equations and feature vectors, and was used for debugging and investigating simple cases. 27 | 28 | ```LSTM_sequence.py``` trains an linear LSTM sequence model on the dataset and returns equations containing special elements for parentheses. For example, sin(x) would be represented as [ sin , ( , x , ) ] 29 | 30 | ```LSTM_tree.py``` trains an tree-based LSTM sequence model that is intended to mirror the basic representation of equations as trees. This script trains a full binary tree of LSTMs using the original dataset. On prediction time, it returns another full binary equation tree with special characters, which are then pruned to leave the predicted equation. 31 | 32 | These three files show both training and prediction statistics to the user. 33 | 34 | ### Curve Fitting 35 | 36 | After generating the equations, we provide a file ```fitter.py``` for doing curve fitting to the original (x,y) data points. This script contains an example, which fits when running the script. The functions from this script can also be imported for post-processing. 37 | 38 | ## Dependencies 39 | 40 | - Python 2.7.10 41 | - [Tensorflow](https://www.tensorflow.org/) 1.4.0 42 | - [Dill](https://pypi.python.org/pypi/dill) 0.2.7.1 43 | 44 | ## References 45 | 46 | [1] Josh Bongard and Hod Lipson. *Automated reverse engineering of nonlinear dynamical systems*. Proceedings 47 | of the National Academy of Sciences, 104(24):9943–9948, 2007. 48 | 49 | [2] John Duffy and Jim Engle-Warnick. *Using symbolic regression to infer strategies from experimental data*. 50 | In Evolutionary computation in Economics and Finance, pages 61–82. Springer, 2002. 51 | 52 | [3] Wouter Minnebo, Sean Stijven, and Katya Vladislavleva. *Empowering knowledge computing with variable 53 | selection*, 2011. 54 | 55 | -------------------------------------------------------------------------------- /data/allowed_d2.p: -------------------------------------------------------------------------------- 1 | (lp0 2 | (S'sin' 3 | p1 4 | S'fn' 5 | p2 6 | cdill.dill 7 | _create_function 8 | p3 9 | (cdill.dill 10 | _load_type 11 | p4 12 | (S'CodeType' 13 | p5 14 | tp6 15 | Rp7 16 | (I1 17 | I1 18 | I2 19 | I67 20 | S't\x00\x00j\x01\x00|\x00\x00\x83\x01\x00S' 21 | p8 22 | (Ntp9 23 | (S'np' 24 | p10 25 | g1 26 | tp11 27 | (S'x' 28 | p12 29 | tp13 30 | S'generate_examples.py' 31 | p14 32 | S'' 33 | p15 34 | I20 35 | S'' 36 | p16 37 | (t(ttp17 38 | Rp18 39 | c__main__ 40 | __dict__ 41 | g15 42 | NN(dp19 43 | tp20 44 | Rp21 45 | tp22 46 | a(g12 47 | S'var' 48 | p23 49 | g3 50 | (g7 51 | (I1 52 | I1 53 | I1 54 | I67 55 | S't\x00\x00S' 56 | p24 57 | (Ntp25 58 | (S'True' 59 | p26 60 | tp27 61 | (S'_' 62 | p28 63 | tp29 64 | S'generate_examples.py' 65 | p30 66 | g15 67 | I22 68 | S'' 69 | p31 70 | (t(ttp32 71 | Rp33 72 | c__main__ 73 | __dict__ 74 | g15 75 | NN(dp34 76 | tp35 77 | Rp36 78 | tp37 79 | a(S'+' 80 | p38 81 | S'op' 82 | p39 83 | g3 84 | (g7 85 | (I2 86 | I2 87 | I2 88 | I67 89 | S'|\x00\x00|\x01\x00\x17S' 90 | p40 91 | (Ntp41 92 | (t(g12 93 | S'y' 94 | p42 95 | tp43 96 | S'generate_examples.py' 97 | p44 98 | g15 99 | I23 100 | S'' 101 | p45 102 | (t(ttp46 103 | Rp47 104 | c__main__ 105 | __dict__ 106 | g15 107 | NN(dp48 108 | tp49 109 | Rp50 110 | tp51 111 | a(S'tanh' 112 | p52 113 | g2 114 | g3 115 | (g7 116 | (I1 117 | I1 118 | I2 119 | I67 120 | S't\x00\x00j\x01\x00|\x00\x00\x83\x01\x00S' 121 | p53 122 | (Ntp54 123 | (g10 124 | g52 125 | tp55 126 | (g12 127 | tp56 128 | S'generate_examples.py' 129 | p57 130 | g15 131 | I25 132 | S'' 133 | p58 134 | (t(ttp59 135 | Rp60 136 | c__main__ 137 | __dict__ 138 | g15 139 | NN(dp61 140 | tp62 141 | Rp63 142 | tp64 143 | a(S'c' 144 | p65 145 | S'const' 146 | p66 147 | g3 148 | (g7 149 | (I1 150 | I1 151 | I1 152 | I67 153 | S't\x00\x00S' 154 | p67 155 | (Ntp68 156 | (g26 157 | tp69 158 | (g28 159 | tp70 160 | S'generate_examples.py' 161 | p71 162 | g15 163 | I26 164 | S'' 165 | p72 166 | (t(ttp73 167 | Rp74 168 | c__main__ 169 | __dict__ 170 | g15 171 | NN(dp75 172 | tp76 173 | Rp77 174 | tp78 175 | a. -------------------------------------------------------------------------------- /data/allowed_d3.p: -------------------------------------------------------------------------------- 1 | (lp0 2 | (S'sin' 3 | p1 4 | S'fn' 5 | p2 6 | cdill.dill 7 | _create_function 8 | p3 9 | (cdill.dill 10 | _load_type 11 | p4 12 | (S'CodeType' 13 | p5 14 | tp6 15 | Rp7 16 | (I1 17 | I1 18 | I2 19 | I67 20 | S't\x00\x00j\x01\x00|\x00\x00\x83\x01\x00S' 21 | p8 22 | (Ntp9 23 | (S'np' 24 | p10 25 | g1 26 | tp11 27 | (S'x' 28 | p12 29 | tp13 30 | S'generate_examples.py' 31 | p14 32 | S'' 33 | p15 34 | I20 35 | S'' 36 | p16 37 | (t(ttp17 38 | Rp18 39 | c__main__ 40 | __dict__ 41 | g15 42 | NN(dp19 43 | tp20 44 | Rp21 45 | tp22 46 | a(g12 47 | S'var' 48 | p23 49 | g3 50 | (g7 51 | (I1 52 | I1 53 | I1 54 | I67 55 | S't\x00\x00S' 56 | p24 57 | (Ntp25 58 | (S'True' 59 | p26 60 | tp27 61 | (S'_' 62 | p28 63 | tp29 64 | S'generate_examples.py' 65 | p30 66 | g15 67 | I22 68 | S'' 69 | p31 70 | (t(ttp32 71 | Rp33 72 | c__main__ 73 | __dict__ 74 | g15 75 | NN(dp34 76 | tp35 77 | Rp36 78 | tp37 79 | a(S'+' 80 | p38 81 | S'op' 82 | p39 83 | g3 84 | (g7 85 | (I2 86 | I2 87 | I2 88 | I67 89 | S'|\x00\x00|\x01\x00\x17S' 90 | p40 91 | (Ntp41 92 | (t(g12 93 | S'y' 94 | p42 95 | tp43 96 | S'generate_examples.py' 97 | p44 98 | g15 99 | I23 100 | S'' 101 | p45 102 | (t(ttp46 103 | Rp47 104 | c__main__ 105 | __dict__ 106 | g15 107 | NN(dp48 108 | tp49 109 | Rp50 110 | tp51 111 | a(S'tanh' 112 | p52 113 | g2 114 | g3 115 | (g7 116 | (I1 117 | I1 118 | I2 119 | I67 120 | S't\x00\x00j\x01\x00|\x00\x00\x83\x01\x00S' 121 | p53 122 | (Ntp54 123 | (g10 124 | g52 125 | tp55 126 | (g12 127 | tp56 128 | S'generate_examples.py' 129 | p57 130 | g15 131 | I25 132 | S'' 133 | p58 134 | (t(ttp59 135 | Rp60 136 | c__main__ 137 | __dict__ 138 | g15 139 | NN(dp61 140 | tp62 141 | Rp63 142 | tp64 143 | a(S'c' 144 | p65 145 | S'const' 146 | p66 147 | g3 148 | (g7 149 | (I1 150 | I1 151 | I1 152 | I67 153 | S't\x00\x00S' 154 | p67 155 | (Ntp68 156 | (g26 157 | tp69 158 | (g28 159 | tp70 160 | S'generate_examples.py' 161 | p71 162 | g15 163 | I26 164 | S'' 165 | p72 166 | (t(ttp73 167 | Rp74 168 | c__main__ 169 | __dict__ 170 | g15 171 | NN(dp75 172 | tp76 173 | Rp77 174 | tp78 175 | a. -------------------------------------------------------------------------------- /data/allowed_d4.p: -------------------------------------------------------------------------------- 1 | (lp0 2 | (S'sin' 3 | p1 4 | S'fn' 5 | p2 6 | cdill.dill 7 | _create_function 8 | p3 9 | (cdill.dill 10 | _load_type 11 | p4 12 | (S'CodeType' 13 | p5 14 | tp6 15 | Rp7 16 | (I1 17 | I1 18 | I2 19 | I67 20 | S't\x00\x00j\x01\x00|\x00\x00\x83\x01\x00S' 21 | p8 22 | (Ntp9 23 | (S'np' 24 | p10 25 | g1 26 | tp11 27 | (S'x' 28 | p12 29 | tp13 30 | S'generate_examples.py' 31 | p14 32 | S'' 33 | p15 34 | I20 35 | S'' 36 | p16 37 | (t(ttp17 38 | Rp18 39 | c__main__ 40 | __dict__ 41 | g15 42 | NN(dp19 43 | tp20 44 | Rp21 45 | tp22 46 | a(g12 47 | S'var' 48 | p23 49 | g3 50 | (g7 51 | (I1 52 | I1 53 | I1 54 | I67 55 | S't\x00\x00S' 56 | p24 57 | (Ntp25 58 | (S'True' 59 | p26 60 | tp27 61 | (S'_' 62 | p28 63 | tp29 64 | S'generate_examples.py' 65 | p30 66 | g15 67 | I22 68 | S'' 69 | p31 70 | (t(ttp32 71 | Rp33 72 | c__main__ 73 | __dict__ 74 | g15 75 | NN(dp34 76 | tp35 77 | Rp36 78 | tp37 79 | a(S'+' 80 | p38 81 | S'op' 82 | p39 83 | g3 84 | (g7 85 | (I2 86 | I2 87 | I2 88 | I67 89 | S'|\x00\x00|\x01\x00\x17S' 90 | p40 91 | (Ntp41 92 | (t(g12 93 | S'y' 94 | p42 95 | tp43 96 | S'generate_examples.py' 97 | p44 98 | g15 99 | I23 100 | S'' 101 | p45 102 | (t(ttp46 103 | Rp47 104 | c__main__ 105 | __dict__ 106 | g15 107 | NN(dp48 108 | tp49 109 | Rp50 110 | tp51 111 | a(S'tanh' 112 | p52 113 | g2 114 | g3 115 | (g7 116 | (I1 117 | I1 118 | I2 119 | I67 120 | S't\x00\x00j\x01\x00|\x00\x00\x83\x01\x00S' 121 | p53 122 | (Ntp54 123 | (g10 124 | g52 125 | tp55 126 | (g12 127 | tp56 128 | S'generate_examples.py' 129 | p57 130 | g15 131 | I25 132 | S'' 133 | p58 134 | (t(ttp59 135 | Rp60 136 | c__main__ 137 | __dict__ 138 | g15 139 | NN(dp61 140 | tp62 141 | Rp63 142 | tp64 143 | a(S'c' 144 | p65 145 | S'const' 146 | p66 147 | g3 148 | (g7 149 | (I1 150 | I1 151 | I1 152 | I67 153 | S't\x00\x00S' 154 | p67 155 | (Ntp68 156 | (g26 157 | tp69 158 | (g28 159 | tp70 160 | S'generate_examples.py' 161 | p71 162 | g15 163 | I26 164 | S'' 165 | p72 166 | (t(ttp73 167 | Rp74 168 | c__main__ 169 | __dict__ 170 | g15 171 | NN(dp75 172 | tp76 173 | Rp77 174 | tp78 175 | a. -------------------------------------------------------------------------------- /data/desired_equation_components_d2.txt: -------------------------------------------------------------------------------- 1 | x,+,c 2 | x,+,x 3 | x,+,c 4 | tanh,(,x,) 5 | tanh,(,x,) 6 | x,+,c 7 | x,+,c 8 | tanh,(,x,) 9 | x,+,x 10 | sin,(,x,) 11 | sin,(,x,) 12 | sin,(,x,) 13 | x,+,x 14 | sin,(,x,) 15 | x,+,x 16 | sin,(,x,) 17 | tanh,(,x,) 18 | sin,(,x,) 19 | sin,(,x,) 20 | sin,(,x,) 21 | sin,(,x,) 22 | sin,(,x,) 23 | tanh,(,x,) 24 | sin,(,x,) 25 | sin,(,x,) 26 | x,+,c 27 | x,+,c 28 | x,+,x 29 | sin,(,x,) 30 | sin,(,x,) 31 | x,+,c 32 | tanh,(,x,) 33 | x,+,x 34 | tanh,(,x,) 35 | x,+,x 36 | tanh,(,x,) 37 | tanh,(,x,) 38 | x,+,c 39 | x,+,c 40 | x,+,c 41 | tanh,(,x,) 42 | sin,(,x,) 43 | x,+,x 44 | x,+,c 45 | x,+,x 46 | x,+,x 47 | x,+,x 48 | x,+,x 49 | sin,(,x,) 50 | x,+,c 51 | x,+,x 52 | x,+,c 53 | sin,(,x,) 54 | x,+,c 55 | x,+,c 56 | x,+,c 57 | tanh,(,x,) 58 | x,+,x 59 | x,+,x 60 | x,+,x 61 | tanh,(,x,) 62 | x,+,x 63 | tanh,(,x,) 64 | tanh,(,x,) 65 | sin,(,x,) 66 | x,+,c 67 | tanh,(,x,) 68 | x,+,c 69 | x,+,c 70 | tanh,(,x,) 71 | tanh,(,x,) 72 | x,+,c 73 | sin,(,x,) 74 | x,+,x 75 | tanh,(,x,) 76 | x,+,c 77 | x,+,x 78 | tanh,(,x,) 79 | x,+,x 80 | sin,(,x,) 81 | tanh,(,x,) 82 | x,+,x 83 | sin,(,x,) 84 | tanh,(,x,) 85 | sin,(,x,) 86 | x,+,c 87 | sin,(,x,) 88 | x,+,c 89 | tanh,(,x,) 90 | x,+,x 91 | sin,(,x,) 92 | x,+,x 93 | sin,(,x,) 94 | tanh,(,x,) 95 | tanh,(,x,) 96 | x,+,x 97 | tanh,(,x,) 98 | sin,(,x,) 99 | x,+,c 100 | tanh,(,x,) 101 | tanh,(,x,) 102 | x,+,c 103 | sin,(,x,) 104 | sin,(,x,) 105 | x,+,c 106 | x,+,x 107 | sin,(,x,) 108 | tanh,(,x,) 109 | x,+,x 110 | sin,(,x,) 111 | sin,(,x,) 112 | sin,(,x,) 113 | tanh,(,x,) 114 | x,+,x 115 | sin,(,x,) 116 | sin,(,x,) 117 | x,+,x 118 | x,+,x 119 | x,+,c 120 | tanh,(,x,) 121 | sin,(,x,) 122 | x,+,x 123 | x,+,x 124 | sin,(,x,) 125 | sin,(,x,) 126 | sin,(,x,) 127 | x,+,c 128 | x,+,c 129 | sin,(,x,) 130 | x,+,c 131 | tanh,(,x,) 132 | sin,(,x,) 133 | x,+,c 134 | sin,(,x,) 135 | x,+,c 136 | sin,(,x,) 137 | tanh,(,x,) 138 | tanh,(,x,) 139 | x,+,c 140 | x,+,c 141 | sin,(,x,) 142 | x,+,x 143 | x,+,x 144 | tanh,(,x,) 145 | tanh,(,x,) 146 | x,+,x 147 | x,+,x 148 | sin,(,x,) 149 | sin,(,x,) 150 | x,+,c 151 | tanh,(,x,) 152 | tanh,(,x,) 153 | sin,(,x,) 154 | tanh,(,x,) 155 | x,+,c 156 | x,+,x 157 | x,+,c 158 | tanh,(,x,) 159 | sin,(,x,) 160 | tanh,(,x,) 161 | tanh,(,x,) 162 | sin,(,x,) 163 | tanh,(,x,) 164 | tanh,(,x,) 165 | x,+,c 166 | x,+,c 167 | x,+,c 168 | x,+,c 169 | tanh,(,x,) 170 | x,+,x 171 | sin,(,x,) 172 | sin,(,x,) 173 | x,+,x 174 | sin,(,x,) 175 | sin,(,x,) 176 | x,+,x 177 | sin,(,x,) 178 | sin,(,x,) 179 | sin,(,x,) 180 | tanh,(,x,) 181 | sin,(,x,) 182 | x,+,x 183 | x,+,c 184 | sin,(,x,) 185 | sin,(,x,) 186 | x,+,x 187 | sin,(,x,) 188 | x,+,x 189 | tanh,(,x,) 190 | x,+,x 191 | x,+,c 192 | x,+,c 193 | x,+,c 194 | tanh,(,x,) 195 | tanh,(,x,) 196 | sin,(,x,) 197 | x,+,c 198 | sin,(,x,) 199 | x,+,c 200 | x,+,c 201 | sin,(,x,) 202 | tanh,(,x,) 203 | tanh,(,x,) 204 | x,+,x 205 | x,+,c 206 | x,+,c 207 | x,+,c 208 | sin,(,x,) 209 | sin,(,x,) 210 | x,+,x 211 | x,+,c 212 | x,+,c 213 | tanh,(,x,) 214 | sin,(,x,) 215 | sin,(,x,) 216 | x,+,c 217 | sin,(,x,) 218 | x,+,c 219 | x,+,c 220 | x,+,x 221 | tanh,(,x,) 222 | x,+,c 223 | tanh,(,x,) 224 | x,+,c 225 | x,+,c 226 | sin,(,x,) 227 | x,+,x 228 | tanh,(,x,) 229 | x,+,x 230 | x,+,c 231 | tanh,(,x,) 232 | tanh,(,x,) 233 | x,+,x 234 | x,+,c 235 | tanh,(,x,) 236 | tanh,(,x,) 237 | sin,(,x,) 238 | sin,(,x,) 239 | tanh,(,x,) 240 | sin,(,x,) 241 | tanh,(,x,) 242 | tanh,(,x,) 243 | tanh,(,x,) 244 | sin,(,x,) 245 | x,+,x 246 | tanh,(,x,) 247 | x,+,c 248 | x,+,c 249 | x,+,x 250 | x,+,x 251 | x,+,x 252 | x,+,c 253 | x,+,x 254 | x,+,c 255 | tanh,(,x,) 256 | tanh,(,x,) 257 | sin,(,x,) 258 | x,+,x 259 | sin,(,x,) 260 | x,+,x 261 | x,+,x 262 | x,+,c 263 | x,+,c 264 | x,+,c 265 | tanh,(,x,) 266 | tanh,(,x,) 267 | tanh,(,x,) 268 | tanh,(,x,) 269 | tanh,(,x,) 270 | x,+,c 271 | sin,(,x,) 272 | x,+,x 273 | sin,(,x,) 274 | tanh,(,x,) 275 | tanh,(,x,) 276 | x,+,c 277 | tanh,(,x,) 278 | x,+,x 279 | tanh,(,x,) 280 | x,+,c 281 | x,+,c 282 | sin,(,x,) 283 | sin,(,x,) 284 | x,+,c 285 | x,+,x 286 | tanh,(,x,) 287 | tanh,(,x,) 288 | x,+,c 289 | sin,(,x,) 290 | tanh,(,x,) 291 | tanh,(,x,) 292 | tanh,(,x,) 293 | x,+,c 294 | x,+,c 295 | sin,(,x,) 296 | tanh,(,x,) 297 | tanh,(,x,) 298 | tanh,(,x,) 299 | x,+,x 300 | sin,(,x,) 301 | tanh,(,x,) 302 | tanh,(,x,) 303 | x,+,c 304 | tanh,(,x,) 305 | x,+,c 306 | x,+,c 307 | sin,(,x,) 308 | sin,(,x,) 309 | x,+,x 310 | tanh,(,x,) 311 | x,+,x 312 | tanh,(,x,) 313 | x,+,x 314 | x,+,x 315 | x,+,x 316 | x,+,x 317 | tanh,(,x,) 318 | x,+,x 319 | sin,(,x,) 320 | x,+,c 321 | tanh,(,x,) 322 | x,+,c 323 | tanh,(,x,) 324 | sin,(,x,) 325 | x,+,x 326 | x,+,x 327 | sin,(,x,) 328 | sin,(,x,) 329 | sin,(,x,) 330 | x,+,x 331 | tanh,(,x,) 332 | tanh,(,x,) 333 | sin,(,x,) 334 | sin,(,x,) 335 | x,+,c 336 | tanh,(,x,) 337 | x,+,x 338 | x,+,c 339 | x,+,c 340 | tanh,(,x,) 341 | x,+,x 342 | x,+,c 343 | x,+,x 344 | x,+,x 345 | x,+,x 346 | x,+,c 347 | x,+,c 348 | sin,(,x,) 349 | x,+,c 350 | tanh,(,x,) 351 | x,+,x 352 | x,+,x 353 | tanh,(,x,) 354 | sin,(,x,) 355 | tanh,(,x,) 356 | sin,(,x,) 357 | tanh,(,x,) 358 | sin,(,x,) 359 | sin,(,x,) 360 | x,+,x 361 | sin,(,x,) 362 | sin,(,x,) 363 | tanh,(,x,) 364 | x,+,c 365 | x,+,x 366 | tanh,(,x,) 367 | sin,(,x,) 368 | sin,(,x,) 369 | x,+,c 370 | tanh,(,x,) 371 | tanh,(,x,) 372 | x,+,x 373 | x,+,c 374 | x,+,c 375 | tanh,(,x,) 376 | x,+,x 377 | x,+,c 378 | x,+,c 379 | x,+,x 380 | sin,(,x,) 381 | tanh,(,x,) 382 | x,+,x 383 | x,+,c 384 | sin,(,x,) 385 | sin,(,x,) 386 | x,+,x 387 | x,+,c 388 | x,+,c 389 | x,+,x 390 | sin,(,x,) 391 | tanh,(,x,) 392 | x,+,c 393 | x,+,x 394 | x,+,x 395 | tanh,(,x,) 396 | x,+,c 397 | x,+,c 398 | x,+,x 399 | x,+,x 400 | x,+,c 401 | sin,(,x,) 402 | x,+,x 403 | x,+,x 404 | sin,(,x,) 405 | sin,(,x,) 406 | sin,(,x,) 407 | sin,(,x,) 408 | tanh,(,x,) 409 | tanh,(,x,) 410 | sin,(,x,) 411 | x,+,c 412 | x,+,x 413 | sin,(,x,) 414 | x,+,x 415 | x,+,c 416 | tanh,(,x,) 417 | x,+,c 418 | x,+,x 419 | sin,(,x,) 420 | x,+,c 421 | x,+,c 422 | sin,(,x,) 423 | tanh,(,x,) 424 | x,+,x 425 | tanh,(,x,) 426 | sin,(,x,) 427 | tanh,(,x,) 428 | x,+,c 429 | x,+,c 430 | sin,(,x,) 431 | x,+,x 432 | sin,(,x,) 433 | sin,(,x,) 434 | x,+,c 435 | tanh,(,x,) 436 | x,+,c 437 | tanh,(,x,) 438 | tanh,(,x,) 439 | tanh,(,x,) 440 | tanh,(,x,) 441 | x,+,c 442 | x,+,c 443 | x,+,x 444 | x,+,c 445 | x,+,c 446 | x,+,c 447 | tanh,(,x,) 448 | tanh,(,x,) 449 | sin,(,x,) 450 | sin,(,x,) 451 | x,+,x 452 | x,+,c 453 | x,+,x 454 | x,+,c 455 | tanh,(,x,) 456 | x,+,x 457 | tanh,(,x,) 458 | tanh,(,x,) 459 | x,+,c 460 | x,+,x 461 | x,+,x 462 | sin,(,x,) 463 | x,+,x 464 | x,+,c 465 | tanh,(,x,) 466 | sin,(,x,) 467 | tanh,(,x,) 468 | x,+,x 469 | tanh,(,x,) 470 | sin,(,x,) 471 | x,+,c 472 | x,+,c 473 | x,+,c 474 | sin,(,x,) 475 | x,+,x 476 | tanh,(,x,) 477 | x,+,c 478 | x,+,x 479 | x,+,c 480 | tanh,(,x,) 481 | x,+,c 482 | x,+,c 483 | x,+,c 484 | tanh,(,x,) 485 | sin,(,x,) 486 | sin,(,x,) 487 | x,+,x 488 | x,+,x 489 | x,+,x 490 | x,+,x 491 | tanh,(,x,) 492 | x,+,c 493 | tanh,(,x,) 494 | x,+,x 495 | tanh,(,x,) 496 | x,+,x 497 | x,+,c 498 | x,+,x 499 | x,+,c 500 | x,+,x 501 | tanh,(,x,) 502 | x,+,c 503 | x,+,x 504 | x,+,x 505 | x,+,x 506 | tanh,(,x,) 507 | tanh,(,x,) 508 | tanh,(,x,) 509 | sin,(,x,) 510 | sin,(,x,) 511 | x,+,c 512 | sin,(,x,) 513 | tanh,(,x,) 514 | x,+,x 515 | tanh,(,x,) 516 | sin,(,x,) 517 | x,+,c 518 | tanh,(,x,) 519 | x,+,c 520 | x,+,x 521 | sin,(,x,) 522 | sin,(,x,) 523 | sin,(,x,) 524 | x,+,c 525 | sin,(,x,) 526 | sin,(,x,) 527 | x,+,c 528 | tanh,(,x,) 529 | sin,(,x,) 530 | x,+,c 531 | x,+,x 532 | sin,(,x,) 533 | sin,(,x,) 534 | x,+,x 535 | sin,(,x,) 536 | x,+,x 537 | x,+,x 538 | x,+,x 539 | tanh,(,x,) 540 | sin,(,x,) 541 | x,+,x 542 | x,+,x 543 | tanh,(,x,) 544 | x,+,x 545 | sin,(,x,) 546 | tanh,(,x,) 547 | tanh,(,x,) 548 | x,+,x 549 | sin,(,x,) 550 | x,+,x 551 | x,+,c 552 | x,+,c 553 | x,+,c 554 | sin,(,x,) 555 | sin,(,x,) 556 | tanh,(,x,) 557 | tanh,(,x,) 558 | tanh,(,x,) 559 | tanh,(,x,) 560 | x,+,x 561 | sin,(,x,) 562 | tanh,(,x,) 563 | x,+,c 564 | sin,(,x,) 565 | tanh,(,x,) 566 | x,+,c 567 | x,+,c 568 | tanh,(,x,) 569 | x,+,x 570 | x,+,x 571 | sin,(,x,) 572 | x,+,c 573 | x,+,c 574 | x,+,c 575 | tanh,(,x,) 576 | x,+,x 577 | x,+,x 578 | x,+,x 579 | sin,(,x,) 580 | tanh,(,x,) 581 | x,+,x 582 | x,+,x 583 | tanh,(,x,) 584 | x,+,x 585 | tanh,(,x,) 586 | tanh,(,x,) 587 | sin,(,x,) 588 | x,+,x 589 | tanh,(,x,) 590 | sin,(,x,) 591 | sin,(,x,) 592 | tanh,(,x,) 593 | tanh,(,x,) 594 | sin,(,x,) 595 | sin,(,x,) 596 | tanh,(,x,) 597 | tanh,(,x,) 598 | x,+,c 599 | x,+,c 600 | x,+,x 601 | x,+,c 602 | sin,(,x,) 603 | tanh,(,x,) 604 | sin,(,x,) 605 | tanh,(,x,) 606 | tanh,(,x,) 607 | tanh,(,x,) 608 | tanh,(,x,) 609 | sin,(,x,) 610 | x,+,x 611 | tanh,(,x,) 612 | tanh,(,x,) 613 | x,+,c 614 | x,+,x 615 | tanh,(,x,) 616 | sin,(,x,) 617 | sin,(,x,) 618 | tanh,(,x,) 619 | tanh,(,x,) 620 | sin,(,x,) 621 | x,+,x 622 | x,+,c 623 | x,+,c 624 | tanh,(,x,) 625 | x,+,c 626 | x,+,c 627 | x,+,x 628 | x,+,x 629 | tanh,(,x,) 630 | x,+,x 631 | tanh,(,x,) 632 | x,+,x 633 | x,+,c 634 | sin,(,x,) 635 | x,+,c 636 | x,+,x 637 | tanh,(,x,) 638 | x,+,x 639 | x,+,c 640 | x,+,c 641 | x,+,x 642 | x,+,x 643 | x,+,c 644 | x,+,x 645 | x,+,x 646 | x,+,x 647 | x,+,x 648 | tanh,(,x,) 649 | tanh,(,x,) 650 | x,+,c 651 | tanh,(,x,) 652 | x,+,c 653 | x,+,x 654 | x,+,c 655 | sin,(,x,) 656 | x,+,x 657 | tanh,(,x,) 658 | x,+,x 659 | sin,(,x,) 660 | x,+,x 661 | sin,(,x,) 662 | x,+,x 663 | sin,(,x,) 664 | x,+,c 665 | tanh,(,x,) 666 | sin,(,x,) 667 | x,+,x 668 | sin,(,x,) 669 | x,+,x 670 | sin,(,x,) 671 | tanh,(,x,) 672 | sin,(,x,) 673 | x,+,c 674 | x,+,x 675 | x,+,x 676 | sin,(,x,) 677 | x,+,c 678 | x,+,c 679 | x,+,x 680 | x,+,x 681 | tanh,(,x,) 682 | x,+,x 683 | x,+,c 684 | tanh,(,x,) 685 | tanh,(,x,) 686 | x,+,c 687 | sin,(,x,) 688 | sin,(,x,) 689 | x,+,x 690 | sin,(,x,) 691 | tanh,(,x,) 692 | sin,(,x,) 693 | x,+,c 694 | sin,(,x,) 695 | x,+,c 696 | x,+,x 697 | x,+,c 698 | tanh,(,x,) 699 | tanh,(,x,) 700 | x,+,c 701 | x,+,x 702 | x,+,x 703 | x,+,x 704 | x,+,x 705 | x,+,x 706 | sin,(,x,) 707 | x,+,x 708 | x,+,c 709 | x,+,x 710 | sin,(,x,) 711 | x,+,c 712 | tanh,(,x,) 713 | sin,(,x,) 714 | x,+,c 715 | tanh,(,x,) 716 | tanh,(,x,) 717 | x,+,x 718 | x,+,c 719 | tanh,(,x,) 720 | tanh,(,x,) 721 | x,+,c 722 | sin,(,x,) 723 | sin,(,x,) 724 | tanh,(,x,) 725 | tanh,(,x,) 726 | sin,(,x,) 727 | x,+,c 728 | x,+,x 729 | tanh,(,x,) 730 | x,+,x 731 | sin,(,x,) 732 | x,+,x 733 | x,+,x 734 | tanh,(,x,) 735 | x,+,x 736 | tanh,(,x,) 737 | tanh,(,x,) 738 | tanh,(,x,) 739 | x,+,c 740 | x,+,x 741 | x,+,c 742 | tanh,(,x,) 743 | x,+,c 744 | sin,(,x,) 745 | sin,(,x,) 746 | x,+,x 747 | x,+,x 748 | sin,(,x,) 749 | x,+,x 750 | x,+,x 751 | x,+,c 752 | x,+,x 753 | x,+,x 754 | x,+,c 755 | sin,(,x,) 756 | tanh,(,x,) 757 | x,+,c 758 | sin,(,x,) 759 | sin,(,x,) 760 | sin,(,x,) 761 | x,+,c 762 | tanh,(,x,) 763 | tanh,(,x,) 764 | x,+,c 765 | x,+,x 766 | x,+,c 767 | x,+,x 768 | x,+,x 769 | sin,(,x,) 770 | x,+,x 771 | x,+,x 772 | tanh,(,x,) 773 | tanh,(,x,) 774 | tanh,(,x,) 775 | tanh,(,x,) 776 | tanh,(,x,) 777 | tanh,(,x,) 778 | x,+,x 779 | x,+,x 780 | x,+,c 781 | tanh,(,x,) 782 | sin,(,x,) 783 | sin,(,x,) 784 | tanh,(,x,) 785 | x,+,x 786 | x,+,x 787 | x,+,c 788 | x,+,x 789 | x,+,c 790 | tanh,(,x,) 791 | tanh,(,x,) 792 | tanh,(,x,) 793 | tanh,(,x,) 794 | sin,(,x,) 795 | x,+,c 796 | tanh,(,x,) 797 | sin,(,x,) 798 | x,+,c 799 | tanh,(,x,) 800 | x,+,c 801 | tanh,(,x,) 802 | x,+,c 803 | x,+,x 804 | x,+,c 805 | x,+,x 806 | x,+,x 807 | sin,(,x,) 808 | x,+,x 809 | tanh,(,x,) 810 | sin,(,x,) 811 | sin,(,x,) 812 | x,+,x 813 | tanh,(,x,) 814 | x,+,c 815 | x,+,c 816 | x,+,c 817 | x,+,x 818 | x,+,x 819 | x,+,c 820 | x,+,x 821 | x,+,x 822 | tanh,(,x,) 823 | x,+,c 824 | x,+,x 825 | x,+,x 826 | sin,(,x,) 827 | sin,(,x,) 828 | tanh,(,x,) 829 | x,+,c 830 | x,+,c 831 | x,+,x 832 | sin,(,x,) 833 | x,+,c 834 | tanh,(,x,) 835 | x,+,x 836 | tanh,(,x,) 837 | sin,(,x,) 838 | x,+,x 839 | x,+,x 840 | tanh,(,x,) 841 | tanh,(,x,) 842 | sin,(,x,) 843 | x,+,x 844 | x,+,c 845 | sin,(,x,) 846 | x,+,c 847 | x,+,x 848 | x,+,x 849 | x,+,c 850 | sin,(,x,) 851 | sin,(,x,) 852 | x,+,c 853 | tanh,(,x,) 854 | sin,(,x,) 855 | tanh,(,x,) 856 | tanh,(,x,) 857 | tanh,(,x,) 858 | tanh,(,x,) 859 | x,+,c 860 | x,+,c 861 | tanh,(,x,) 862 | x,+,x 863 | tanh,(,x,) 864 | tanh,(,x,) 865 | x,+,x 866 | tanh,(,x,) 867 | sin,(,x,) 868 | x,+,c 869 | x,+,c 870 | tanh,(,x,) 871 | tanh,(,x,) 872 | tanh,(,x,) 873 | sin,(,x,) 874 | x,+,x 875 | x,+,c 876 | tanh,(,x,) 877 | x,+,c 878 | x,+,x 879 | x,+,c 880 | tanh,(,x,) 881 | sin,(,x,) 882 | sin,(,x,) 883 | sin,(,x,) 884 | sin,(,x,) 885 | x,+,x 886 | x,+,c 887 | x,+,c 888 | x,+,x 889 | x,+,c 890 | tanh,(,x,) 891 | x,+,x 892 | sin,(,x,) 893 | sin,(,x,) 894 | x,+,c 895 | sin,(,x,) 896 | sin,(,x,) 897 | tanh,(,x,) 898 | tanh,(,x,) 899 | x,+,c 900 | x,+,x 901 | x,+,c 902 | sin,(,x,) 903 | tanh,(,x,) 904 | x,+,c 905 | x,+,c 906 | x,+,x 907 | sin,(,x,) 908 | tanh,(,x,) 909 | x,+,c 910 | sin,(,x,) 911 | sin,(,x,) 912 | sin,(,x,) 913 | x,+,x 914 | tanh,(,x,) 915 | x,+,x 916 | sin,(,x,) 917 | sin,(,x,) 918 | x,+,x 919 | x,+,c 920 | tanh,(,x,) 921 | x,+,c 922 | sin,(,x,) 923 | tanh,(,x,) 924 | sin,(,x,) 925 | sin,(,x,) 926 | x,+,x 927 | tanh,(,x,) 928 | x,+,c 929 | tanh,(,x,) 930 | x,+,x 931 | sin,(,x,) 932 | x,+,c 933 | sin,(,x,) 934 | x,+,x 935 | x,+,x 936 | x,+,x 937 | x,+,x 938 | x,+,x 939 | x,+,c 940 | x,+,x 941 | tanh,(,x,) 942 | tanh,(,x,) 943 | x,+,c 944 | x,+,c 945 | x,+,c 946 | x,+,x 947 | x,+,c 948 | tanh,(,x,) 949 | x,+,c 950 | x,+,c 951 | tanh,(,x,) 952 | sin,(,x,) 953 | sin,(,x,) 954 | tanh,(,x,) 955 | tanh,(,x,) 956 | x,+,c 957 | x,+,x 958 | sin,(,x,) 959 | x,+,c 960 | tanh,(,x,) 961 | x,+,x 962 | sin,(,x,) 963 | x,+,x 964 | sin,(,x,) 965 | tanh,(,x,) 966 | x,+,x 967 | x,+,x 968 | tanh,(,x,) 969 | sin,(,x,) 970 | x,+,x 971 | x,+,x 972 | tanh,(,x,) 973 | tanh,(,x,) 974 | x,+,x 975 | x,+,c 976 | x,+,c 977 | tanh,(,x,) 978 | x,+,x 979 | x,+,x 980 | sin,(,x,) 981 | tanh,(,x,) 982 | x,+,x 983 | tanh,(,x,) 984 | x,+,c 985 | tanh,(,x,) 986 | x,+,c 987 | tanh,(,x,) 988 | tanh,(,x,) 989 | x,+,c 990 | x,+,c 991 | tanh,(,x,) 992 | tanh,(,x,) 993 | x,+,x 994 | sin,(,x,) 995 | x,+,c 996 | sin,(,x,) 997 | tanh,(,x,) 998 | sin,(,x,) 999 | sin,(,x,) 1000 | x,+,c 1001 | x,+,c 1002 | x,+,x 1003 | x,+,c 1004 | x,+,x 1005 | x,+,x 1006 | sin,(,x,) 1007 | tanh,(,x,) 1008 | sin,(,x,) 1009 | sin,(,x,) 1010 | tanh,(,x,) 1011 | x,+,x 1012 | x,+,x 1013 | sin,(,x,) 1014 | x,+,x 1015 | x,+,c 1016 | x,+,c 1017 | tanh,(,x,) 1018 | tanh,(,x,) 1019 | x,+,c 1020 | sin,(,x,) 1021 | x,+,c 1022 | sin,(,x,) 1023 | x,+,c 1024 | tanh,(,x,) 1025 | x,+,c 1026 | sin,(,x,) 1027 | x,+,x 1028 | sin,(,x,) 1029 | x,+,x 1030 | sin,(,x,) 1031 | x,+,x 1032 | tanh,(,x,) 1033 | sin,(,x,) 1034 | x,+,x 1035 | x,+,x 1036 | sin,(,x,) 1037 | sin,(,x,) 1038 | x,+,c 1039 | tanh,(,x,) 1040 | x,+,x 1041 | sin,(,x,) 1042 | sin,(,x,) 1043 | tanh,(,x,) 1044 | x,+,x 1045 | sin,(,x,) 1046 | sin,(,x,) 1047 | sin,(,x,) 1048 | tanh,(,x,) 1049 | x,+,x 1050 | x,+,c 1051 | x,+,c 1052 | tanh,(,x,) 1053 | sin,(,x,) 1054 | tanh,(,x,) 1055 | x,+,x 1056 | sin,(,x,) 1057 | x,+,c 1058 | x,+,x 1059 | x,+,c 1060 | x,+,c 1061 | x,+,c 1062 | x,+,x 1063 | sin,(,x,) 1064 | x,+,c 1065 | tanh,(,x,) 1066 | sin,(,x,) 1067 | sin,(,x,) 1068 | x,+,x 1069 | x,+,c 1070 | x,+,x 1071 | tanh,(,x,) 1072 | tanh,(,x,) 1073 | sin,(,x,) 1074 | x,+,x 1075 | sin,(,x,) 1076 | sin,(,x,) 1077 | sin,(,x,) 1078 | tanh,(,x,) 1079 | x,+,c 1080 | sin,(,x,) 1081 | x,+,x 1082 | x,+,c 1083 | tanh,(,x,) 1084 | x,+,x 1085 | x,+,x 1086 | tanh,(,x,) 1087 | x,+,c 1088 | x,+,x 1089 | x,+,x 1090 | tanh,(,x,) 1091 | x,+,c 1092 | tanh,(,x,) 1093 | x,+,x 1094 | x,+,c 1095 | x,+,x 1096 | tanh,(,x,) 1097 | sin,(,x,) 1098 | sin,(,x,) 1099 | sin,(,x,) 1100 | x,+,c 1101 | sin,(,x,) 1102 | sin,(,x,) 1103 | x,+,c 1104 | sin,(,x,) 1105 | tanh,(,x,) 1106 | x,+,c 1107 | x,+,c 1108 | x,+,x 1109 | x,+,x 1110 | sin,(,x,) 1111 | x,+,x 1112 | sin,(,x,) 1113 | x,+,c 1114 | x,+,x 1115 | x,+,c 1116 | tanh,(,x,) 1117 | sin,(,x,) 1118 | x,+,c 1119 | x,+,c 1120 | x,+,c 1121 | sin,(,x,) 1122 | x,+,x 1123 | tanh,(,x,) 1124 | x,+,x 1125 | sin,(,x,) 1126 | x,+,c 1127 | sin,(,x,) 1128 | tanh,(,x,) 1129 | sin,(,x,) 1130 | x,+,c 1131 | x,+,c 1132 | tanh,(,x,) 1133 | x,+,c 1134 | x,+,c 1135 | tanh,(,x,) 1136 | x,+,c 1137 | x,+,c 1138 | x,+,c 1139 | x,+,x 1140 | x,+,x 1141 | sin,(,x,) 1142 | x,+,x 1143 | x,+,c 1144 | sin,(,x,) 1145 | tanh,(,x,) 1146 | x,+,c 1147 | sin,(,x,) 1148 | x,+,x 1149 | x,+,x 1150 | tanh,(,x,) 1151 | x,+,c 1152 | x,+,x 1153 | x,+,c 1154 | tanh,(,x,) 1155 | x,+,x 1156 | x,+,c 1157 | tanh,(,x,) 1158 | sin,(,x,) 1159 | tanh,(,x,) 1160 | x,+,x 1161 | tanh,(,x,) 1162 | tanh,(,x,) 1163 | sin,(,x,) 1164 | tanh,(,x,) 1165 | tanh,(,x,) 1166 | tanh,(,x,) 1167 | x,+,x 1168 | tanh,(,x,) 1169 | tanh,(,x,) 1170 | x,+,c 1171 | x,+,x 1172 | x,+,c 1173 | sin,(,x,) 1174 | sin,(,x,) 1175 | sin,(,x,) 1176 | tanh,(,x,) 1177 | x,+,c 1178 | tanh,(,x,) 1179 | tanh,(,x,) 1180 | x,+,c 1181 | x,+,c 1182 | sin,(,x,) 1183 | sin,(,x,) 1184 | sin,(,x,) 1185 | tanh,(,x,) 1186 | tanh,(,x,) 1187 | x,+,c 1188 | tanh,(,x,) 1189 | x,+,x 1190 | x,+,c 1191 | x,+,c 1192 | x,+,x 1193 | tanh,(,x,) 1194 | tanh,(,x,) 1195 | tanh,(,x,) 1196 | sin,(,x,) 1197 | x,+,c 1198 | tanh,(,x,) 1199 | sin,(,x,) 1200 | sin,(,x,) 1201 | x,+,c 1202 | sin,(,x,) 1203 | x,+,c 1204 | x,+,c 1205 | sin,(,x,) 1206 | x,+,c 1207 | sin,(,x,) 1208 | x,+,c 1209 | x,+,c 1210 | sin,(,x,) 1211 | tanh,(,x,) 1212 | sin,(,x,) 1213 | x,+,c 1214 | tanh,(,x,) 1215 | x,+,x 1216 | x,+,c 1217 | tanh,(,x,) 1218 | x,+,x 1219 | sin,(,x,) 1220 | tanh,(,x,) 1221 | sin,(,x,) 1222 | x,+,x 1223 | x,+,x 1224 | x,+,c 1225 | x,+,x 1226 | x,+,c 1227 | sin,(,x,) 1228 | sin,(,x,) 1229 | tanh,(,x,) 1230 | x,+,x 1231 | tanh,(,x,) 1232 | tanh,(,x,) 1233 | x,+,x 1234 | x,+,c 1235 | tanh,(,x,) 1236 | sin,(,x,) 1237 | x,+,c 1238 | tanh,(,x,) 1239 | sin,(,x,) 1240 | sin,(,x,) 1241 | x,+,x 1242 | x,+,x 1243 | x,+,x 1244 | tanh,(,x,) 1245 | x,+,c 1246 | tanh,(,x,) 1247 | x,+,c 1248 | x,+,x 1249 | sin,(,x,) 1250 | x,+,c 1251 | x,+,x 1252 | tanh,(,x,) 1253 | x,+,x 1254 | tanh,(,x,) 1255 | tanh,(,x,) 1256 | tanh,(,x,) 1257 | x,+,x 1258 | x,+,c 1259 | tanh,(,x,) 1260 | tanh,(,x,) 1261 | tanh,(,x,) 1262 | tanh,(,x,) 1263 | x,+,c 1264 | x,+,x 1265 | x,+,x 1266 | tanh,(,x,) 1267 | x,+,x 1268 | sin,(,x,) 1269 | x,+,x 1270 | tanh,(,x,) 1271 | x,+,x 1272 | tanh,(,x,) 1273 | sin,(,x,) 1274 | x,+,c 1275 | sin,(,x,) 1276 | x,+,c 1277 | tanh,(,x,) 1278 | x,+,x 1279 | x,+,x 1280 | x,+,x 1281 | tanh,(,x,) 1282 | sin,(,x,) 1283 | x,+,c 1284 | x,+,x 1285 | tanh,(,x,) 1286 | sin,(,x,) 1287 | sin,(,x,) 1288 | x,+,x 1289 | tanh,(,x,) 1290 | x,+,x 1291 | sin,(,x,) 1292 | tanh,(,x,) 1293 | tanh,(,x,) 1294 | x,+,x 1295 | x,+,x 1296 | tanh,(,x,) 1297 | sin,(,x,) 1298 | x,+,c 1299 | x,+,c 1300 | sin,(,x,) 1301 | x,+,c 1302 | tanh,(,x,) 1303 | tanh,(,x,) 1304 | sin,(,x,) 1305 | sin,(,x,) 1306 | x,+,c 1307 | x,+,x 1308 | x,+,x 1309 | x,+,x 1310 | sin,(,x,) 1311 | tanh,(,x,) 1312 | sin,(,x,) 1313 | tanh,(,x,) 1314 | tanh,(,x,) 1315 | tanh,(,x,) 1316 | tanh,(,x,) 1317 | sin,(,x,) 1318 | tanh,(,x,) 1319 | x,+,x 1320 | x,+,c 1321 | x,+,c 1322 | x,+,x 1323 | x,+,c 1324 | sin,(,x,) 1325 | x,+,c 1326 | sin,(,x,) 1327 | tanh,(,x,) 1328 | x,+,c 1329 | x,+,x 1330 | x,+,c 1331 | sin,(,x,) 1332 | tanh,(,x,) 1333 | tanh,(,x,) 1334 | tanh,(,x,) 1335 | sin,(,x,) 1336 | sin,(,x,) 1337 | x,+,c 1338 | x,+,x 1339 | x,+,x 1340 | x,+,x 1341 | x,+,c 1342 | x,+,c 1343 | x,+,c 1344 | x,+,c 1345 | x,+,x 1346 | tanh,(,x,) 1347 | tanh,(,x,) 1348 | tanh,(,x,) 1349 | tanh,(,x,) 1350 | tanh,(,x,) 1351 | tanh,(,x,) 1352 | x,+,x 1353 | x,+,x 1354 | tanh,(,x,) 1355 | sin,(,x,) 1356 | x,+,c 1357 | tanh,(,x,) 1358 | x,+,x 1359 | sin,(,x,) 1360 | x,+,c 1361 | x,+,c 1362 | tanh,(,x,) 1363 | tanh,(,x,) 1364 | sin,(,x,) 1365 | x,+,c 1366 | x,+,c 1367 | tanh,(,x,) 1368 | sin,(,x,) 1369 | tanh,(,x,) 1370 | x,+,c 1371 | tanh,(,x,) 1372 | x,+,c 1373 | x,+,x 1374 | x,+,c 1375 | x,+,c 1376 | x,+,c 1377 | x,+,c 1378 | x,+,c 1379 | x,+,c 1380 | sin,(,x,) 1381 | sin,(,x,) 1382 | sin,(,x,) 1383 | x,+,c 1384 | tanh,(,x,) 1385 | x,+,x 1386 | x,+,x 1387 | tanh,(,x,) 1388 | tanh,(,x,) 1389 | x,+,c 1390 | x,+,c 1391 | sin,(,x,) 1392 | x,+,c 1393 | x,+,x 1394 | tanh,(,x,) 1395 | x,+,x 1396 | x,+,c 1397 | x,+,c 1398 | x,+,c 1399 | sin,(,x,) 1400 | tanh,(,x,) 1401 | x,+,x 1402 | sin,(,x,) 1403 | x,+,c 1404 | x,+,c 1405 | sin,(,x,) 1406 | x,+,c 1407 | tanh,(,x,) 1408 | x,+,c 1409 | x,+,c 1410 | x,+,c 1411 | x,+,x 1412 | tanh,(,x,) 1413 | tanh,(,x,) 1414 | tanh,(,x,) 1415 | tanh,(,x,) 1416 | x,+,x 1417 | x,+,c 1418 | tanh,(,x,) 1419 | x,+,c 1420 | x,+,x 1421 | sin,(,x,) 1422 | tanh,(,x,) 1423 | x,+,c 1424 | x,+,x 1425 | sin,(,x,) 1426 | x,+,x 1427 | tanh,(,x,) 1428 | sin,(,x,) 1429 | tanh,(,x,) 1430 | x,+,c 1431 | x,+,x 1432 | x,+,c 1433 | sin,(,x,) 1434 | x,+,c 1435 | x,+,x 1436 | x,+,x 1437 | x,+,x 1438 | tanh,(,x,) 1439 | x,+,x 1440 | x,+,c 1441 | x,+,c 1442 | sin,(,x,) 1443 | sin,(,x,) 1444 | sin,(,x,) 1445 | tanh,(,x,) 1446 | x,+,c 1447 | x,+,x 1448 | sin,(,x,) 1449 | sin,(,x,) 1450 | tanh,(,x,) 1451 | x,+,x 1452 | x,+,x 1453 | tanh,(,x,) 1454 | x,+,c 1455 | tanh,(,x,) 1456 | x,+,x 1457 | tanh,(,x,) 1458 | x,+,x 1459 | sin,(,x,) 1460 | x,+,x 1461 | x,+,x 1462 | sin,(,x,) 1463 | tanh,(,x,) 1464 | x,+,c 1465 | sin,(,x,) 1466 | x,+,x 1467 | x,+,c 1468 | x,+,c 1469 | sin,(,x,) 1470 | x,+,c 1471 | tanh,(,x,) 1472 | x,+,c 1473 | x,+,c 1474 | x,+,c 1475 | x,+,x 1476 | sin,(,x,) 1477 | sin,(,x,) 1478 | x,+,x 1479 | tanh,(,x,) 1480 | tanh,(,x,) 1481 | x,+,x 1482 | tanh,(,x,) 1483 | tanh,(,x,) 1484 | tanh,(,x,) 1485 | tanh,(,x,) 1486 | x,+,x 1487 | x,+,c 1488 | tanh,(,x,) 1489 | x,+,x 1490 | x,+,c 1491 | x,+,c 1492 | sin,(,x,) 1493 | sin,(,x,) 1494 | x,+,c 1495 | sin,(,x,) 1496 | tanh,(,x,) 1497 | x,+,x 1498 | sin,(,x,) 1499 | x,+,c 1500 | sin,(,x,) 1501 | -------------------------------------------------------------------------------- /data/desired_equation_components_d3.txt: -------------------------------------------------------------------------------- 1 | x,+,x,+,c 2 | x,+,c,+,x 3 | tanh,(,x,),+,x 4 | tanh,(,x,),+,tanh,(,x,) 5 | tanh,(,x,+,x,) 6 | x,+,x 7 | tanh,(,x,) 8 | sin,(,tanh,(,x,),) 9 | sin,(,x,),+,tanh,(,x,) 10 | x,+,x,+,x,+,x 11 | tanh,(,sin,(,x,),) 12 | x,+,x,+,x 13 | sin,(,x,),+,x,+,x 14 | tanh,(,sin,(,x,),) 15 | sin,(,x,),+,sin,(,x,) 16 | tanh,(,x,) 17 | tanh,(,x,),+,c 18 | sin,(,x,+,c,) 19 | x,+,x,+,c 20 | sin,(,x,),+,x 21 | sin,(,x,) 22 | sin,(,tanh,(,x,),) 23 | x,+,x,+,c 24 | sin,(,x,+,c,) 25 | x,+,c,+,x,+,c 26 | x,+,x,+,x 27 | tanh,(,x,) 28 | sin,(,tanh,(,x,),) 29 | tanh,(,tanh,(,x,),) 30 | sin,(,x,),+,x 31 | x,+,x,+,c 32 | sin,(,x,),+,x,+,x 33 | tanh,(,sin,(,x,),) 34 | sin,(,x,+,x,) 35 | sin,(,x,+,x,) 36 | x,+,x 37 | tanh,(,x,),+,sin,(,x,) 38 | x,+,x,+,x 39 | tanh,(,tanh,(,x,),) 40 | tanh,(,x,+,c,) 41 | x,+,c 42 | sin,(,x,+,x,) 43 | x,+,x,+,x 44 | sin,(,x,+,x,) 45 | sin,(,sin,(,x,),) 46 | tanh,(,x,),+,x 47 | x,+,c,+,x,+,c 48 | x,+,x 49 | x,+,x,+,x,+,x 50 | tanh,(,sin,(,x,),) 51 | sin,(,x,+,c,) 52 | sin,(,sin,(,x,),) 53 | x,+,x,+,x 54 | sin,(,x,) 55 | x,+,c,+,tanh,(,x,) 56 | x,+,x,+,tanh,(,x,) 57 | sin,(,x,) 58 | x,+,x,+,c 59 | x,+,x 60 | tanh,(,x,) 61 | tanh,(,tanh,(,x,),) 62 | tanh,(,sin,(,x,),) 63 | sin,(,x,),+,c 64 | tanh,(,tanh,(,x,),) 65 | sin,(,sin,(,x,),) 66 | sin,(,x,+,x,) 67 | x,+,c,+,x 68 | x,+,x,+,x 69 | x,+,x,+,x,+,c 70 | tanh,(,x,) 71 | tanh,(,x,+,c,) 72 | sin,(,tanh,(,x,),) 73 | tanh,(,x,),+,x 74 | tanh,(,x,) 75 | tanh,(,tanh,(,x,),) 76 | sin,(,x,+,x,) 77 | x,+,c,+,x 78 | sin,(,x,) 79 | tanh,(,x,) 80 | sin,(,x,),+,x,+,x 81 | tanh,(,x,+,x,) 82 | tanh,(,tanh,(,x,),) 83 | tanh,(,x,+,x,) 84 | x,+,x,+,c 85 | x,+,x,+,x 86 | sin,(,x,),+,c 87 | sin,(,x,) 88 | x,+,x,+,x 89 | sin,(,x,) 90 | x,+,c,+,sin,(,x,) 91 | sin,(,x,+,x,) 92 | tanh,(,tanh,(,x,),) 93 | sin,(,x,) 94 | tanh,(,x,),+,x,+,x 95 | x,+,x,+,x 96 | sin,(,x,),+,x,+,x 97 | tanh,(,x,+,x,) 98 | sin,(,x,),+,sin,(,x,) 99 | tanh,(,x,),+,sin,(,x,) 100 | sin,(,tanh,(,x,),) 101 | sin,(,x,+,x,) 102 | tanh,(,x,) 103 | tanh,(,x,),+,x 104 | tanh,(,x,) 105 | tanh,(,x,),+,x 106 | tanh,(,x,),+,x 107 | sin,(,x,+,c,) 108 | sin,(,x,+,c,) 109 | sin,(,x,),+,x 110 | tanh,(,x,),+,x 111 | sin,(,x,),+,x 112 | tanh,(,x,),+,x,+,x 113 | tanh,(,sin,(,x,),) 114 | x,+,x,+,x 115 | sin,(,x,),+,sin,(,x,) 116 | x,+,x,+,x,+,c 117 | sin,(,x,) 118 | sin,(,x,) 119 | sin,(,sin,(,x,),) 120 | x,+,x,+,x 121 | tanh,(,x,+,c,) 122 | sin,(,x,),+,tanh,(,x,) 123 | sin,(,tanh,(,x,),) 124 | x,+,x,+,x 125 | sin,(,x,) 126 | sin,(,sin,(,x,),) 127 | x,+,x 128 | x,+,c,+,x 129 | tanh,(,x,) 130 | tanh,(,tanh,(,x,),) 131 | tanh,(,x,) 132 | x,+,c,+,sin,(,x,) 133 | sin,(,x,),+,x 134 | sin,(,x,),+,x 135 | x,+,x,+,c 136 | x,+,c 137 | tanh,(,x,) 138 | tanh,(,x,) 139 | x,+,c,+,sin,(,x,) 140 | tanh,(,x,),+,x,+,x 141 | x,+,x,+,c 142 | x,+,c 143 | tanh,(,tanh,(,x,),) 144 | sin,(,x,+,x,) 145 | x,+,c 146 | tanh,(,x,+,x,) 147 | tanh,(,x,),+,sin,(,x,) 148 | sin,(,x,),+,x 149 | x,+,x,+,sin,(,x,) 150 | tanh,(,tanh,(,x,),) 151 | sin,(,x,) 152 | x,+,x,+,x 153 | tanh,(,tanh,(,x,),) 154 | x,+,c,+,sin,(,x,) 155 | x,+,x,+,x,+,x 156 | x,+,c 157 | sin,(,x,),+,x 158 | tanh,(,x,+,x,) 159 | tanh,(,x,+,x,) 160 | sin,(,x,+,x,) 161 | x,+,x,+,c 162 | x,+,c,+,x 163 | x,+,c 164 | tanh,(,x,),+,sin,(,x,) 165 | tanh,(,x,) 166 | tanh,(,x,+,c,) 167 | sin,(,x,+,x,) 168 | tanh,(,x,) 169 | tanh,(,x,),+,tanh,(,x,) 170 | sin,(,x,) 171 | sin,(,x,+,c,) 172 | tanh,(,x,+,x,) 173 | tanh,(,x,) 174 | x,+,x,+,c 175 | tanh,(,x,+,x,) 176 | tanh,(,sin,(,x,),) 177 | sin,(,x,+,x,) 178 | x,+,c 179 | sin,(,sin,(,x,),) 180 | sin,(,x,+,c,) 181 | x,+,c,+,tanh,(,x,) 182 | sin,(,x,),+,x 183 | sin,(,x,) 184 | x,+,c,+,tanh,(,x,) 185 | sin,(,x,) 186 | tanh,(,x,),+,x,+,x 187 | tanh,(,x,),+,x 188 | x,+,c,+,c 189 | x,+,x,+,c 190 | sin,(,x,+,x,) 191 | tanh,(,tanh,(,x,),) 192 | sin,(,x,),+,c 193 | tanh,(,sin,(,x,),) 194 | sin,(,sin,(,x,),) 195 | tanh,(,x,),+,c 196 | tanh,(,x,+,x,) 197 | sin,(,x,),+,x 198 | tanh,(,x,) 199 | sin,(,x,),+,x 200 | sin,(,x,) 201 | x,+,x,+,x,+,x 202 | sin,(,x,),+,x 203 | sin,(,x,+,x,) 204 | tanh,(,x,) 205 | sin,(,x,) 206 | sin,(,sin,(,x,),) 207 | tanh,(,x,+,c,) 208 | sin,(,x,),+,c 209 | x,+,x,+,c 210 | tanh,(,x,) 211 | tanh,(,x,+,c,) 212 | sin,(,x,) 213 | x,+,c,+,x,+,x 214 | tanh,(,x,),+,x 215 | x,+,c 216 | x,+,x,+,c 217 | x,+,x,+,c 218 | tanh,(,x,),+,sin,(,x,) 219 | tanh,(,x,) 220 | x,+,x 221 | tanh,(,x,),+,x 222 | x,+,c 223 | x,+,x,+,x 224 | x,+,x,+,x,+,c 225 | tanh,(,x,+,x,) 226 | tanh,(,x,+,c,) 227 | x,+,x,+,sin,(,x,) 228 | sin,(,x,),+,x 229 | tanh,(,x,) 230 | tanh,(,x,),+,x 231 | x,+,c,+,c 232 | tanh,(,x,),+,x,+,c 233 | x,+,x,+,x 234 | x,+,c,+,x,+,c 235 | sin,(,x,),+,sin,(,x,) 236 | x,+,x,+,x,+,c 237 | x,+,x,+,sin,(,x,) 238 | tanh,(,x,+,x,) 239 | sin,(,x,+,c,) 240 | tanh,(,x,+,c,) 241 | x,+,c,+,x 242 | tanh,(,sin,(,x,),) 243 | x,+,c,+,x 244 | x,+,x,+,tanh,(,x,) 245 | sin,(,x,) 246 | sin,(,x,),+,c 247 | sin,(,x,+,x,) 248 | sin,(,x,),+,x 249 | sin,(,tanh,(,x,),) 250 | x,+,x,+,tanh,(,x,) 251 | sin,(,x,+,c,) 252 | tanh,(,x,),+,tanh,(,x,) 253 | tanh,(,sin,(,x,),) 254 | tanh,(,x,) 255 | sin,(,x,),+,c 256 | sin,(,x,) 257 | tanh,(,x,+,c,) 258 | tanh,(,x,+,c,) 259 | x,+,c 260 | tanh,(,sin,(,x,),) 261 | x,+,c 262 | sin,(,x,),+,x 263 | tanh,(,x,),+,sin,(,x,) 264 | sin,(,tanh,(,x,),) 265 | tanh,(,sin,(,x,),) 266 | tanh,(,x,) 267 | sin,(,x,),+,x 268 | sin,(,x,),+,x 269 | x,+,x,+,x,+,c 270 | tanh,(,x,),+,c 271 | sin,(,x,),+,x 272 | tanh,(,tanh,(,x,),) 273 | tanh,(,x,),+,tanh,(,x,) 274 | x,+,c 275 | x,+,c,+,c 276 | x,+,c,+,tanh,(,x,) 277 | tanh,(,x,),+,x 278 | sin,(,x,+,c,) 279 | x,+,c,+,c 280 | x,+,x,+,x 281 | tanh,(,x,+,c,) 282 | tanh,(,sin,(,x,),) 283 | tanh,(,x,) 284 | tanh,(,x,+,x,) 285 | sin,(,x,),+,c 286 | sin,(,x,),+,x 287 | tanh,(,tanh,(,x,),) 288 | tanh,(,tanh,(,x,),) 289 | sin,(,tanh,(,x,),) 290 | tanh,(,tanh,(,x,),) 291 | sin,(,x,+,c,) 292 | sin,(,x,) 293 | sin,(,x,),+,x 294 | sin,(,x,),+,c 295 | x,+,x,+,c 296 | tanh,(,x,) 297 | tanh,(,x,),+,c 298 | sin,(,tanh,(,x,),) 299 | tanh,(,x,) 300 | sin,(,x,),+,x,+,c 301 | x,+,c,+,sin,(,x,) 302 | x,+,c,+,c 303 | sin,(,x,+,c,) 304 | x,+,x,+,x 305 | tanh,(,x,),+,x,+,x 306 | x,+,x,+,sin,(,x,) 307 | sin,(,x,),+,x,+,x 308 | sin,(,x,) 309 | x,+,c,+,c 310 | tanh,(,x,) 311 | x,+,c 312 | x,+,x,+,c 313 | tanh,(,x,) 314 | x,+,c,+,x,+,c 315 | x,+,c,+,c 316 | tanh,(,x,),+,x,+,x 317 | sin,(,x,),+,sin,(,x,) 318 | sin,(,tanh,(,x,),) 319 | tanh,(,x,+,x,) 320 | sin,(,x,) 321 | tanh,(,x,) 322 | sin,(,x,+,x,) 323 | tanh,(,x,+,x,) 324 | sin,(,x,+,c,) 325 | sin,(,x,+,x,) 326 | tanh,(,x,),+,x 327 | sin,(,x,),+,x 328 | x,+,x 329 | tanh,(,tanh,(,x,),) 330 | x,+,x,+,sin,(,x,) 331 | tanh,(,x,+,c,) 332 | sin,(,x,+,c,) 333 | tanh,(,x,) 334 | sin,(,x,) 335 | sin,(,x,),+,x 336 | tanh,(,x,+,x,) 337 | x,+,c,+,x 338 | sin,(,x,) 339 | tanh,(,x,+,c,) 340 | x,+,c,+,tanh,(,x,) 341 | x,+,x,+,c 342 | sin,(,x,) 343 | sin,(,x,),+,x,+,c 344 | sin,(,x,) 345 | tanh,(,x,+,c,) 346 | sin,(,x,),+,sin,(,x,) 347 | sin,(,x,) 348 | tanh,(,x,),+,x 349 | tanh,(,x,+,x,) 350 | x,+,x,+,sin,(,x,) 351 | sin,(,x,),+,x 352 | sin,(,x,),+,x 353 | tanh,(,x,+,x,) 354 | x,+,c,+,x 355 | x,+,x 356 | x,+,c,+,x,+,c 357 | x,+,x,+,c 358 | x,+,c 359 | tanh,(,x,) 360 | x,+,x,+,x,+,x 361 | x,+,c 362 | tanh,(,x,),+,x 363 | tanh,(,x,),+,x 364 | sin,(,x,+,c,) 365 | tanh,(,x,),+,x 366 | tanh,(,x,) 367 | x,+,c,+,c 368 | tanh,(,x,),+,tanh,(,x,) 369 | sin,(,x,),+,x,+,x 370 | tanh,(,x,) 371 | sin,(,x,) 372 | tanh,(,x,),+,sin,(,x,) 373 | sin,(,x,) 374 | x,+,c,+,x,+,x 375 | x,+,x,+,x,+,c 376 | sin,(,x,),+,x,+,c 377 | x,+,c,+,x,+,c 378 | x,+,c 379 | sin,(,x,),+,c 380 | tanh,(,x,),+,tanh,(,x,) 381 | x,+,x 382 | x,+,c 383 | tanh,(,tanh,(,x,),) 384 | tanh,(,x,+,x,) 385 | x,+,x,+,x,+,c 386 | tanh,(,sin,(,x,),) 387 | x,+,x,+,x 388 | x,+,x,+,c 389 | x,+,x,+,x 390 | sin,(,x,+,x,) 391 | sin,(,x,),+,sin,(,x,) 392 | sin,(,x,),+,x 393 | x,+,c,+,x 394 | sin,(,x,),+,x 395 | sin,(,x,+,x,) 396 | x,+,x 397 | sin,(,x,) 398 | tanh,(,x,+,c,) 399 | sin,(,sin,(,x,),) 400 | sin,(,x,),+,x,+,c 401 | sin,(,sin,(,x,),) 402 | x,+,x,+,x,+,c 403 | x,+,c 404 | tanh,(,x,+,x,) 405 | tanh,(,x,),+,x 406 | x,+,c,+,tanh,(,x,) 407 | tanh,(,x,) 408 | sin,(,sin,(,x,),) 409 | sin,(,x,+,x,) 410 | tanh,(,sin,(,x,),) 411 | tanh,(,x,+,x,) 412 | x,+,x,+,x 413 | tanh,(,x,),+,x 414 | tanh,(,sin,(,x,),) 415 | sin,(,x,) 416 | tanh,(,x,),+,sin,(,x,) 417 | sin,(,tanh,(,x,),) 418 | sin,(,x,) 419 | tanh,(,sin,(,x,),) 420 | tanh,(,x,) 421 | tanh,(,tanh,(,x,),) 422 | x,+,c,+,sin,(,x,) 423 | tanh,(,x,+,x,) 424 | sin,(,x,),+,c 425 | x,+,x,+,x 426 | sin,(,x,) 427 | sin,(,x,) 428 | sin,(,tanh,(,x,),) 429 | tanh,(,x,),+,tanh,(,x,) 430 | tanh,(,x,),+,tanh,(,x,) 431 | sin,(,x,) 432 | x,+,c,+,c 433 | sin,(,x,) 434 | sin,(,x,+,c,) 435 | sin,(,x,) 436 | x,+,x 437 | x,+,c 438 | sin,(,x,),+,tanh,(,x,) 439 | sin,(,x,+,c,) 440 | x,+,x,+,x,+,c 441 | tanh,(,x,),+,c 442 | sin,(,x,),+,tanh,(,x,) 443 | tanh,(,x,) 444 | x,+,c,+,x 445 | tanh,(,x,) 446 | sin,(,x,),+,x 447 | x,+,c 448 | tanh,(,sin,(,x,),) 449 | sin,(,x,+,x,) 450 | tanh,(,sin,(,x,),) 451 | tanh,(,x,+,x,) 452 | sin,(,x,+,c,) 453 | tanh,(,x,),+,sin,(,x,) 454 | tanh,(,x,+,x,) 455 | tanh,(,x,),+,c 456 | tanh,(,x,+,x,) 457 | tanh,(,x,),+,x,+,c 458 | sin,(,tanh,(,x,),) 459 | x,+,c,+,c 460 | x,+,x,+,c 461 | tanh,(,x,) 462 | x,+,c,+,sin,(,x,) 463 | tanh,(,x,),+,tanh,(,x,) 464 | x,+,c,+,x 465 | tanh,(,x,+,x,) 466 | sin,(,sin,(,x,),) 467 | sin,(,x,+,c,) 468 | sin,(,x,+,c,) 469 | x,+,c 470 | sin,(,tanh,(,x,),) 471 | x,+,x 472 | sin,(,x,+,c,) 473 | x,+,x,+,x 474 | sin,(,sin,(,x,),) 475 | tanh,(,x,),+,c 476 | tanh,(,x,+,c,) 477 | tanh,(,x,+,x,) 478 | x,+,x 479 | sin,(,sin,(,x,),) 480 | sin,(,x,+,c,) 481 | sin,(,x,),+,c 482 | sin,(,x,) 483 | tanh,(,x,+,c,) 484 | tanh,(,x,),+,tanh,(,x,) 485 | sin,(,x,+,x,) 486 | sin,(,x,) 487 | sin,(,x,) 488 | sin,(,x,),+,x 489 | sin,(,x,),+,c 490 | tanh,(,x,+,x,) 491 | sin,(,x,),+,sin,(,x,) 492 | tanh,(,x,),+,sin,(,x,) 493 | tanh,(,tanh,(,x,),) 494 | tanh,(,x,) 495 | tanh,(,x,+,c,) 496 | tanh,(,tanh,(,x,),) 497 | tanh,(,sin,(,x,),) 498 | sin,(,sin,(,x,),) 499 | tanh,(,x,) 500 | sin,(,x,) 501 | tanh,(,x,+,c,) 502 | tanh,(,x,+,x,) 503 | x,+,x,+,c 504 | sin,(,x,),+,sin,(,x,) 505 | sin,(,x,+,x,) 506 | x,+,x,+,c 507 | tanh,(,x,),+,x,+,c 508 | tanh,(,sin,(,x,),) 509 | sin,(,tanh,(,x,),) 510 | x,+,x,+,x,+,c 511 | tanh,(,tanh,(,x,),) 512 | x,+,x,+,c 513 | x,+,c,+,c 514 | x,+,x,+,c 515 | tanh,(,x,+,x,) 516 | x,+,x,+,x,+,c 517 | sin,(,x,) 518 | tanh,(,x,),+,c 519 | sin,(,x,),+,x 520 | tanh,(,x,),+,x 521 | x,+,c 522 | sin,(,x,+,c,) 523 | x,+,x,+,c 524 | x,+,x 525 | tanh,(,tanh,(,x,),) 526 | sin,(,x,) 527 | tanh,(,x,) 528 | x,+,x,+,sin,(,x,) 529 | tanh,(,x,+,c,) 530 | sin,(,x,),+,x 531 | sin,(,x,+,x,) 532 | tanh,(,x,) 533 | x,+,x,+,x 534 | x,+,x 535 | x,+,x,+,x 536 | tanh,(,x,),+,c 537 | sin,(,sin,(,x,),) 538 | sin,(,x,),+,sin,(,x,) 539 | sin,(,x,),+,tanh,(,x,) 540 | sin,(,sin,(,x,),) 541 | tanh,(,x,),+,x 542 | tanh,(,sin,(,x,),) 543 | x,+,x,+,c 544 | tanh,(,sin,(,x,),) 545 | x,+,x,+,c 546 | x,+,c,+,x,+,x 547 | x,+,c 548 | x,+,c,+,tanh,(,x,) 549 | x,+,x,+,x,+,x 550 | tanh,(,x,) 551 | x,+,c,+,c 552 | tanh,(,x,) 553 | sin,(,x,),+,x,+,c 554 | tanh,(,x,+,c,) 555 | x,+,x,+,c 556 | tanh,(,tanh,(,x,),) 557 | x,+,x 558 | x,+,x,+,tanh,(,x,) 559 | tanh,(,sin,(,x,),) 560 | sin,(,x,),+,sin,(,x,) 561 | sin,(,x,+,c,) 562 | x,+,c,+,c 563 | sin,(,x,) 564 | tanh,(,x,),+,x 565 | tanh,(,x,+,x,) 566 | tanh,(,x,+,c,) 567 | sin,(,x,),+,x 568 | sin,(,x,+,x,) 569 | tanh,(,x,) 570 | tanh,(,x,) 571 | x,+,x,+,x 572 | tanh,(,x,) 573 | tanh,(,x,+,x,) 574 | tanh,(,x,) 575 | x,+,c 576 | sin,(,x,) 577 | x,+,x,+,x 578 | sin,(,x,+,x,) 579 | tanh,(,tanh,(,x,),) 580 | x,+,x,+,x 581 | tanh,(,x,),+,x 582 | sin,(,x,),+,x,+,x 583 | x,+,x,+,sin,(,x,) 584 | sin,(,x,),+,sin,(,x,) 585 | x,+,c 586 | x,+,c,+,c 587 | sin,(,tanh,(,x,),) 588 | x,+,x,+,c 589 | sin,(,x,) 590 | x,+,x,+,x 591 | sin,(,x,) 592 | x,+,c 593 | sin,(,x,+,c,) 594 | tanh,(,x,+,c,) 595 | x,+,x,+,c 596 | tanh,(,tanh,(,x,),) 597 | tanh,(,tanh,(,x,),) 598 | x,+,c 599 | x,+,c,+,tanh,(,x,) 600 | sin,(,sin,(,x,),) 601 | sin,(,x,),+,tanh,(,x,) 602 | x,+,c 603 | sin,(,x,) 604 | x,+,c 605 | tanh,(,x,),+,x,+,c 606 | sin,(,x,) 607 | tanh,(,x,+,c,) 608 | x,+,x 609 | sin,(,x,),+,x,+,x 610 | x,+,x,+,x 611 | sin,(,x,),+,x 612 | sin,(,x,),+,x 613 | sin,(,x,) 614 | sin,(,x,),+,x,+,c 615 | tanh,(,x,+,c,) 616 | x,+,c 617 | tanh,(,x,) 618 | x,+,c 619 | sin,(,sin,(,x,),) 620 | tanh,(,tanh,(,x,),) 621 | tanh,(,x,) 622 | tanh,(,x,+,x,) 623 | sin,(,x,+,x,) 624 | sin,(,x,),+,x 625 | sin,(,x,) 626 | sin,(,x,+,c,) 627 | tanh,(,x,+,c,) 628 | sin,(,x,) 629 | x,+,x,+,x 630 | x,+,x,+,sin,(,x,) 631 | x,+,c 632 | tanh,(,x,) 633 | x,+,c 634 | sin,(,x,+,x,) 635 | tanh,(,sin,(,x,),) 636 | sin,(,x,),+,x 637 | sin,(,x,),+,x 638 | tanh,(,x,) 639 | tanh,(,x,+,x,) 640 | tanh,(,x,+,x,) 641 | x,+,x,+,x 642 | tanh,(,tanh,(,x,),) 643 | sin,(,sin,(,x,),) 644 | tanh,(,x,+,c,) 645 | sin,(,x,),+,x 646 | x,+,x,+,x 647 | sin,(,x,),+,x 648 | x,+,x,+,c 649 | sin,(,tanh,(,x,),) 650 | sin,(,x,),+,x 651 | sin,(,tanh,(,x,),) 652 | tanh,(,x,+,x,) 653 | tanh,(,x,),+,x 654 | sin,(,x,) 655 | sin,(,x,+,c,) 656 | tanh,(,x,),+,sin,(,x,) 657 | sin,(,x,) 658 | x,+,c,+,x,+,c 659 | sin,(,sin,(,x,),) 660 | sin,(,x,+,c,) 661 | tanh,(,x,),+,tanh,(,x,) 662 | sin,(,x,),+,x,+,c 663 | x,+,x 664 | x,+,c,+,c 665 | x,+,c 666 | x,+,c,+,x 667 | tanh,(,x,),+,sin,(,x,) 668 | sin,(,sin,(,x,),) 669 | x,+,x,+,x 670 | tanh,(,x,) 671 | x,+,c,+,x 672 | sin,(,x,+,c,) 673 | tanh,(,x,+,x,) 674 | x,+,c,+,x 675 | tanh,(,x,) 676 | x,+,c 677 | tanh,(,x,),+,x 678 | sin,(,x,) 679 | sin,(,sin,(,x,),) 680 | x,+,x,+,x 681 | tanh,(,x,) 682 | tanh,(,x,),+,x,+,c 683 | x,+,x 684 | x,+,x,+,x,+,x 685 | sin,(,x,+,c,) 686 | sin,(,x,),+,x,+,x 687 | sin,(,x,+,c,) 688 | x,+,x,+,c 689 | sin,(,x,) 690 | sin,(,tanh,(,x,),) 691 | x,+,x,+,c 692 | tanh,(,x,),+,x 693 | sin,(,x,) 694 | tanh,(,x,),+,x 695 | tanh,(,x,+,c,) 696 | tanh,(,x,),+,x 697 | sin,(,tanh,(,x,),) 698 | tanh,(,x,) 699 | tanh,(,x,) 700 | sin,(,sin,(,x,),) 701 | tanh,(,x,),+,x 702 | x,+,c,+,sin,(,x,) 703 | x,+,x,+,x 704 | tanh,(,x,) 705 | tanh,(,x,),+,tanh,(,x,) 706 | sin,(,x,) 707 | tanh,(,tanh,(,x,),) 708 | sin,(,x,),+,x 709 | x,+,c,+,c 710 | sin,(,tanh,(,x,),) 711 | sin,(,x,+,x,) 712 | x,+,x,+,c 713 | x,+,c 714 | sin,(,x,) 715 | tanh,(,x,+,c,) 716 | sin,(,tanh,(,x,),) 717 | tanh,(,x,+,x,) 718 | x,+,x,+,x 719 | tanh,(,tanh,(,x,),) 720 | sin,(,x,) 721 | x,+,x,+,x 722 | sin,(,x,+,c,) 723 | sin,(,x,),+,x 724 | sin,(,x,+,x,) 725 | sin,(,sin,(,x,),) 726 | sin,(,sin,(,x,),) 727 | sin,(,x,+,c,) 728 | x,+,x,+,x 729 | tanh,(,x,),+,x,+,c 730 | tanh,(,x,),+,x 731 | sin,(,x,) 732 | tanh,(,tanh,(,x,),) 733 | tanh,(,x,),+,tanh,(,x,) 734 | tanh,(,x,) 735 | tanh,(,x,),+,x 736 | sin,(,x,+,x,) 737 | x,+,c,+,x,+,c 738 | x,+,c,+,c 739 | x,+,c 740 | sin,(,x,),+,x 741 | tanh,(,sin,(,x,),) 742 | x,+,x,+,x 743 | tanh,(,x,+,x,) 744 | tanh,(,x,),+,x,+,c 745 | x,+,c,+,x,+,x 746 | tanh,(,x,+,c,) 747 | sin,(,x,) 748 | tanh,(,x,+,c,) 749 | x,+,c,+,sin,(,x,) 750 | sin,(,tanh,(,x,),) 751 | sin,(,x,+,c,) 752 | sin,(,x,+,x,) 753 | sin,(,x,) 754 | tanh,(,tanh,(,x,),) 755 | sin,(,x,),+,c 756 | sin,(,x,+,x,) 757 | sin,(,x,) 758 | sin,(,x,+,c,) 759 | sin,(,sin,(,x,),) 760 | sin,(,x,),+,x 761 | x,+,c,+,sin,(,x,) 762 | tanh,(,x,+,c,) 763 | tanh,(,x,+,c,) 764 | sin,(,x,),+,c 765 | x,+,c,+,c 766 | tanh,(,sin,(,x,),) 767 | tanh,(,x,+,c,) 768 | x,+,c,+,c 769 | sin,(,x,),+,x,+,x 770 | x,+,c 771 | sin,(,x,) 772 | sin,(,x,+,x,) 773 | sin,(,x,),+,x 774 | tanh,(,x,) 775 | tanh,(,x,),+,c 776 | tanh,(,tanh,(,x,),) 777 | tanh,(,x,+,c,) 778 | sin,(,x,+,c,) 779 | tanh,(,x,+,c,) 780 | tanh,(,sin,(,x,),) 781 | sin,(,x,),+,sin,(,x,) 782 | tanh,(,tanh,(,x,),) 783 | tanh,(,tanh,(,x,),) 784 | x,+,c,+,tanh,(,x,) 785 | sin,(,x,) 786 | tanh,(,x,),+,x 787 | tanh,(,sin,(,x,),) 788 | tanh,(,x,),+,x,+,c 789 | sin,(,sin,(,x,),) 790 | tanh,(,tanh,(,x,),) 791 | x,+,x,+,x 792 | sin,(,x,) 793 | sin,(,x,) 794 | x,+,x,+,sin,(,x,) 795 | tanh,(,x,+,x,) 796 | sin,(,x,),+,x,+,x 797 | sin,(,x,),+,tanh,(,x,) 798 | sin,(,x,),+,x,+,x 799 | sin,(,x,),+,sin,(,x,) 800 | tanh,(,x,+,x,) 801 | tanh,(,tanh,(,x,),) 802 | sin,(,x,+,c,) 803 | sin,(,x,+,x,) 804 | sin,(,x,),+,x 805 | sin,(,x,) 806 | sin,(,x,) 807 | x,+,c,+,x 808 | sin,(,tanh,(,x,),) 809 | x,+,c,+,x,+,x 810 | x,+,x 811 | sin,(,x,) 812 | sin,(,x,+,c,) 813 | sin,(,x,),+,x,+,x 814 | tanh,(,x,),+,sin,(,x,) 815 | tanh,(,x,+,x,) 816 | tanh,(,x,) 817 | sin,(,sin,(,x,),) 818 | x,+,c,+,x 819 | sin,(,x,) 820 | tanh,(,x,+,x,) 821 | sin,(,x,) 822 | x,+,c 823 | sin,(,x,+,x,) 824 | tanh,(,sin,(,x,),) 825 | sin,(,x,+,x,) 826 | tanh,(,x,),+,tanh,(,x,) 827 | x,+,x,+,x,+,c 828 | x,+,x,+,c 829 | sin,(,x,+,c,) 830 | sin,(,x,+,c,) 831 | sin,(,sin,(,x,),) 832 | sin,(,x,) 833 | sin,(,x,+,c,) 834 | sin,(,x,) 835 | tanh,(,x,) 836 | tanh,(,x,+,c,) 837 | sin,(,x,) 838 | tanh,(,x,),+,c 839 | sin,(,tanh,(,x,),) 840 | tanh,(,x,),+,x,+,x 841 | x,+,x,+,tanh,(,x,) 842 | sin,(,x,+,x,) 843 | sin,(,x,),+,tanh,(,x,) 844 | sin,(,x,+,x,) 845 | tanh,(,x,),+,x 846 | x,+,c,+,c 847 | tanh,(,tanh,(,x,),) 848 | x,+,x,+,sin,(,x,) 849 | tanh,(,x,+,c,) 850 | tanh,(,x,+,x,) 851 | tanh,(,x,) 852 | tanh,(,sin,(,x,),) 853 | x,+,c 854 | x,+,x,+,x,+,c 855 | x,+,x,+,c 856 | sin,(,x,) 857 | sin,(,x,+,x,) 858 | tanh,(,x,+,c,) 859 | x,+,x,+,c 860 | sin,(,tanh,(,x,),) 861 | sin,(,x,+,x,) 862 | x,+,c,+,x,+,c 863 | tanh,(,x,) 864 | tanh,(,x,+,x,) 865 | x,+,x,+,sin,(,x,) 866 | tanh,(,x,),+,x 867 | tanh,(,sin,(,x,),) 868 | sin,(,x,) 869 | tanh,(,x,),+,x,+,c 870 | tanh,(,x,) 871 | tanh,(,x,+,x,) 872 | sin,(,tanh,(,x,),) 873 | tanh,(,sin,(,x,),) 874 | sin,(,x,),+,c 875 | sin,(,tanh,(,x,),) 876 | tanh,(,x,),+,c 877 | sin,(,x,),+,sin,(,x,) 878 | x,+,x,+,c 879 | sin,(,x,),+,x 880 | sin,(,sin,(,x,),) 881 | sin,(,x,+,x,) 882 | sin,(,x,+,x,) 883 | tanh,(,tanh,(,x,),) 884 | sin,(,x,) 885 | x,+,x,+,x,+,c 886 | sin,(,x,) 887 | tanh,(,x,+,c,) 888 | x,+,x,+,x,+,x 889 | sin,(,x,+,x,) 890 | tanh,(,tanh,(,x,),) 891 | sin,(,x,+,x,) 892 | x,+,x,+,c 893 | sin,(,x,),+,x,+,c 894 | sin,(,x,) 895 | x,+,x,+,sin,(,x,) 896 | x,+,x,+,x 897 | sin,(,x,),+,x,+,x 898 | sin,(,x,+,x,) 899 | x,+,x,+,x 900 | x,+,c 901 | x,+,c,+,c 902 | sin,(,x,) 903 | sin,(,x,) 904 | sin,(,x,+,x,) 905 | tanh,(,x,),+,c 906 | tanh,(,x,),+,sin,(,x,) 907 | sin,(,x,),+,x 908 | tanh,(,tanh,(,x,),) 909 | tanh,(,x,),+,x,+,x 910 | sin,(,x,) 911 | x,+,x,+,x 912 | sin,(,x,),+,x 913 | sin,(,x,+,c,) 914 | tanh,(,x,+,c,) 915 | sin,(,x,) 916 | sin,(,x,),+,x 917 | x,+,x,+,x,+,c 918 | x,+,c,+,x 919 | tanh,(,x,) 920 | tanh,(,tanh,(,x,),) 921 | x,+,x,+,c 922 | sin,(,sin,(,x,),) 923 | sin,(,x,+,c,) 924 | x,+,c 925 | x,+,x 926 | x,+,c 927 | tanh,(,x,) 928 | tanh,(,tanh,(,x,),) 929 | tanh,(,tanh,(,x,),) 930 | sin,(,x,) 931 | x,+,x,+,c 932 | tanh,(,x,+,c,) 933 | tanh,(,sin,(,x,),) 934 | x,+,c,+,x,+,x 935 | x,+,x,+,x 936 | sin,(,x,) 937 | sin,(,sin,(,x,),) 938 | sin,(,x,) 939 | tanh,(,x,) 940 | x,+,c,+,x 941 | tanh,(,x,) 942 | tanh,(,x,),+,x,+,x 943 | sin,(,sin,(,x,),) 944 | sin,(,sin,(,x,),) 945 | tanh,(,x,+,x,) 946 | sin,(,x,),+,x 947 | x,+,x,+,c 948 | tanh,(,x,) 949 | tanh,(,x,) 950 | sin,(,x,),+,x,+,c 951 | x,+,x 952 | sin,(,x,) 953 | tanh,(,x,) 954 | sin,(,x,),+,x,+,x 955 | tanh,(,x,),+,c 956 | tanh,(,tanh,(,x,),) 957 | tanh,(,x,),+,x,+,x 958 | tanh,(,x,),+,tanh,(,x,) 959 | tanh,(,x,+,c,) 960 | x,+,c,+,c 961 | x,+,x,+,x,+,c 962 | x,+,x 963 | x,+,c 964 | x,+,x,+,x,+,c 965 | sin,(,x,) 966 | sin,(,x,+,c,) 967 | sin,(,x,) 968 | x,+,c,+,sin,(,x,) 969 | x,+,x,+,sin,(,x,) 970 | x,+,c,+,tanh,(,x,) 971 | x,+,c,+,tanh,(,x,) 972 | x,+,x 973 | tanh,(,x,),+,x,+,x 974 | sin,(,x,),+,x,+,c 975 | x,+,c 976 | tanh,(,x,),+,x,+,c 977 | tanh,(,x,),+,tanh,(,x,) 978 | sin,(,tanh,(,x,),) 979 | x,+,c,+,x 980 | sin,(,sin,(,x,),) 981 | sin,(,sin,(,x,),) 982 | x,+,x,+,sin,(,x,) 983 | tanh,(,x,) 984 | x,+,c,+,sin,(,x,) 985 | tanh,(,sin,(,x,),) 986 | tanh,(,x,) 987 | sin,(,x,+,c,) 988 | tanh,(,x,),+,x 989 | sin,(,x,),+,tanh,(,x,) 990 | x,+,c,+,x,+,c 991 | tanh,(,x,),+,tanh,(,x,) 992 | x,+,x,+,x,+,c 993 | sin,(,x,+,c,) 994 | tanh,(,x,),+,x 995 | sin,(,x,+,x,) 996 | sin,(,x,),+,sin,(,x,) 997 | sin,(,x,+,c,) 998 | x,+,c 999 | tanh,(,x,+,c,) 1000 | x,+,x,+,x,+,c 1001 | sin,(,x,+,c,) 1002 | sin,(,tanh,(,x,),) 1003 | x,+,x,+,x 1004 | x,+,c 1005 | x,+,c,+,x 1006 | x,+,x 1007 | tanh,(,sin,(,x,),) 1008 | x,+,x,+,c 1009 | x,+,x,+,tanh,(,x,) 1010 | tanh,(,x,+,c,) 1011 | sin,(,tanh,(,x,),) 1012 | tanh,(,x,),+,x,+,x 1013 | sin,(,x,),+,c 1014 | tanh,(,x,),+,c 1015 | tanh,(,x,) 1016 | tanh,(,tanh,(,x,),) 1017 | x,+,c,+,c 1018 | x,+,x 1019 | x,+,x,+,x,+,x 1020 | tanh,(,x,),+,c 1021 | sin,(,x,+,c,) 1022 | x,+,x,+,c 1023 | tanh,(,x,) 1024 | sin,(,x,),+,x,+,c 1025 | sin,(,x,),+,c 1026 | sin,(,x,) 1027 | sin,(,x,) 1028 | sin,(,x,) 1029 | sin,(,sin,(,x,),) 1030 | tanh,(,x,) 1031 | tanh,(,x,+,x,) 1032 | sin,(,x,+,x,) 1033 | tanh,(,sin,(,x,),) 1034 | tanh,(,x,),+,x 1035 | tanh,(,x,),+,x 1036 | tanh,(,x,),+,sin,(,x,) 1037 | tanh,(,x,+,x,) 1038 | x,+,c 1039 | sin,(,x,),+,x,+,x 1040 | sin,(,x,) 1041 | sin,(,x,+,x,) 1042 | sin,(,x,) 1043 | tanh,(,sin,(,x,),) 1044 | sin,(,x,),+,x 1045 | x,+,x,+,sin,(,x,) 1046 | x,+,x,+,x 1047 | tanh,(,x,),+,x 1048 | tanh,(,x,) 1049 | sin,(,x,+,c,) 1050 | tanh,(,x,+,x,) 1051 | sin,(,x,+,x,) 1052 | sin,(,x,),+,c 1053 | sin,(,x,),+,x 1054 | x,+,x,+,c 1055 | tanh,(,x,) 1056 | tanh,(,x,) 1057 | tanh,(,x,) 1058 | tanh,(,x,+,x,) 1059 | tanh,(,sin,(,x,),) 1060 | sin,(,x,),+,c 1061 | sin,(,x,),+,x,+,c 1062 | tanh,(,x,+,x,) 1063 | tanh,(,x,) 1064 | sin,(,x,),+,x 1065 | sin,(,x,),+,c 1066 | tanh,(,sin,(,x,),) 1067 | x,+,c,+,x,+,x 1068 | x,+,x,+,c 1069 | sin,(,x,) 1070 | x,+,x,+,x 1071 | sin,(,x,+,x,) 1072 | x,+,c,+,tanh,(,x,) 1073 | tanh,(,x,+,x,) 1074 | tanh,(,x,) 1075 | sin,(,x,),+,x 1076 | x,+,c,+,x,+,x 1077 | x,+,c 1078 | tanh,(,x,+,c,) 1079 | sin,(,x,),+,sin,(,x,) 1080 | tanh,(,x,),+,tanh,(,x,) 1081 | tanh,(,x,) 1082 | x,+,c 1083 | sin,(,x,),+,x,+,x 1084 | sin,(,x,),+,x 1085 | tanh,(,x,) 1086 | tanh,(,x,) 1087 | tanh,(,x,+,c,) 1088 | tanh,(,x,) 1089 | x,+,x,+,c 1090 | sin,(,x,) 1091 | x,+,x,+,x 1092 | tanh,(,x,+,c,) 1093 | sin,(,x,) 1094 | sin,(,x,),+,c 1095 | tanh,(,x,+,c,) 1096 | x,+,c,+,x 1097 | sin,(,x,) 1098 | sin,(,tanh,(,x,),) 1099 | x,+,c,+,x,+,x 1100 | tanh,(,x,),+,c 1101 | sin,(,tanh,(,x,),) 1102 | sin,(,x,) 1103 | sin,(,tanh,(,x,),) 1104 | sin,(,x,+,x,) 1105 | sin,(,x,+,x,) 1106 | tanh,(,x,),+,x 1107 | tanh,(,sin,(,x,),) 1108 | x,+,x 1109 | sin,(,sin,(,x,),) 1110 | sin,(,x,),+,x,+,x 1111 | x,+,x 1112 | tanh,(,tanh,(,x,),) 1113 | sin,(,sin,(,x,),) 1114 | sin,(,sin,(,x,),) 1115 | sin,(,x,) 1116 | tanh,(,x,+,c,) 1117 | sin,(,x,) 1118 | sin,(,x,),+,c 1119 | tanh,(,x,),+,c 1120 | sin,(,sin,(,x,),) 1121 | x,+,x 1122 | tanh,(,x,+,x,) 1123 | sin,(,x,+,c,) 1124 | tanh,(,x,) 1125 | x,+,x 1126 | sin,(,x,) 1127 | x,+,x 1128 | sin,(,x,),+,x 1129 | x,+,c,+,c 1130 | sin,(,sin,(,x,),) 1131 | x,+,c 1132 | sin,(,x,+,c,) 1133 | tanh,(,tanh,(,x,),) 1134 | sin,(,x,),+,sin,(,x,) 1135 | tanh,(,x,+,x,) 1136 | x,+,x,+,x 1137 | tanh,(,x,) 1138 | tanh,(,x,),+,c 1139 | sin,(,x,+,c,) 1140 | x,+,c,+,x,+,x 1141 | tanh,(,x,+,c,) 1142 | tanh,(,sin,(,x,),) 1143 | x,+,c,+,x 1144 | sin,(,x,+,x,) 1145 | x,+,c,+,x,+,c 1146 | x,+,c 1147 | sin,(,x,) 1148 | x,+,x 1149 | tanh,(,x,+,x,) 1150 | x,+,x,+,x,+,x 1151 | sin,(,tanh,(,x,),) 1152 | x,+,c 1153 | sin,(,x,) 1154 | x,+,x,+,x,+,c 1155 | sin,(,x,+,x,) 1156 | sin,(,x,) 1157 | sin,(,x,),+,x,+,x 1158 | x,+,c,+,x,+,x 1159 | tanh,(,x,+,c,) 1160 | sin,(,x,),+,x 1161 | sin,(,sin,(,x,),) 1162 | tanh,(,x,),+,x 1163 | tanh,(,x,),+,sin,(,x,) 1164 | sin,(,x,),+,c 1165 | x,+,c,+,x,+,c 1166 | tanh,(,x,) 1167 | tanh,(,tanh,(,x,),) 1168 | tanh,(,x,+,c,) 1169 | sin,(,x,+,c,) 1170 | tanh,(,x,),+,sin,(,x,) 1171 | tanh,(,x,+,x,) 1172 | sin,(,x,+,x,) 1173 | tanh,(,x,) 1174 | x,+,x,+,x 1175 | sin,(,x,) 1176 | sin,(,x,) 1177 | x,+,x,+,c 1178 | sin,(,x,),+,c 1179 | x,+,x,+,x 1180 | x,+,c 1181 | sin,(,x,+,x,) 1182 | x,+,c,+,c 1183 | x,+,x,+,c 1184 | x,+,x,+,c 1185 | x,+,x,+,c 1186 | x,+,x,+,x,+,x 1187 | tanh,(,sin,(,x,),) 1188 | x,+,c,+,c 1189 | sin,(,sin,(,x,),) 1190 | x,+,c,+,c 1191 | tanh,(,x,+,x,) 1192 | x,+,x,+,x 1193 | tanh,(,x,+,c,) 1194 | x,+,x,+,tanh,(,x,) 1195 | sin,(,x,+,x,) 1196 | x,+,x,+,x 1197 | x,+,x,+,x,+,c 1198 | sin,(,x,+,x,) 1199 | x,+,c,+,x 1200 | tanh,(,x,+,x,) 1201 | tanh,(,x,),+,sin,(,x,) 1202 | tanh,(,tanh,(,x,),) 1203 | sin,(,x,+,x,) 1204 | sin,(,sin,(,x,),) 1205 | sin,(,x,) 1206 | sin,(,x,) 1207 | tanh,(,x,),+,x,+,x 1208 | x,+,x,+,sin,(,x,) 1209 | x,+,x,+,x,+,c 1210 | sin,(,x,),+,c 1211 | x,+,c,+,x,+,c 1212 | tanh,(,x,),+,c 1213 | tanh,(,x,+,x,) 1214 | tanh,(,x,),+,sin,(,x,) 1215 | sin,(,x,),+,sin,(,x,) 1216 | sin,(,x,),+,sin,(,x,) 1217 | tanh,(,sin,(,x,),) 1218 | x,+,x 1219 | x,+,x,+,c 1220 | tanh,(,x,) 1221 | x,+,x,+,c 1222 | sin,(,tanh,(,x,),) 1223 | sin,(,x,),+,x 1224 | x,+,x,+,c 1225 | tanh,(,x,) 1226 | sin,(,tanh,(,x,),) 1227 | x,+,x 1228 | tanh,(,x,),+,x,+,c 1229 | tanh,(,x,+,c,) 1230 | tanh,(,x,),+,x 1231 | sin,(,x,+,c,) 1232 | x,+,c,+,x,+,c 1233 | tanh,(,sin,(,x,),) 1234 | tanh,(,x,+,c,) 1235 | tanh,(,x,),+,c 1236 | sin,(,sin,(,x,),) 1237 | tanh,(,x,+,c,) 1238 | x,+,x,+,c 1239 | tanh,(,x,),+,c 1240 | x,+,x,+,x 1241 | sin,(,x,),+,sin,(,x,) 1242 | sin,(,x,+,x,) 1243 | sin,(,x,),+,c 1244 | x,+,x,+,c 1245 | x,+,x,+,x 1246 | x,+,c,+,c 1247 | sin,(,sin,(,x,),) 1248 | sin,(,sin,(,x,),) 1249 | sin,(,sin,(,x,),) 1250 | tanh,(,x,) 1251 | x,+,c 1252 | sin,(,x,+,c,) 1253 | tanh,(,x,),+,x,+,c 1254 | tanh,(,x,+,x,) 1255 | tanh,(,x,+,c,) 1256 | x,+,c 1257 | tanh,(,x,),+,x,+,x 1258 | sin,(,tanh,(,x,),) 1259 | tanh,(,tanh,(,x,),) 1260 | sin,(,sin,(,x,),) 1261 | sin,(,x,+,c,) 1262 | tanh,(,x,+,c,) 1263 | sin,(,x,) 1264 | tanh,(,tanh,(,x,),) 1265 | x,+,x,+,c 1266 | tanh,(,x,),+,x,+,c 1267 | x,+,c,+,c 1268 | tanh,(,sin,(,x,),) 1269 | tanh,(,sin,(,x,),) 1270 | tanh,(,x,) 1271 | tanh,(,x,+,c,) 1272 | x,+,c 1273 | sin,(,x,+,x,) 1274 | sin,(,x,+,c,) 1275 | tanh,(,x,) 1276 | sin,(,sin,(,x,),) 1277 | tanh,(,tanh,(,x,),) 1278 | x,+,c 1279 | sin,(,x,),+,x,+,c 1280 | sin,(,x,+,x,) 1281 | sin,(,x,) 1282 | tanh,(,x,) 1283 | x,+,x,+,x,+,c 1284 | sin,(,x,),+,x 1285 | tanh,(,x,),+,c 1286 | tanh,(,x,+,x,) 1287 | sin,(,x,) 1288 | sin,(,x,) 1289 | tanh,(,x,+,x,) 1290 | x,+,x,+,tanh,(,x,) 1291 | sin,(,x,+,x,) 1292 | tanh,(,x,) 1293 | sin,(,sin,(,x,),) 1294 | sin,(,x,) 1295 | x,+,c,+,x 1296 | sin,(,x,),+,c 1297 | sin,(,tanh,(,x,),) 1298 | x,+,x,+,tanh,(,x,) 1299 | sin,(,x,),+,x 1300 | x,+,x 1301 | sin,(,x,+,c,) 1302 | x,+,c 1303 | tanh,(,x,+,x,) 1304 | sin,(,x,),+,x,+,x 1305 | x,+,c 1306 | x,+,x,+,tanh,(,x,) 1307 | x,+,x,+,x,+,c 1308 | tanh,(,x,+,c,) 1309 | tanh,(,x,),+,x 1310 | tanh,(,x,) 1311 | sin,(,x,) 1312 | sin,(,x,+,c,) 1313 | sin,(,sin,(,x,),) 1314 | sin,(,x,) 1315 | sin,(,x,),+,x 1316 | tanh,(,x,),+,tanh,(,x,) 1317 | sin,(,x,+,x,) 1318 | tanh,(,x,+,x,) 1319 | tanh,(,x,) 1320 | x,+,x,+,x 1321 | sin,(,x,),+,c 1322 | sin,(,sin,(,x,),) 1323 | tanh,(,x,) 1324 | sin,(,x,) 1325 | tanh,(,x,),+,x,+,x 1326 | tanh,(,x,),+,tanh,(,x,) 1327 | x,+,c 1328 | sin,(,x,+,c,) 1329 | sin,(,tanh,(,x,),) 1330 | tanh,(,x,) 1331 | tanh,(,x,),+,c 1332 | tanh,(,tanh,(,x,),) 1333 | x,+,c 1334 | tanh,(,x,) 1335 | sin,(,tanh,(,x,),) 1336 | sin,(,tanh,(,x,),) 1337 | tanh,(,sin,(,x,),) 1338 | sin,(,x,) 1339 | x,+,c 1340 | x,+,c,+,x 1341 | tanh,(,x,) 1342 | x,+,x 1343 | tanh,(,sin,(,x,),) 1344 | tanh,(,sin,(,x,),) 1345 | x,+,x,+,c 1346 | sin,(,x,+,c,) 1347 | sin,(,sin,(,x,),) 1348 | tanh,(,sin,(,x,),) 1349 | sin,(,x,+,x,) 1350 | sin,(,x,),+,x 1351 | sin,(,x,),+,x 1352 | sin,(,x,+,x,) 1353 | sin,(,x,+,c,) 1354 | x,+,x,+,x 1355 | tanh,(,x,) 1356 | tanh,(,x,) 1357 | tanh,(,x,+,c,) 1358 | sin,(,x,+,x,) 1359 | tanh,(,x,+,x,) 1360 | tanh,(,x,+,c,) 1361 | tanh,(,x,),+,x 1362 | sin,(,x,),+,x 1363 | x,+,x,+,x 1364 | x,+,x,+,x 1365 | x,+,c 1366 | x,+,x,+,c 1367 | tanh,(,x,),+,sin,(,x,) 1368 | sin,(,tanh,(,x,),) 1369 | tanh,(,tanh,(,x,),) 1370 | x,+,c,+,x,+,c 1371 | x,+,x 1372 | sin,(,tanh,(,x,),) 1373 | tanh,(,x,),+,x,+,x 1374 | x,+,x,+,c 1375 | tanh,(,x,+,x,) 1376 | x,+,x,+,x 1377 | tanh,(,x,) 1378 | tanh,(,x,+,x,) 1379 | sin,(,x,) 1380 | sin,(,x,+,x,) 1381 | x,+,x,+,x 1382 | tanh,(,x,) 1383 | sin,(,sin,(,x,),) 1384 | tanh,(,x,),+,x 1385 | tanh,(,x,) 1386 | tanh,(,x,) 1387 | tanh,(,x,+,x,) 1388 | x,+,x,+,c 1389 | x,+,c,+,x 1390 | x,+,x,+,sin,(,x,) 1391 | sin,(,x,+,c,) 1392 | tanh,(,x,),+,x,+,x 1393 | x,+,x 1394 | sin,(,tanh,(,x,),) 1395 | sin,(,x,),+,x 1396 | sin,(,tanh,(,x,),) 1397 | sin,(,x,+,c,) 1398 | x,+,x,+,sin,(,x,) 1399 | x,+,c,+,x 1400 | sin,(,x,) 1401 | sin,(,x,) 1402 | tanh,(,tanh,(,x,),) 1403 | x,+,c,+,x,+,c 1404 | tanh,(,x,+,c,) 1405 | x,+,c,+,tanh,(,x,) 1406 | sin,(,x,) 1407 | tanh,(,tanh,(,x,),) 1408 | tanh,(,x,) 1409 | x,+,x,+,c 1410 | sin,(,x,+,x,) 1411 | sin,(,x,),+,x 1412 | sin,(,tanh,(,x,),) 1413 | x,+,c 1414 | tanh,(,x,),+,x,+,c 1415 | x,+,c,+,sin,(,x,) 1416 | tanh,(,x,),+,x 1417 | sin,(,x,) 1418 | x,+,x 1419 | tanh,(,x,),+,c 1420 | x,+,x,+,c 1421 | x,+,x,+,x 1422 | tanh,(,x,+,x,) 1423 | sin,(,sin,(,x,),) 1424 | tanh,(,x,),+,x,+,c 1425 | x,+,c,+,x,+,c 1426 | sin,(,x,+,x,) 1427 | tanh,(,x,),+,x 1428 | sin,(,x,) 1429 | tanh,(,x,),+,x 1430 | tanh,(,x,),+,x 1431 | sin,(,x,),+,x 1432 | x,+,c,+,x 1433 | x,+,x,+,x 1434 | x,+,c,+,x,+,x 1435 | tanh,(,x,),+,x 1436 | sin,(,sin,(,x,),) 1437 | x,+,c 1438 | tanh,(,x,),+,c 1439 | x,+,x 1440 | sin,(,tanh,(,x,),) 1441 | tanh,(,x,),+,x 1442 | sin,(,sin,(,x,),) 1443 | x,+,c,+,x,+,x 1444 | sin,(,x,+,x,) 1445 | x,+,x,+,x 1446 | tanh,(,x,),+,x,+,c 1447 | tanh,(,x,) 1448 | sin,(,x,) 1449 | x,+,x 1450 | x,+,x,+,x 1451 | x,+,x,+,x,+,x 1452 | tanh,(,x,+,c,) 1453 | sin,(,x,) 1454 | x,+,c,+,tanh,(,x,) 1455 | sin,(,x,+,x,) 1456 | tanh,(,tanh,(,x,),) 1457 | sin,(,x,),+,c 1458 | x,+,c,+,sin,(,x,) 1459 | sin,(,sin,(,x,),) 1460 | tanh,(,x,),+,x,+,x 1461 | tanh,(,x,) 1462 | sin,(,sin,(,x,),) 1463 | tanh,(,x,),+,sin,(,x,) 1464 | sin,(,x,),+,x 1465 | tanh,(,x,+,c,) 1466 | x,+,x,+,x,+,c 1467 | sin,(,x,),+,x 1468 | sin,(,tanh,(,x,),) 1469 | sin,(,x,) 1470 | sin,(,x,),+,x,+,c 1471 | sin,(,sin,(,x,),) 1472 | sin,(,x,) 1473 | tanh,(,x,) 1474 | x,+,x,+,x,+,x 1475 | tanh,(,x,),+,c 1476 | sin,(,x,),+,sin,(,x,) 1477 | tanh,(,x,+,c,) 1478 | tanh,(,x,+,x,) 1479 | tanh,(,x,) 1480 | sin,(,sin,(,x,),) 1481 | tanh,(,x,),+,x,+,c 1482 | x,+,c,+,x,+,x 1483 | sin,(,x,),+,tanh,(,x,) 1484 | sin,(,x,) 1485 | sin,(,x,),+,x,+,x 1486 | tanh,(,tanh,(,x,),) 1487 | sin,(,x,),+,x,+,x 1488 | tanh,(,x,),+,x 1489 | x,+,x,+,c 1490 | x,+,c 1491 | tanh,(,x,),+,x 1492 | x,+,c,+,x,+,c 1493 | x,+,c 1494 | x,+,x,+,x 1495 | x,+,c,+,sin,(,x,) 1496 | tanh,(,sin,(,x,),) 1497 | x,+,c,+,x,+,c 1498 | sin,(,x,),+,tanh,(,x,) 1499 | tanh,(,x,),+,tanh,(,x,) 1500 | tanh,(,sin,(,x,),) 1501 | -------------------------------------------------------------------------------- /data/desired_equation_components_d4.txt: -------------------------------------------------------------------------------- 1 | x,+,x 2 | tanh,(,tanh,(,x,),),+,tanh,(,tanh,(,x,),) 3 | sin,(,sin,(,tanh,(,x,),),) 4 | tanh,(,tanh,(,x,),+,x,) 5 | x,+,c 6 | sin,(,x,+,x,) 7 | tanh,(,x,),+,x,+,x 8 | tanh,(,x,+,c,),+,tanh,(,x,) 9 | tanh,(,x,+,x,+,tanh,(,x,),) 10 | tanh,(,x,) 11 | tanh,(,x,),+,x,+,c 12 | sin,(,x,+,x,+,c,) 13 | x,+,c 14 | sin,(,sin,(,x,),),+,x 15 | tanh,(,x,) 16 | tanh,(,x,) 17 | sin,(,x,),+,tanh,(,sin,(,x,),) 18 | tanh,(,x,+,x,+,x,) 19 | x,+,sin,(,x,),+,x 20 | tanh,(,sin,(,x,),),+,x,+,x,+,c 21 | x,+,c 22 | sin,(,tanh,(,x,),) 23 | x,+,tanh,(,x,),+,c 24 | sin,(,x,) 25 | sin,(,sin,(,x,),),+,x,+,x,+,tanh,(,x,) 26 | tanh,(,x,+,x,+,c,) 27 | x,+,x,+,x,+,x,+,x 28 | tanh,(,x,),+,tanh,(,sin,(,x,),) 29 | x,+,c 30 | tanh,(,sin,(,x,+,x,),) 31 | sin,(,x,+,c,+,c,) 32 | x,+,sin,(,x,),+,tanh,(,x,) 33 | sin,(,tanh,(,x,),+,sin,(,x,),) 34 | tanh,(,sin,(,x,),) 35 | tanh,(,x,) 36 | sin,(,x,+,x,+,x,) 37 | x,+,c,+,x,+,sin,(,x,),+,x,+,x 38 | tanh,(,sin,(,x,),),+,sin,(,x,) 39 | x,+,c,+,tanh,(,tanh,(,x,),) 40 | sin,(,sin,(,x,+,x,),) 41 | tanh,(,sin,(,x,),) 42 | sin,(,sin,(,x,+,c,),) 43 | tanh,(,sin,(,tanh,(,x,),),) 44 | tanh,(,tanh,(,x,),) 45 | tanh,(,x,+,c,+,sin,(,x,),) 46 | x,+,x,+,x 47 | sin,(,tanh,(,x,),+,x,) 48 | x,+,c,+,c,+,tanh,(,x,),+,sin,(,x,) 49 | tanh,(,x,+,c,+,c,) 50 | sin,(,x,),+,c,+,x,+,c 51 | tanh,(,x,) 52 | sin,(,x,) 53 | x,+,x 54 | tanh,(,x,+,c,) 55 | x,+,c,+,sin,(,x,),+,tanh,(,x,) 56 | tanh,(,sin,(,tanh,(,x,),),) 57 | tanh,(,sin,(,x,),) 58 | x,+,x 59 | tanh,(,tanh,(,x,),+,tanh,(,x,),) 60 | tanh,(,tanh,(,x,),),+,x 61 | tanh,(,x,) 62 | tanh,(,sin,(,x,+,c,),) 63 | tanh,(,x,+,c,+,x,) 64 | tanh,(,x,+,x,),+,x 65 | x,+,c 66 | sin,(,sin,(,tanh,(,x,),),) 67 | tanh,(,x,),+,x 68 | sin,(,tanh,(,x,),) 69 | sin,(,x,),+,c 70 | tanh,(,x,) 71 | tanh,(,x,) 72 | tanh,(,x,+,x,+,tanh,(,x,),) 73 | tanh,(,x,+,x,) 74 | sin,(,x,) 75 | tanh,(,x,+,x,+,c,) 76 | x,+,x,+,x,+,x,+,c 77 | tanh,(,x,) 78 | sin,(,tanh,(,x,),+,sin,(,x,),) 79 | x,+,x 80 | tanh,(,tanh,(,x,),+,tanh,(,x,),) 81 | sin,(,x,),+,c,+,c 82 | x,+,x,+,x,+,c 83 | sin,(,x,+,x,),+,x 84 | sin,(,x,+,x,+,x,) 85 | tanh,(,x,) 86 | tanh,(,x,+,c,),+,x 87 | sin,(,x,),+,x 88 | sin,(,x,),+,c,+,x 89 | tanh,(,x,+,x,+,c,) 90 | sin,(,tanh,(,x,),),+,c 91 | sin,(,sin,(,x,),) 92 | x,+,x,+,x 93 | x,+,c,+,tanh,(,x,),+,sin,(,x,),+,x 94 | x,+,c 95 | tanh,(,x,+,c,),+,x,+,c 96 | tanh,(,x,) 97 | x,+,x 98 | tanh,(,x,),+,x,+,x,+,x 99 | sin,(,x,+,c,),+,c 100 | sin,(,x,+,x,),+,x 101 | x,+,x 102 | tanh,(,x,+,c,+,c,) 103 | sin,(,x,),+,c,+,x,+,c,+,c 104 | sin,(,x,+,x,+,x,) 105 | sin,(,x,+,c,) 106 | tanh,(,sin,(,x,),) 107 | tanh,(,x,) 108 | tanh,(,sin,(,x,+,c,),) 109 | sin,(,x,) 110 | tanh,(,x,+,c,),+,tanh,(,x,) 111 | sin,(,x,+,x,+,x,) 112 | tanh,(,x,) 113 | sin,(,x,),+,x 114 | x,+,x 115 | tanh,(,tanh,(,x,+,x,),) 116 | sin,(,tanh,(,x,),),+,x,+,c,+,c 117 | sin,(,sin,(,x,),) 118 | x,+,sin,(,x,),+,c 119 | x,+,sin,(,x,),+,x,+,c 120 | tanh,(,sin,(,x,),) 121 | sin,(,x,),+,x 122 | tanh,(,x,) 123 | x,+,c 124 | sin,(,tanh,(,x,+,c,),) 125 | tanh,(,tanh,(,x,+,x,),) 126 | sin,(,x,),+,sin,(,x,+,x,) 127 | sin,(,x,+,c,),+,x 128 | sin,(,x,) 129 | sin,(,x,+,x,),+,sin,(,x,) 130 | sin,(,x,+,x,),+,x 131 | tanh,(,sin,(,x,),) 132 | sin,(,tanh,(,x,),+,tanh,(,x,),) 133 | tanh,(,x,+,c,+,x,) 134 | tanh,(,x,) 135 | sin,(,x,+,x,) 136 | sin,(,sin,(,x,),) 137 | sin,(,sin,(,x,),+,x,) 138 | tanh,(,x,) 139 | x,+,c 140 | x,+,c 141 | sin,(,x,+,c,),+,x 142 | tanh,(,x,+,x,) 143 | sin,(,sin,(,tanh,(,x,),),) 144 | x,+,x,+,c,+,c 145 | sin,(,x,) 146 | x,+,x,+,sin,(,x,),+,c 147 | x,+,x,+,x,+,x,+,c 148 | sin,(,x,+,x,),+,c 149 | tanh,(,x,+,x,),+,c 150 | x,+,x 151 | x,+,x 152 | x,+,c 153 | sin,(,tanh,(,x,),) 154 | x,+,x,+,sin,(,x,),+,tanh,(,x,+,x,) 155 | tanh,(,x,+,x,+,x,+,x,) 156 | x,+,c,+,tanh,(,x,) 157 | tanh,(,sin,(,x,),+,x,) 158 | x,+,c 159 | sin,(,tanh,(,tanh,(,x,),),) 160 | tanh,(,x,+,c,+,c,) 161 | sin,(,x,),+,c,+,x 162 | sin,(,sin,(,sin,(,x,),),) 163 | x,+,x 164 | tanh,(,sin,(,x,),+,x,+,x,) 165 | sin,(,sin,(,x,),) 166 | tanh,(,x,),+,tanh,(,x,),+,c 167 | x,+,tanh,(,x,),+,sin,(,x,) 168 | tanh,(,x,+,c,),+,c 169 | tanh,(,x,+,x,),+,c 170 | x,+,x,+,x,+,x 171 | sin,(,x,),+,x,+,c,+,sin,(,x,+,c,) 172 | tanh,(,x,) 173 | sin,(,x,),+,x,+,sin,(,x,) 174 | tanh,(,x,+,x,+,x,) 175 | tanh,(,x,),+,sin,(,x,),+,sin,(,sin,(,x,),) 176 | x,+,x,+,x,+,x,+,c 177 | sin,(,tanh,(,x,),) 178 | sin,(,tanh,(,x,),+,sin,(,x,),) 179 | sin,(,sin,(,x,),) 180 | sin,(,x,) 181 | sin,(,x,),+,x,+,sin,(,x,),+,x 182 | sin,(,sin,(,x,),) 183 | sin,(,x,),+,c 184 | sin,(,tanh,(,x,),+,c,) 185 | sin,(,x,) 186 | tanh,(,tanh,(,x,+,x,),) 187 | sin,(,tanh,(,x,),),+,x 188 | tanh,(,x,) 189 | x,+,c 190 | sin,(,x,) 191 | tanh,(,sin,(,x,),) 192 | tanh,(,tanh,(,sin,(,x,),),) 193 | sin,(,x,),+,sin,(,x,),+,x 194 | tanh,(,x,),+,sin,(,x,+,c,) 195 | tanh,(,tanh,(,x,),),+,x 196 | x,+,tanh,(,x,),+,x 197 | x,+,x 198 | x,+,x,+,x,+,x,+,x 199 | sin,(,x,) 200 | sin,(,x,) 201 | tanh,(,tanh,(,x,),),+,x 202 | x,+,tanh,(,x,),+,x,+,x 203 | sin,(,sin,(,x,),+,x,+,c,) 204 | tanh,(,x,) 205 | x,+,x 206 | tanh,(,tanh,(,tanh,(,x,),),) 207 | sin,(,x,),+,c,+,x 208 | tanh,(,x,) 209 | sin,(,x,+,c,+,x,+,x,) 210 | sin,(,x,),+,tanh,(,sin,(,x,),) 211 | sin,(,x,+,c,),+,sin,(,x,) 212 | sin,(,sin,(,x,),+,sin,(,x,),) 213 | tanh,(,x,+,c,) 214 | tanh,(,sin,(,x,+,c,),) 215 | tanh,(,x,+,x,) 216 | x,+,tanh,(,x,),+,x 217 | tanh,(,x,) 218 | tanh,(,x,),+,sin,(,sin,(,x,),) 219 | x,+,x,+,x,+,x,+,tanh,(,x,),+,x 220 | sin,(,x,+,c,+,x,+,x,) 221 | sin,(,sin,(,x,),) 222 | sin,(,x,+,c,+,x,+,c,) 223 | tanh,(,tanh,(,x,),) 224 | x,+,c 225 | tanh,(,x,) 226 | sin,(,tanh,(,x,),+,x,) 227 | tanh,(,x,+,c,) 228 | tanh,(,x,+,c,) 229 | tanh,(,sin,(,tanh,(,x,),),) 230 | tanh,(,tanh,(,x,),),+,x 231 | sin,(,x,),+,c,+,sin,(,x,),+,x,+,c 232 | tanh,(,x,) 233 | tanh,(,x,) 234 | tanh,(,x,+,x,),+,x 235 | x,+,x,+,x,+,c,+,sin,(,x,),+,x,+,x 236 | sin,(,x,+,x,) 237 | sin,(,sin,(,sin,(,x,),),) 238 | sin,(,tanh,(,x,),+,x,+,x,) 239 | sin,(,x,) 240 | sin,(,x,),+,tanh,(,x,),+,c 241 | tanh,(,tanh,(,x,),) 242 | x,+,c 243 | sin,(,x,) 244 | sin,(,x,+,x,),+,x 245 | x,+,c,+,x,+,x,+,x 246 | sin,(,x,),+,x 247 | x,+,c,+,sin,(,x,),+,x,+,x 248 | x,+,c 249 | tanh,(,sin,(,x,),+,x,) 250 | tanh,(,x,) 251 | sin,(,x,),+,tanh,(,sin,(,x,),) 252 | sin,(,x,) 253 | x,+,c,+,x,+,c,+,c 254 | tanh,(,tanh,(,sin,(,x,),),) 255 | x,+,x,+,c,+,tanh,(,x,) 256 | tanh,(,x,+,c,+,x,+,c,) 257 | tanh,(,x,+,c,) 258 | x,+,c,+,sin,(,x,),+,c 259 | sin,(,x,),+,x 260 | sin,(,x,) 261 | tanh,(,x,) 262 | tanh,(,x,) 263 | sin,(,x,+,c,) 264 | tanh,(,x,+,c,+,c,) 265 | tanh,(,tanh,(,x,),),+,x 266 | tanh,(,tanh,(,x,),+,x,) 267 | x,+,x,+,tanh,(,x,),+,x,+,x 268 | tanh,(,tanh,(,x,+,c,),) 269 | sin,(,x,) 270 | sin,(,x,),+,c,+,tanh,(,sin,(,x,),) 271 | sin,(,x,+,c,),+,c 272 | x,+,c,+,c,+,c 273 | sin,(,x,) 274 | tanh,(,x,) 275 | sin,(,x,),+,x,+,x,+,sin,(,x,),+,x 276 | tanh,(,sin,(,x,+,c,),) 277 | x,+,sin,(,x,),+,x,+,x 278 | tanh,(,tanh,(,x,),),+,c 279 | sin,(,x,) 280 | x,+,x,+,x,+,c 281 | sin,(,x,),+,x,+,x,+,c,+,c 282 | sin,(,sin,(,x,+,x,),) 283 | sin,(,x,+,x,+,c,) 284 | tanh,(,x,) 285 | sin,(,tanh,(,x,),) 286 | tanh,(,sin,(,x,),+,sin,(,x,),) 287 | sin,(,sin,(,x,),) 288 | tanh,(,x,),+,x 289 | x,+,c,+,tanh,(,x,),+,x 290 | sin,(,tanh,(,x,),),+,c 291 | tanh,(,sin,(,sin,(,x,),),) 292 | sin,(,x,+,x,) 293 | tanh,(,x,+,x,),+,x 294 | sin,(,x,) 295 | tanh,(,tanh,(,x,),),+,sin,(,sin,(,x,),) 296 | tanh,(,tanh,(,x,+,x,),) 297 | sin,(,tanh,(,x,+,x,),) 298 | tanh,(,x,) 299 | tanh,(,x,+,c,+,x,+,x,) 300 | sin,(,x,),+,c 301 | tanh,(,tanh,(,x,),+,x,) 302 | x,+,x,+,x,+,c,+,tanh,(,x,+,x,) 303 | tanh,(,x,),+,c,+,c 304 | x,+,c 305 | tanh,(,tanh,(,x,),) 306 | sin,(,x,) 307 | x,+,tanh,(,x,),+,tanh,(,x,) 308 | sin,(,x,+,x,+,c,) 309 | sin,(,sin,(,x,),+,x,) 310 | x,+,x,+,c 311 | sin,(,x,),+,c,+,sin,(,x,+,c,) 312 | tanh,(,x,+,x,+,x,) 313 | tanh,(,x,),+,x,+,x,+,c 314 | tanh,(,tanh,(,x,),+,x,+,x,) 315 | sin,(,sin,(,x,),+,x,) 316 | tanh,(,x,),+,x,+,c 317 | sin,(,sin,(,x,),+,sin,(,x,),) 318 | x,+,x,+,x 319 | tanh,(,x,+,x,),+,c 320 | tanh,(,sin,(,x,),) 321 | x,+,c,+,tanh,(,x,),+,x 322 | sin,(,tanh,(,x,),),+,c 323 | x,+,c 324 | sin,(,x,),+,x 325 | tanh,(,x,) 326 | sin,(,sin,(,sin,(,x,),),) 327 | tanh,(,x,),+,sin,(,x,),+,c 328 | sin,(,x,+,c,+,tanh,(,x,),) 329 | x,+,c 330 | sin,(,x,),+,x 331 | tanh,(,x,) 332 | sin,(,x,),+,x 333 | sin,(,x,) 334 | x,+,x,+,sin,(,x,),+,sin,(,tanh,(,x,),) 335 | tanh,(,tanh,(,sin,(,x,),),) 336 | sin,(,x,),+,sin,(,x,),+,x,+,x 337 | sin,(,tanh,(,x,),) 338 | x,+,x,+,c,+,c 339 | x,+,x 340 | tanh,(,x,),+,tanh,(,x,),+,c 341 | tanh,(,sin,(,x,),) 342 | tanh,(,x,) 343 | x,+,x 344 | tanh,(,sin,(,x,),) 345 | x,+,tanh,(,x,),+,x 346 | tanh,(,x,),+,c,+,tanh,(,x,+,c,) 347 | x,+,c,+,tanh,(,x,),+,sin,(,x,) 348 | sin,(,sin,(,x,),+,x,) 349 | sin,(,x,),+,tanh,(,x,+,x,) 350 | x,+,c,+,c,+,tanh,(,x,),+,tanh,(,x,) 351 | sin,(,tanh,(,x,),),+,c 352 | sin,(,x,) 353 | tanh,(,sin,(,tanh,(,x,),),) 354 | x,+,x 355 | tanh,(,x,),+,x 356 | sin,(,x,) 357 | sin,(,x,),+,sin,(,x,),+,sin,(,sin,(,x,),) 358 | sin,(,sin,(,x,),+,x,) 359 | sin,(,x,) 360 | sin,(,x,+,c,),+,tanh,(,sin,(,x,),) 361 | tanh,(,sin,(,x,),+,x,) 362 | tanh,(,x,) 363 | tanh,(,sin,(,x,+,x,),) 364 | x,+,x,+,x,+,x 365 | sin,(,x,+,x,),+,x,+,x,+,c 366 | sin,(,x,) 367 | sin,(,sin,(,x,),) 368 | sin,(,x,),+,c 369 | x,+,x,+,x,+,x 370 | sin,(,x,),+,x,+,c,+,x 371 | x,+,c 372 | x,+,x,+,c,+,x 373 | sin,(,sin,(,x,),),+,tanh,(,x,),+,tanh,(,x,) 374 | sin,(,sin,(,x,),+,tanh,(,x,),) 375 | sin,(,x,),+,x,+,x,+,x 376 | x,+,x 377 | x,+,x,+,sin,(,x,),+,c 378 | tanh,(,sin,(,sin,(,x,),),) 379 | sin,(,x,+,x,) 380 | sin,(,x,) 381 | tanh,(,x,+,x,+,c,) 382 | sin,(,x,+,x,),+,x 383 | tanh,(,x,),+,c 384 | x,+,c 385 | sin,(,x,) 386 | sin,(,x,) 387 | sin,(,sin,(,x,+,c,),) 388 | x,+,x,+,x 389 | tanh,(,x,) 390 | sin,(,sin,(,sin,(,x,),),) 391 | tanh,(,x,) 392 | x,+,c 393 | tanh,(,x,),+,x,+,c,+,sin,(,x,) 394 | sin,(,x,) 395 | tanh,(,tanh,(,tanh,(,x,),),) 396 | x,+,x,+,x,+,x 397 | sin,(,x,+,c,+,x,) 398 | tanh,(,x,+,c,+,x,) 399 | x,+,x,+,c 400 | sin,(,sin,(,x,),),+,x 401 | tanh,(,sin,(,x,),+,tanh,(,x,),) 402 | tanh,(,x,),+,c,+,tanh,(,tanh,(,x,),) 403 | x,+,x,+,c 404 | sin,(,tanh,(,x,),) 405 | sin,(,x,),+,x,+,sin,(,x,) 406 | tanh,(,sin,(,sin,(,x,),),) 407 | x,+,x,+,x,+,x,+,c,+,x,+,x 408 | tanh,(,x,) 409 | tanh,(,x,+,x,) 410 | tanh,(,sin,(,x,),),+,sin,(,x,) 411 | tanh,(,tanh,(,x,),),+,x 412 | sin,(,x,+,x,),+,x 413 | sin,(,sin,(,x,),+,x,+,c,) 414 | sin,(,sin,(,x,),),+,c 415 | tanh,(,x,),+,c,+,x 416 | x,+,c 417 | tanh,(,sin,(,x,),),+,sin,(,sin,(,x,),) 418 | x,+,x 419 | x,+,c,+,c,+,c 420 | sin,(,sin,(,x,),+,tanh,(,x,),) 421 | sin,(,x,) 422 | x,+,x,+,x,+,c 423 | sin,(,x,) 424 | tanh,(,x,),+,x,+,x 425 | tanh,(,sin,(,x,+,c,),) 426 | sin,(,sin,(,x,),+,x,) 427 | x,+,x,+,x,+,x,+,sin,(,sin,(,x,),) 428 | sin,(,sin,(,x,),),+,tanh,(,tanh,(,x,),) 429 | x,+,x 430 | sin,(,sin,(,x,+,c,),) 431 | tanh,(,x,),+,c 432 | tanh,(,x,+,c,+,c,) 433 | sin,(,x,+,x,+,c,) 434 | sin,(,x,),+,c,+,sin,(,x,) 435 | sin,(,x,),+,x 436 | x,+,c,+,c,+,sin,(,x,+,c,) 437 | sin,(,x,) 438 | sin,(,x,+,c,+,sin,(,x,),) 439 | tanh,(,sin,(,x,+,c,),) 440 | tanh,(,sin,(,x,),+,x,+,x,) 441 | sin,(,x,),+,c 442 | tanh,(,x,) 443 | sin,(,tanh,(,x,),) 444 | tanh,(,x,),+,c 445 | x,+,c,+,sin,(,x,),+,c 446 | tanh,(,sin,(,x,),),+,tanh,(,x,) 447 | sin,(,x,) 448 | sin,(,x,+,x,),+,x 449 | sin,(,x,+,c,+,x,) 450 | tanh,(,x,),+,x 451 | x,+,c 452 | tanh,(,tanh,(,x,+,c,),) 453 | x,+,c,+,tanh,(,x,+,c,) 454 | sin,(,tanh,(,x,),),+,x 455 | tanh,(,x,),+,x,+,x 456 | x,+,x,+,x,+,sin,(,sin,(,x,),) 457 | tanh,(,sin,(,x,),+,c,) 458 | tanh,(,sin,(,tanh,(,x,),),) 459 | tanh,(,x,+,c,),+,sin,(,x,),+,x,+,c 460 | x,+,x,+,c 461 | tanh,(,x,+,x,),+,c 462 | sin,(,x,+,x,),+,sin,(,tanh,(,x,),) 463 | sin,(,x,) 464 | sin,(,x,+,c,) 465 | tanh,(,sin,(,x,),+,c,) 466 | tanh,(,x,),+,x 467 | sin,(,sin,(,x,+,c,),) 468 | sin,(,x,) 469 | sin,(,x,) 470 | sin,(,x,+,c,) 471 | tanh,(,sin,(,x,),) 472 | sin,(,tanh,(,tanh,(,x,),),) 473 | tanh,(,x,+,c,+,tanh,(,x,),) 474 | tanh,(,x,),+,tanh,(,x,),+,x 475 | sin,(,x,+,x,),+,x 476 | sin,(,tanh,(,x,+,x,),) 477 | sin,(,sin,(,x,),) 478 | sin,(,x,+,c,),+,sin,(,x,),+,x,+,c 479 | tanh,(,x,),+,x,+,c 480 | sin,(,x,+,c,),+,c 481 | tanh,(,x,+,c,) 482 | tanh,(,tanh,(,sin,(,x,),),) 483 | tanh,(,sin,(,x,+,x,),) 484 | sin,(,tanh,(,x,),) 485 | tanh,(,x,+,x,),+,x 486 | tanh,(,sin,(,x,),),+,x 487 | sin,(,x,+,c,) 488 | tanh,(,x,),+,x,+,x,+,c,+,x 489 | sin,(,tanh,(,sin,(,x,),),) 490 | tanh,(,x,+,x,),+,tanh,(,x,+,x,) 491 | tanh,(,x,) 492 | sin,(,x,) 493 | tanh,(,x,) 494 | sin,(,x,),+,x 495 | tanh,(,x,) 496 | tanh,(,x,),+,x,+,x,+,x 497 | sin,(,tanh,(,x,),),+,c 498 | tanh,(,tanh,(,x,),+,x,+,x,) 499 | sin,(,x,) 500 | tanh,(,x,) 501 | tanh,(,x,) 502 | tanh,(,x,+,c,),+,tanh,(,x,),+,x 503 | tanh,(,x,+,x,),+,x 504 | tanh,(,tanh,(,x,),) 505 | sin,(,x,),+,x,+,x,+,x,+,c 506 | sin,(,sin,(,x,),) 507 | sin,(,x,) 508 | tanh,(,x,+,x,),+,c 509 | tanh,(,x,+,c,+,tanh,(,x,),) 510 | sin,(,x,),+,c 511 | sin,(,x,),+,sin,(,x,),+,c 512 | sin,(,x,) 513 | tanh,(,tanh,(,x,),+,c,) 514 | tanh,(,tanh,(,x,),),+,x,+,x,+,x 515 | sin,(,x,+,c,+,x,+,c,) 516 | x,+,c,+,c 517 | sin,(,x,+,c,) 518 | tanh,(,sin,(,x,),),+,sin,(,x,+,c,) 519 | tanh,(,x,) 520 | tanh,(,x,+,x,),+,c 521 | sin,(,x,+,x,+,c,) 522 | tanh,(,x,) 523 | sin,(,x,+,x,),+,x 524 | tanh,(,x,+,x,),+,x 525 | sin,(,x,) 526 | sin,(,tanh,(,x,),),+,x 527 | sin,(,x,+,x,+,c,) 528 | sin,(,x,) 529 | sin,(,x,),+,x,+,sin,(,x,),+,x 530 | sin,(,x,+,c,),+,tanh,(,tanh,(,x,),) 531 | tanh,(,tanh,(,x,+,c,),) 532 | x,+,x,+,tanh,(,x,),+,c 533 | sin,(,sin,(,x,),+,x,) 534 | tanh,(,x,+,x,+,x,) 535 | x,+,x,+,x,+,x 536 | tanh,(,tanh,(,x,),),+,x 537 | x,+,x,+,x,+,c 538 | sin,(,sin,(,x,+,c,),) 539 | x,+,c,+,sin,(,x,),+,x 540 | tanh,(,x,),+,x,+,c,+,sin,(,x,) 541 | tanh,(,x,+,c,),+,sin,(,tanh,(,x,),) 542 | tanh,(,tanh,(,x,),) 543 | tanh,(,x,),+,sin,(,x,),+,x,+,c 544 | sin,(,x,) 545 | sin,(,x,) 546 | sin,(,tanh,(,sin,(,x,),),) 547 | tanh,(,x,+,c,+,x,+,x,) 548 | sin,(,tanh,(,x,),) 549 | x,+,c,+,x,+,c,+,x,+,x,+,x,+,x 550 | tanh,(,x,+,c,),+,x 551 | sin,(,x,+,x,),+,x,+,x 552 | sin,(,tanh,(,x,),),+,x,+,c,+,sin,(,x,) 553 | tanh,(,sin,(,x,+,x,),) 554 | x,+,x 555 | x,+,c,+,x 556 | sin,(,tanh,(,x,+,x,),) 557 | tanh,(,sin,(,sin,(,x,),),) 558 | sin,(,x,),+,tanh,(,x,),+,x 559 | x,+,c,+,x,+,c,+,x 560 | sin,(,x,) 561 | tanh,(,x,),+,tanh,(,x,),+,tanh,(,x,),+,sin,(,x,) 562 | tanh,(,tanh,(,x,),) 563 | x,+,c 564 | sin,(,x,+,c,),+,x 565 | tanh,(,x,+,x,+,c,) 566 | x,+,c 567 | tanh,(,x,),+,x,+,x,+,c 568 | tanh,(,x,),+,c,+,x 569 | sin,(,sin,(,x,),+,x,) 570 | x,+,x,+,x,+,x,+,x 571 | tanh,(,tanh,(,x,),+,x,) 572 | tanh,(,x,),+,sin,(,x,),+,x,+,c 573 | tanh,(,x,),+,x,+,c 574 | sin,(,sin,(,x,),+,tanh,(,x,),) 575 | sin,(,sin,(,x,),+,x,+,c,) 576 | tanh,(,x,) 577 | sin,(,x,),+,x 578 | x,+,x,+,c 579 | sin,(,x,) 580 | sin,(,tanh,(,x,),),+,sin,(,sin,(,x,),) 581 | tanh,(,x,),+,x 582 | tanh,(,x,),+,c,+,c 583 | sin,(,sin,(,x,),),+,x 584 | tanh,(,sin,(,tanh,(,x,),),) 585 | tanh,(,x,) 586 | x,+,x 587 | sin,(,x,) 588 | sin,(,x,+,x,+,x,+,c,) 589 | tanh,(,x,+,c,) 590 | sin,(,sin,(,x,),+,sin,(,x,),) 591 | tanh,(,x,+,c,+,x,) 592 | tanh,(,tanh,(,tanh,(,x,),),) 593 | sin,(,x,),+,x,+,c 594 | tanh,(,tanh,(,x,),),+,c 595 | tanh,(,x,+,c,) 596 | sin,(,sin,(,x,),) 597 | tanh,(,x,) 598 | sin,(,tanh,(,x,),) 599 | tanh,(,x,+,c,+,c,) 600 | tanh,(,sin,(,x,),) 601 | x,+,c 602 | tanh,(,x,) 603 | tanh,(,x,),+,c,+,x,+,x,+,c 604 | x,+,tanh,(,x,),+,tanh,(,x,) 605 | tanh,(,x,),+,x 606 | tanh,(,x,),+,x 607 | tanh,(,x,) 608 | sin,(,x,),+,x,+,c 609 | x,+,x,+,x,+,tanh,(,x,) 610 | sin,(,x,),+,x,+,x,+,x 611 | sin,(,x,) 612 | tanh,(,sin,(,x,),+,x,) 613 | tanh,(,x,),+,tanh,(,x,),+,x,+,x,+,x,+,x 614 | tanh,(,x,+,x,),+,c 615 | tanh,(,x,) 616 | x,+,c 617 | sin,(,tanh,(,tanh,(,x,),),) 618 | tanh,(,x,) 619 | sin,(,tanh,(,x,),+,x,+,c,) 620 | sin,(,x,) 621 | tanh,(,sin,(,x,),),+,x,+,x 622 | sin,(,tanh,(,x,+,c,),) 623 | x,+,c,+,c,+,x 624 | tanh,(,x,) 625 | sin,(,x,) 626 | tanh,(,tanh,(,sin,(,x,),),) 627 | x,+,x,+,c 628 | sin,(,x,),+,x 629 | tanh,(,sin,(,x,),) 630 | x,+,c,+,sin,(,tanh,(,x,),) 631 | x,+,c,+,x,+,x 632 | sin,(,x,+,x,),+,tanh,(,x,) 633 | tanh,(,sin,(,x,+,x,),) 634 | sin,(,x,) 635 | x,+,c 636 | tanh,(,x,),+,x 637 | sin,(,x,) 638 | x,+,x 639 | x,+,c,+,x,+,x,+,c 640 | tanh,(,sin,(,x,),+,c,) 641 | tanh,(,tanh,(,x,),+,c,) 642 | tanh,(,x,) 643 | x,+,c,+,c,+,tanh,(,x,),+,x 644 | sin,(,tanh,(,sin,(,x,),),) 645 | tanh,(,x,+,x,+,c,) 646 | sin,(,x,),+,sin,(,x,),+,x,+,x 647 | sin,(,x,+,x,+,tanh,(,x,),) 648 | tanh,(,x,) 649 | tanh,(,sin,(,x,),) 650 | tanh,(,x,+,x,) 651 | sin,(,tanh,(,x,),) 652 | x,+,x 653 | x,+,x 654 | tanh,(,x,+,x,),+,x 655 | tanh,(,x,+,x,),+,c 656 | sin,(,x,+,c,) 657 | tanh,(,x,+,x,),+,x,+,c,+,sin,(,x,) 658 | sin,(,x,) 659 | sin,(,tanh,(,x,),) 660 | sin,(,tanh,(,x,),+,tanh,(,x,),) 661 | tanh,(,x,+,c,),+,x 662 | x,+,c 663 | sin,(,sin,(,x,+,x,),) 664 | sin,(,x,) 665 | tanh,(,sin,(,x,),+,x,+,x,) 666 | x,+,c 667 | tanh,(,tanh,(,x,),),+,x,+,c,+,x 668 | tanh,(,x,) 669 | sin,(,x,) 670 | tanh,(,tanh,(,x,),) 671 | tanh,(,x,),+,sin,(,x,),+,x 672 | x,+,c,+,x,+,c,+,c 673 | tanh,(,tanh,(,tanh,(,x,),),) 674 | x,+,c 675 | tanh,(,tanh,(,x,),) 676 | tanh,(,x,+,c,+,x,+,x,) 677 | tanh,(,tanh,(,x,),),+,x,+,x,+,sin,(,x,) 678 | x,+,x 679 | sin,(,x,+,x,+,x,+,x,) 680 | sin,(,x,+,x,),+,c 681 | tanh,(,tanh,(,sin,(,x,),),) 682 | sin,(,x,) 683 | sin,(,x,),+,sin,(,tanh,(,x,),) 684 | tanh,(,x,) 685 | sin,(,tanh,(,x,),) 686 | x,+,c 687 | tanh,(,x,) 688 | sin,(,sin,(,x,),) 689 | x,+,x,+,x,+,c 690 | tanh,(,x,) 691 | sin,(,x,+,x,+,x,+,x,) 692 | sin,(,x,) 693 | sin,(,x,),+,x,+,x 694 | x,+,x 695 | sin,(,x,) 696 | sin,(,sin,(,x,),),+,tanh,(,x,) 697 | sin,(,tanh,(,x,+,x,),) 698 | x,+,x 699 | tanh,(,x,+,c,) 700 | tanh,(,tanh,(,x,),),+,x 701 | sin,(,tanh,(,x,),),+,sin,(,x,) 702 | sin,(,x,+,c,),+,tanh,(,x,),+,c 703 | tanh,(,x,),+,x 704 | sin,(,x,) 705 | x,+,c 706 | tanh,(,sin,(,x,+,x,),) 707 | x,+,sin,(,x,),+,x 708 | sin,(,sin,(,sin,(,x,),),) 709 | tanh,(,tanh,(,x,),+,x,) 710 | sin,(,x,+,c,) 711 | tanh,(,tanh,(,x,+,c,),) 712 | sin,(,x,) 713 | sin,(,x,) 714 | tanh,(,x,+,c,+,c,) 715 | tanh,(,x,+,c,+,x,+,c,) 716 | sin,(,sin,(,x,),) 717 | x,+,c,+,x,+,c,+,c 718 | tanh,(,x,),+,x 719 | sin,(,x,),+,c,+,c 720 | sin,(,x,) 721 | tanh,(,x,) 722 | sin,(,sin,(,x,+,x,),) 723 | sin,(,tanh,(,tanh,(,x,),),) 724 | tanh,(,tanh,(,sin,(,x,),),) 725 | tanh,(,x,) 726 | sin,(,sin,(,tanh,(,x,),),) 727 | x,+,x,+,x,+,c 728 | tanh,(,x,),+,x,+,c 729 | x,+,x,+,tanh,(,x,),+,x 730 | sin,(,x,) 731 | tanh,(,sin,(,x,),) 732 | sin,(,x,) 733 | tanh,(,x,),+,x,+,c,+,c 734 | tanh,(,x,),+,c,+,sin,(,x,),+,x 735 | tanh,(,x,+,c,+,tanh,(,x,),) 736 | sin,(,x,) 737 | tanh,(,x,+,x,) 738 | sin,(,x,) 739 | tanh,(,sin,(,x,),) 740 | sin,(,tanh,(,x,),),+,sin,(,x,),+,x,+,c 741 | sin,(,tanh,(,x,),) 742 | x,+,x 743 | tanh,(,x,) 744 | sin,(,x,) 745 | sin,(,x,) 746 | sin,(,x,+,x,+,c,) 747 | x,+,x,+,c 748 | sin,(,sin,(,x,),),+,x 749 | tanh,(,x,+,x,+,x,) 750 | sin,(,x,) 751 | x,+,c,+,sin,(,x,),+,x,+,c,+,c 752 | tanh,(,x,) 753 | tanh,(,x,+,x,),+,c 754 | sin,(,x,) 755 | sin,(,sin,(,x,+,c,),) 756 | sin,(,x,),+,x,+,x 757 | sin,(,x,) 758 | sin,(,x,) 759 | x,+,x 760 | x,+,x 761 | tanh,(,x,+,c,),+,sin,(,x,) 762 | tanh,(,tanh,(,x,),),+,c 763 | tanh,(,tanh,(,x,),+,x,+,c,) 764 | tanh,(,tanh,(,x,),),+,c 765 | tanh,(,x,),+,x 766 | sin,(,x,),+,c,+,c 767 | sin,(,x,+,x,+,sin,(,x,),) 768 | x,+,c 769 | tanh,(,x,),+,x 770 | x,+,x,+,c,+,tanh,(,tanh,(,x,),) 771 | sin,(,tanh,(,x,),) 772 | tanh,(,x,),+,sin,(,tanh,(,x,),) 773 | tanh,(,x,) 774 | tanh,(,x,+,x,),+,c 775 | x,+,x 776 | sin,(,x,),+,x,+,x,+,c 777 | x,+,c,+,tanh,(,x,),+,sin,(,x,) 778 | sin,(,x,),+,x 779 | tanh,(,tanh,(,x,+,c,),) 780 | x,+,x,+,c,+,x 781 | tanh,(,x,+,x,),+,c 782 | sin,(,x,) 783 | x,+,x,+,x,+,sin,(,sin,(,x,),) 784 | tanh,(,x,) 785 | sin,(,x,+,x,+,sin,(,x,),) 786 | sin,(,sin,(,x,+,c,),) 787 | x,+,c,+,x,+,x 788 | tanh,(,tanh,(,x,),) 789 | x,+,x,+,tanh,(,x,),+,c 790 | tanh,(,sin,(,x,),),+,x 791 | x,+,x 792 | sin,(,x,+,x,),+,x 793 | x,+,x,+,tanh,(,sin,(,x,),) 794 | x,+,x 795 | sin,(,sin,(,x,),+,c,) 796 | tanh,(,x,+,x,),+,c 797 | x,+,c,+,c 798 | x,+,x,+,x,+,x,+,x 799 | x,+,tanh,(,x,),+,c 800 | sin,(,x,) 801 | tanh,(,tanh,(,x,),),+,x,+,x,+,x 802 | sin,(,x,),+,c 803 | x,+,x 804 | sin,(,sin,(,x,),),+,x 805 | tanh,(,x,) 806 | x,+,x 807 | sin,(,sin,(,x,+,x,),) 808 | sin,(,x,),+,c 809 | tanh,(,sin,(,x,),) 810 | tanh,(,x,),+,x,+,x,+,c 811 | sin,(,sin,(,x,+,c,),) 812 | sin,(,sin,(,x,+,c,),) 813 | sin,(,tanh,(,x,+,x,),) 814 | tanh,(,x,) 815 | tanh,(,x,) 816 | x,+,x,+,tanh,(,x,),+,x,+,c 817 | tanh,(,x,) 818 | tanh,(,sin,(,x,),) 819 | tanh,(,x,+,x,+,c,) 820 | x,+,c,+,x 821 | x,+,c,+,x,+,c 822 | x,+,c,+,sin,(,x,),+,c 823 | sin,(,x,) 824 | tanh,(,sin,(,sin,(,x,),),) 825 | x,+,c 826 | sin,(,tanh,(,sin,(,x,),),) 827 | x,+,x,+,c 828 | tanh,(,tanh,(,x,),),+,x,+,x,+,c 829 | tanh,(,x,),+,c,+,x 830 | tanh,(,x,),+,x,+,x,+,x 831 | x,+,x 832 | tanh,(,x,),+,x,+,c,+,x 833 | sin,(,x,+,c,),+,c 834 | sin,(,x,) 835 | tanh,(,x,) 836 | sin,(,x,+,c,),+,c 837 | tanh,(,x,) 838 | tanh,(,tanh,(,sin,(,x,),),) 839 | x,+,c,+,x,+,x 840 | tanh,(,x,+,c,),+,x 841 | tanh,(,sin,(,x,),),+,x 842 | sin,(,tanh,(,x,),+,x,+,c,) 843 | tanh,(,x,) 844 | tanh,(,sin,(,tanh,(,x,),),) 845 | sin,(,tanh,(,x,),),+,tanh,(,x,) 846 | sin,(,tanh,(,x,),),+,c 847 | sin,(,x,) 848 | sin,(,x,+,c,+,tanh,(,x,),) 849 | sin,(,x,),+,x,+,x,+,tanh,(,x,) 850 | tanh,(,x,+,x,),+,x 851 | sin,(,x,),+,x,+,sin,(,x,) 852 | x,+,sin,(,x,),+,sin,(,x,) 853 | sin,(,x,),+,x,+,c 854 | x,+,c 855 | tanh,(,sin,(,x,),),+,x 856 | tanh,(,x,),+,x 857 | tanh,(,x,+,x,+,x,) 858 | sin,(,x,),+,x,+,x,+,sin,(,x,+,x,) 859 | x,+,tanh,(,x,),+,x 860 | sin,(,sin,(,x,+,x,),) 861 | sin,(,x,+,c,+,sin,(,x,),) 862 | tanh,(,tanh,(,x,),),+,sin,(,sin,(,x,),) 863 | sin,(,x,+,x,),+,c 864 | tanh,(,x,+,x,),+,c 865 | x,+,x,+,tanh,(,x,),+,sin,(,x,+,x,) 866 | x,+,tanh,(,x,),+,c 867 | sin,(,x,) 868 | sin,(,x,+,c,) 869 | tanh,(,x,) 870 | tanh,(,x,+,x,),+,sin,(,x,+,x,) 871 | tanh,(,x,),+,x,+,x 872 | tanh,(,x,) 873 | tanh,(,x,),+,x,+,tanh,(,x,),+,x 874 | x,+,x,+,sin,(,x,),+,tanh,(,x,+,c,) 875 | sin,(,tanh,(,sin,(,x,),),) 876 | tanh,(,sin,(,sin,(,x,),),) 877 | tanh,(,x,+,c,),+,x 878 | tanh,(,x,) 879 | tanh,(,tanh,(,x,),+,sin,(,x,),) 880 | tanh,(,x,+,c,),+,x 881 | sin,(,sin,(,x,+,x,),) 882 | sin,(,tanh,(,x,+,x,),) 883 | x,+,x 884 | x,+,c 885 | tanh,(,sin,(,x,),) 886 | tanh,(,sin,(,sin,(,x,),),) 887 | x,+,x,+,c,+,sin,(,x,+,c,) 888 | x,+,x,+,tanh,(,x,),+,tanh,(,sin,(,x,),) 889 | tanh,(,sin,(,x,),) 890 | x,+,c,+,sin,(,x,),+,x,+,c,+,tanh,(,x,) 891 | sin,(,tanh,(,sin,(,x,),),) 892 | tanh,(,x,+,x,),+,x,+,x,+,x,+,x 893 | x,+,x,+,x,+,c 894 | sin,(,x,),+,x 895 | sin,(,x,+,x,) 896 | x,+,x,+,c 897 | tanh,(,x,) 898 | tanh,(,tanh,(,x,),),+,x 899 | x,+,x 900 | sin,(,x,),+,sin,(,x,),+,x 901 | x,+,x,+,c 902 | tanh,(,x,) 903 | x,+,tanh,(,x,),+,x 904 | tanh,(,x,),+,c 905 | sin,(,x,) 906 | x,+,x,+,x,+,x 907 | sin,(,x,+,c,),+,x 908 | x,+,x,+,c 909 | tanh,(,x,+,x,) 910 | tanh,(,x,),+,sin,(,x,),+,x,+,c 911 | tanh,(,tanh,(,x,),+,x,) 912 | tanh,(,x,) 913 | x,+,c,+,sin,(,x,),+,x 914 | sin,(,x,) 915 | tanh,(,tanh,(,x,+,x,),) 916 | sin,(,sin,(,x,+,x,),) 917 | x,+,c 918 | tanh,(,x,+,x,),+,x 919 | sin,(,x,),+,c,+,c 920 | sin,(,sin,(,sin,(,x,),),) 921 | tanh,(,sin,(,x,),) 922 | x,+,tanh,(,x,),+,x 923 | sin,(,tanh,(,sin,(,x,),),) 924 | tanh,(,sin,(,x,+,x,),) 925 | sin,(,tanh,(,x,),+,x,) 926 | sin,(,sin,(,x,),) 927 | x,+,c,+,sin,(,x,+,c,) 928 | sin,(,sin,(,x,),),+,x,+,c 929 | sin,(,x,),+,c 930 | x,+,x 931 | sin,(,x,),+,x 932 | sin,(,x,),+,x,+,c,+,c 933 | tanh,(,x,) 934 | tanh,(,x,+,c,),+,sin,(,x,+,x,) 935 | tanh,(,x,) 936 | tanh,(,sin,(,x,),) 937 | tanh,(,sin,(,x,+,x,),) 938 | tanh,(,x,) 939 | sin,(,sin,(,x,+,x,),) 940 | sin,(,x,) 941 | tanh,(,x,) 942 | tanh,(,sin,(,x,),),+,x 943 | sin,(,x,),+,x 944 | sin,(,tanh,(,x,),),+,tanh,(,x,) 945 | tanh,(,x,+,c,+,x,+,c,) 946 | x,+,c,+,x 947 | tanh,(,tanh,(,x,),+,x,) 948 | tanh,(,x,),+,x 949 | sin,(,sin,(,x,),+,tanh,(,x,),) 950 | tanh,(,tanh,(,x,+,c,),) 951 | sin,(,x,+,x,),+,c 952 | tanh,(,x,) 953 | tanh,(,sin,(,x,),) 954 | sin,(,x,) 955 | sin,(,x,),+,x 956 | sin,(,sin,(,sin,(,x,),),) 957 | tanh,(,tanh,(,x,),),+,x 958 | sin,(,sin,(,x,),),+,tanh,(,x,+,x,) 959 | x,+,x,+,x,+,x,+,x,+,c 960 | tanh,(,tanh,(,x,+,x,),) 961 | x,+,x,+,c,+,c 962 | tanh,(,tanh,(,x,),),+,c 963 | sin,(,x,),+,x 964 | tanh,(,x,+,c,),+,x 965 | tanh,(,tanh,(,x,+,x,),) 966 | sin,(,sin,(,sin,(,x,),),) 967 | sin,(,tanh,(,x,),+,x,) 968 | x,+,x,+,x,+,x 969 | tanh,(,x,),+,c,+,x,+,c 970 | x,+,x,+,x,+,x,+,c 971 | sin,(,sin,(,x,),) 972 | tanh,(,tanh,(,x,),) 973 | x,+,x,+,x 974 | x,+,x 975 | sin,(,x,) 976 | sin,(,x,) 977 | x,+,x,+,x,+,c 978 | tanh,(,x,) 979 | sin,(,x,) 980 | tanh,(,x,) 981 | tanh,(,x,) 982 | sin,(,x,),+,x,+,c,+,c 983 | sin,(,x,+,x,) 984 | tanh,(,x,),+,c 985 | sin,(,x,),+,x 986 | tanh,(,x,) 987 | tanh,(,sin,(,x,),),+,x,+,c,+,c 988 | sin,(,sin,(,x,),+,x,) 989 | sin,(,x,) 990 | x,+,c,+,tanh,(,x,),+,sin,(,x,) 991 | sin,(,x,) 992 | sin,(,x,+,x,+,x,) 993 | x,+,x,+,x 994 | sin,(,x,),+,x 995 | sin,(,x,+,c,),+,x 996 | tanh,(,sin,(,x,),) 997 | sin,(,x,),+,c,+,x 998 | tanh,(,tanh,(,tanh,(,x,),),) 999 | sin,(,x,) 1000 | tanh,(,x,+,c,+,x,+,c,) 1001 | tanh,(,x,),+,x,+,c,+,x,+,c 1002 | tanh,(,sin,(,x,),),+,sin,(,sin,(,x,),) 1003 | sin,(,x,) 1004 | x,+,c 1005 | x,+,x 1006 | sin,(,x,+,c,+,x,) 1007 | x,+,c,+,tanh,(,x,),+,sin,(,x,),+,x,+,x 1008 | sin,(,x,) 1009 | tanh,(,x,+,c,),+,x,+,c 1010 | sin,(,sin,(,x,),),+,tanh,(,x,),+,x,+,c 1011 | sin,(,x,),+,tanh,(,tanh,(,x,),) 1012 | tanh,(,x,),+,c,+,c 1013 | x,+,x 1014 | sin,(,sin,(,x,+,x,),) 1015 | tanh,(,x,+,x,),+,x 1016 | tanh,(,x,+,x,),+,x 1017 | x,+,c 1018 | x,+,x,+,x 1019 | tanh,(,x,),+,tanh,(,tanh,(,x,),) 1020 | tanh,(,x,) 1021 | x,+,x,+,x,+,sin,(,x,+,c,) 1022 | tanh,(,sin,(,x,),+,x,) 1023 | tanh,(,x,) 1024 | tanh,(,x,+,x,+,x,) 1025 | tanh,(,x,) 1026 | tanh,(,x,),+,x,+,x 1027 | sin,(,tanh,(,tanh,(,x,),),) 1028 | tanh,(,tanh,(,x,+,c,),) 1029 | x,+,c 1030 | x,+,c,+,x,+,c,+,sin,(,x,) 1031 | sin,(,x,) 1032 | tanh,(,x,),+,sin,(,x,+,x,) 1033 | tanh,(,x,) 1034 | tanh,(,x,) 1035 | sin,(,x,+,c,+,x,+,c,) 1036 | x,+,x,+,x,+,c,+,c 1037 | x,+,x 1038 | sin,(,tanh,(,x,),),+,tanh,(,sin,(,x,),) 1039 | sin,(,sin,(,x,),) 1040 | tanh,(,x,),+,x,+,sin,(,tanh,(,x,),) 1041 | tanh,(,x,),+,tanh,(,x,+,c,) 1042 | sin,(,x,) 1043 | tanh,(,x,) 1044 | x,+,x 1045 | sin,(,sin,(,x,+,c,),) 1046 | sin,(,x,),+,c,+,x 1047 | tanh,(,x,) 1048 | tanh,(,sin,(,x,),+,tanh,(,x,),) 1049 | sin,(,x,+,c,+,sin,(,x,),) 1050 | tanh,(,tanh,(,x,),+,x,) 1051 | x,+,c,+,x,+,c,+,x,+,x,+,x 1052 | sin,(,x,),+,c,+,c 1053 | sin,(,x,+,x,+,c,) 1054 | x,+,x 1055 | x,+,x 1056 | x,+,c 1057 | tanh,(,x,+,x,) 1058 | tanh,(,tanh,(,x,),) 1059 | sin,(,sin,(,tanh,(,x,),),) 1060 | sin,(,x,+,x,+,c,) 1061 | tanh,(,tanh,(,x,),),+,sin,(,tanh,(,x,),) 1062 | sin,(,x,) 1063 | sin,(,x,) 1064 | sin,(,x,) 1065 | tanh,(,sin,(,x,),) 1066 | tanh,(,sin,(,x,),+,c,) 1067 | sin,(,x,) 1068 | x,+,x,+,x,+,x,+,x 1069 | sin,(,sin,(,x,),) 1070 | tanh,(,sin,(,x,),+,tanh,(,x,),) 1071 | tanh,(,x,+,c,),+,x 1072 | tanh,(,x,+,x,),+,x 1073 | x,+,x,+,tanh,(,x,+,c,) 1074 | tanh,(,x,),+,sin,(,x,+,x,) 1075 | sin,(,sin,(,x,),+,x,) 1076 | x,+,c 1077 | x,+,x,+,x,+,tanh,(,x,) 1078 | sin,(,tanh,(,x,),) 1079 | sin,(,x,+,c,+,x,) 1080 | x,+,x,+,c 1081 | sin,(,x,),+,x 1082 | x,+,x,+,c,+,sin,(,x,),+,x,+,c 1083 | x,+,x,+,x,+,c,+,c 1084 | sin,(,x,) 1085 | sin,(,x,) 1086 | x,+,sin,(,x,),+,x,+,x 1087 | tanh,(,x,),+,x 1088 | sin,(,x,) 1089 | sin,(,x,+,c,+,tanh,(,x,),) 1090 | x,+,c,+,c,+,sin,(,x,),+,x 1091 | x,+,x 1092 | tanh,(,x,+,x,) 1093 | tanh,(,x,) 1094 | x,+,x,+,x,+,x 1095 | tanh,(,sin,(,x,),+,x,) 1096 | tanh,(,sin,(,x,+,x,),) 1097 | tanh,(,x,),+,x 1098 | tanh,(,x,+,c,),+,c 1099 | tanh,(,x,),+,x 1100 | tanh,(,sin,(,x,),),+,tanh,(,sin,(,x,),) 1101 | sin,(,x,),+,tanh,(,x,) 1102 | x,+,x,+,c,+,sin,(,tanh,(,x,),) 1103 | sin,(,sin,(,x,),),+,x 1104 | tanh,(,x,) 1105 | tanh,(,x,),+,x,+,c 1106 | sin,(,x,),+,x,+,x,+,x,+,x 1107 | tanh,(,tanh,(,tanh,(,x,),),) 1108 | tanh,(,sin,(,x,),+,x,+,c,) 1109 | x,+,x 1110 | tanh,(,x,+,x,+,c,) 1111 | sin,(,x,+,x,),+,x,+,c 1112 | sin,(,x,) 1113 | sin,(,sin,(,x,),+,x,) 1114 | x,+,x,+,x,+,x,+,x,+,x,+,c 1115 | tanh,(,sin,(,x,),) 1116 | tanh,(,sin,(,x,),),+,tanh,(,sin,(,x,),) 1117 | sin,(,x,) 1118 | tanh,(,sin,(,x,),),+,x 1119 | sin,(,x,+,x,),+,sin,(,x,),+,c 1120 | sin,(,tanh,(,x,),) 1121 | tanh,(,x,+,x,+,x,) 1122 | sin,(,x,+,x,+,c,) 1123 | sin,(,tanh,(,x,),+,x,) 1124 | sin,(,sin,(,x,),+,x,) 1125 | sin,(,tanh,(,x,),+,c,) 1126 | sin,(,tanh,(,sin,(,x,),),) 1127 | sin,(,tanh,(,x,),+,x,) 1128 | sin,(,x,),+,x 1129 | tanh,(,x,) 1130 | tanh,(,x,+,x,+,tanh,(,x,),) 1131 | x,+,x 1132 | tanh,(,tanh,(,x,),) 1133 | tanh,(,sin,(,x,),+,c,) 1134 | tanh,(,tanh,(,x,),),+,x,+,x 1135 | x,+,c,+,x,+,c,+,sin,(,x,+,x,) 1136 | sin,(,x,+,x,+,tanh,(,x,),) 1137 | sin,(,sin,(,x,),) 1138 | tanh,(,x,+,c,),+,sin,(,x,),+,x 1139 | sin,(,sin,(,x,),) 1140 | sin,(,x,+,x,+,c,) 1141 | tanh,(,tanh,(,x,+,x,),) 1142 | sin,(,x,+,x,+,x,) 1143 | sin,(,x,+,x,),+,x 1144 | x,+,c 1145 | tanh,(,tanh,(,tanh,(,x,),),) 1146 | tanh,(,x,),+,c,+,c 1147 | sin,(,x,),+,x 1148 | sin,(,x,) 1149 | tanh,(,x,) 1150 | x,+,x,+,c,+,x,+,x,+,tanh,(,x,) 1151 | tanh,(,x,),+,x,+,tanh,(,x,+,c,) 1152 | x,+,sin,(,x,),+,c 1153 | sin,(,x,) 1154 | x,+,x 1155 | sin,(,x,) 1156 | sin,(,tanh,(,x,),),+,x,+,c,+,x,+,x 1157 | tanh,(,tanh,(,x,),) 1158 | tanh,(,x,),+,x,+,sin,(,x,) 1159 | sin,(,x,),+,x,+,x,+,tanh,(,x,+,c,) 1160 | tanh,(,x,) 1161 | tanh,(,x,),+,x 1162 | x,+,x,+,c 1163 | x,+,x,+,x,+,c 1164 | x,+,x,+,x,+,x,+,x 1165 | x,+,c 1166 | tanh,(,x,+,x,),+,x 1167 | tanh,(,tanh,(,x,),+,tanh,(,x,),) 1168 | sin,(,sin,(,x,+,x,),) 1169 | tanh,(,x,),+,tanh,(,x,),+,tanh,(,sin,(,x,),) 1170 | tanh,(,x,+,x,+,c,) 1171 | tanh,(,sin,(,x,+,x,),) 1172 | tanh,(,x,),+,x 1173 | tanh,(,x,+,x,) 1174 | tanh,(,x,) 1175 | sin,(,x,) 1176 | sin,(,x,),+,x,+,x 1177 | tanh,(,x,) 1178 | tanh,(,x,) 1179 | tanh,(,x,) 1180 | sin,(,x,),+,x,+,c,+,tanh,(,x,) 1181 | x,+,sin,(,x,),+,sin,(,x,) 1182 | x,+,tanh,(,x,),+,tanh,(,x,) 1183 | tanh,(,x,+,c,),+,x 1184 | x,+,c,+,x,+,c,+,sin,(,x,) 1185 | sin,(,x,) 1186 | tanh,(,tanh,(,x,),+,sin,(,x,),) 1187 | x,+,x,+,c 1188 | tanh,(,x,),+,x,+,x,+,c 1189 | x,+,x,+,x,+,x,+,x 1190 | sin,(,x,+,c,),+,tanh,(,x,+,c,) 1191 | tanh,(,x,),+,x,+,sin,(,x,+,x,) 1192 | tanh,(,x,+,c,+,x,) 1193 | tanh,(,tanh,(,x,),) 1194 | x,+,x 1195 | sin,(,x,),+,x,+,c,+,sin,(,sin,(,x,),) 1196 | tanh,(,x,),+,x,+,tanh,(,x,+,x,) 1197 | sin,(,x,),+,x,+,sin,(,x,) 1198 | x,+,sin,(,x,),+,c 1199 | sin,(,x,),+,x,+,sin,(,x,) 1200 | tanh,(,tanh,(,x,),) 1201 | tanh,(,x,+,x,) 1202 | tanh,(,tanh,(,x,),) 1203 | tanh,(,x,) 1204 | sin,(,x,),+,x,+,c,+,x 1205 | tanh,(,x,+,c,+,tanh,(,x,),) 1206 | tanh,(,x,+,x,+,x,) 1207 | x,+,c,+,c,+,c 1208 | sin,(,x,),+,c,+,x,+,x 1209 | tanh,(,x,),+,x 1210 | sin,(,x,+,c,),+,x 1211 | sin,(,x,) 1212 | sin,(,x,) 1213 | sin,(,x,),+,c 1214 | x,+,x 1215 | sin,(,tanh,(,x,),),+,x 1216 | x,+,x 1217 | x,+,x,+,x,+,tanh,(,x,),+,sin,(,x,) 1218 | x,+,c 1219 | tanh,(,tanh,(,x,),+,sin,(,x,),) 1220 | tanh,(,sin,(,x,),) 1221 | x,+,c,+,x,+,c 1222 | x,+,x 1223 | sin,(,sin,(,tanh,(,x,),),) 1224 | x,+,c 1225 | tanh,(,tanh,(,tanh,(,x,),),) 1226 | sin,(,x,) 1227 | sin,(,sin,(,sin,(,x,),),) 1228 | x,+,x,+,c,+,c 1229 | sin,(,x,),+,x 1230 | tanh,(,tanh,(,x,+,c,),) 1231 | sin,(,sin,(,x,),) 1232 | sin,(,x,+,x,+,x,+,x,) 1233 | sin,(,sin,(,x,),+,tanh,(,x,),) 1234 | tanh,(,tanh,(,x,),+,c,) 1235 | tanh,(,x,) 1236 | tanh,(,tanh,(,x,),),+,x,+,c,+,c 1237 | tanh,(,x,) 1238 | sin,(,x,) 1239 | tanh,(,tanh,(,x,),) 1240 | x,+,x,+,x,+,tanh,(,x,) 1241 | x,+,x,+,x,+,c,+,sin,(,x,),+,x 1242 | tanh,(,x,),+,tanh,(,x,),+,x,+,x,+,c 1243 | sin,(,sin,(,x,),+,x,+,c,) 1244 | sin,(,x,) 1245 | x,+,c 1246 | x,+,x,+,c,+,c 1247 | sin,(,sin,(,x,),),+,tanh,(,x,+,x,) 1248 | sin,(,tanh,(,x,),) 1249 | tanh,(,x,),+,x 1250 | tanh,(,x,) 1251 | x,+,c 1252 | x,+,c,+,x,+,c,+,sin,(,x,),+,tanh,(,x,) 1253 | tanh,(,tanh,(,tanh,(,x,),),) 1254 | x,+,x,+,c,+,x,+,x 1255 | sin,(,sin,(,x,),) 1256 | sin,(,x,) 1257 | sin,(,x,) 1258 | tanh,(,x,),+,x 1259 | tanh,(,sin,(,x,),+,x,) 1260 | sin,(,x,) 1261 | sin,(,x,) 1262 | sin,(,x,),+,sin,(,x,),+,x,+,x,+,x 1263 | sin,(,x,+,x,+,x,) 1264 | sin,(,tanh,(,sin,(,x,),),) 1265 | sin,(,sin,(,tanh,(,x,),),) 1266 | sin,(,x,+,x,),+,x,+,x,+,c 1267 | tanh,(,x,+,x,+,c,) 1268 | tanh,(,sin,(,x,),) 1269 | tanh,(,x,) 1270 | tanh,(,tanh,(,x,),+,x,+,c,) 1271 | sin,(,x,+,c,),+,x 1272 | x,+,c,+,x,+,x,+,x 1273 | x,+,x,+,c 1274 | sin,(,sin,(,x,),) 1275 | sin,(,x,) 1276 | sin,(,x,+,c,+,c,) 1277 | x,+,x,+,x 1278 | sin,(,x,),+,c,+,x,+,x,+,x 1279 | x,+,x,+,c,+,tanh,(,x,) 1280 | sin,(,x,+,c,+,x,+,x,) 1281 | tanh,(,x,) 1282 | x,+,c,+,x,+,x 1283 | x,+,x,+,x 1284 | x,+,c,+,tanh,(,x,),+,c 1285 | x,+,x,+,x,+,x,+,c 1286 | tanh,(,tanh,(,tanh,(,x,),),) 1287 | tanh,(,x,),+,x,+,x 1288 | tanh,(,sin,(,x,),) 1289 | sin,(,x,+,c,),+,sin,(,x,),+,x 1290 | x,+,x,+,c,+,c 1291 | x,+,c,+,x,+,c,+,x 1292 | sin,(,x,+,x,+,x,+,x,) 1293 | tanh,(,x,+,c,) 1294 | x,+,x 1295 | sin,(,x,),+,x,+,x,+,sin,(,sin,(,x,),) 1296 | sin,(,x,) 1297 | tanh,(,sin,(,sin,(,x,),),) 1298 | x,+,x 1299 | x,+,c,+,c 1300 | x,+,x 1301 | sin,(,sin,(,x,),),+,x 1302 | tanh,(,x,+,x,+,sin,(,x,),) 1303 | sin,(,x,),+,x,+,c 1304 | tanh,(,x,+,x,+,c,) 1305 | sin,(,x,),+,sin,(,x,),+,sin,(,sin,(,x,),) 1306 | x,+,c 1307 | sin,(,x,),+,c,+,c 1308 | tanh,(,tanh,(,x,),),+,tanh,(,x,) 1309 | sin,(,tanh,(,x,),+,x,+,x,) 1310 | x,+,c 1311 | tanh,(,tanh,(,sin,(,x,),),) 1312 | sin,(,x,+,c,),+,c 1313 | tanh,(,x,) 1314 | tanh,(,x,),+,tanh,(,x,),+,x 1315 | sin,(,sin,(,x,),+,x,) 1316 | tanh,(,x,) 1317 | sin,(,x,),+,tanh,(,x,+,c,) 1318 | sin,(,x,) 1319 | sin,(,sin,(,x,+,c,),) 1320 | tanh,(,x,+,c,+,x,) 1321 | tanh,(,x,),+,x,+,tanh,(,x,),+,x 1322 | sin,(,x,) 1323 | x,+,tanh,(,x,),+,x 1324 | tanh,(,sin,(,x,),+,x,) 1325 | sin,(,x,),+,x,+,c,+,x 1326 | sin,(,sin,(,x,),+,tanh,(,x,),) 1327 | tanh,(,x,) 1328 | sin,(,tanh,(,sin,(,x,),),) 1329 | tanh,(,x,+,c,+,sin,(,x,),) 1330 | tanh,(,tanh,(,tanh,(,x,),),) 1331 | x,+,x 1332 | sin,(,x,) 1333 | tanh,(,x,+,x,),+,tanh,(,x,),+,c 1334 | tanh,(,sin,(,x,),) 1335 | tanh,(,x,+,c,),+,x 1336 | x,+,x 1337 | tanh,(,sin,(,tanh,(,x,),),) 1338 | tanh,(,sin,(,x,),) 1339 | tanh,(,x,) 1340 | tanh,(,x,),+,c 1341 | sin,(,x,),+,x,+,tanh,(,x,),+,x 1342 | x,+,c 1343 | sin,(,x,+,c,) 1344 | sin,(,x,) 1345 | sin,(,x,+,x,) 1346 | sin,(,x,) 1347 | x,+,sin,(,x,),+,x 1348 | sin,(,x,),+,x,+,x,+,x 1349 | tanh,(,x,),+,x 1350 | tanh,(,x,) 1351 | sin,(,x,) 1352 | x,+,x 1353 | x,+,c,+,tanh,(,x,) 1354 | x,+,c,+,x,+,c,+,c 1355 | sin,(,x,+,c,) 1356 | tanh,(,tanh,(,x,),+,tanh,(,x,),) 1357 | tanh,(,sin,(,x,),+,x,) 1358 | tanh,(,x,+,x,+,c,) 1359 | x,+,tanh,(,x,),+,x,+,x 1360 | sin,(,tanh,(,tanh,(,x,),),) 1361 | x,+,c,+,x,+,x 1362 | sin,(,x,+,x,),+,x 1363 | tanh,(,tanh,(,x,+,x,),) 1364 | x,+,x,+,x,+,x 1365 | tanh,(,tanh,(,sin,(,x,),),) 1366 | sin,(,sin,(,tanh,(,x,),),) 1367 | sin,(,tanh,(,x,),+,x,) 1368 | tanh,(,x,+,c,) 1369 | x,+,x,+,x 1370 | sin,(,x,) 1371 | tanh,(,sin,(,x,),),+,sin,(,tanh,(,x,),) 1372 | sin,(,x,+,c,),+,c 1373 | sin,(,x,+,c,+,x,+,c,) 1374 | tanh,(,x,) 1375 | tanh,(,x,) 1376 | x,+,x,+,x,+,tanh,(,x,),+,x 1377 | x,+,c 1378 | tanh,(,tanh,(,x,),) 1379 | sin,(,tanh,(,x,),) 1380 | tanh,(,x,) 1381 | sin,(,sin,(,x,),),+,x 1382 | x,+,c,+,x,+,c,+,x 1383 | tanh,(,sin,(,x,),+,x,) 1384 | sin,(,x,) 1385 | sin,(,x,),+,x,+,c,+,sin,(,sin,(,x,),) 1386 | sin,(,x,),+,x,+,x 1387 | tanh,(,x,+,x,+,c,) 1388 | tanh,(,x,),+,x,+,c 1389 | sin,(,x,) 1390 | x,+,c 1391 | tanh,(,tanh,(,x,+,c,),) 1392 | tanh,(,sin,(,x,),),+,sin,(,x,) 1393 | tanh,(,x,),+,sin,(,x,),+,c 1394 | x,+,x 1395 | sin,(,sin,(,x,),),+,tanh,(,tanh,(,x,),) 1396 | sin,(,x,) 1397 | sin,(,x,) 1398 | sin,(,x,),+,c 1399 | tanh,(,x,+,x,),+,x,+,x,+,c 1400 | sin,(,x,) 1401 | sin,(,x,+,x,+,x,) 1402 | sin,(,x,+,x,),+,x 1403 | x,+,tanh,(,x,),+,c 1404 | x,+,x 1405 | sin,(,sin,(,x,),),+,tanh,(,x,) 1406 | x,+,c,+,tanh,(,x,),+,x 1407 | sin,(,sin,(,tanh,(,x,),),) 1408 | x,+,c 1409 | tanh,(,x,+,c,+,x,) 1410 | tanh,(,sin,(,x,),) 1411 | sin,(,sin,(,x,),),+,sin,(,x,+,x,) 1412 | tanh,(,x,+,x,+,x,) 1413 | sin,(,tanh,(,x,),+,x,+,c,) 1414 | x,+,x,+,x,+,x,+,x 1415 | sin,(,x,),+,tanh,(,x,+,x,) 1416 | tanh,(,x,) 1417 | sin,(,x,+,x,),+,tanh,(,x,),+,x 1418 | x,+,sin,(,x,),+,x 1419 | x,+,c 1420 | sin,(,x,),+,x,+,x,+,c 1421 | x,+,x,+,tanh,(,x,+,c,) 1422 | tanh,(,x,+,x,+,sin,(,x,),) 1423 | sin,(,tanh,(,x,),) 1424 | sin,(,sin,(,x,),+,x,) 1425 | sin,(,x,),+,x,+,tanh,(,x,),+,c 1426 | x,+,c 1427 | sin,(,x,+,x,) 1428 | sin,(,sin,(,sin,(,x,),),) 1429 | tanh,(,sin,(,tanh,(,x,),),) 1430 | x,+,c,+,x,+,sin,(,tanh,(,x,),) 1431 | sin,(,tanh,(,x,),+,x,) 1432 | sin,(,x,) 1433 | x,+,c,+,sin,(,x,),+,tanh,(,tanh,(,x,),) 1434 | sin,(,x,) 1435 | sin,(,sin,(,x,+,x,),) 1436 | sin,(,x,+,x,),+,c 1437 | x,+,x 1438 | sin,(,tanh,(,x,+,x,),) 1439 | tanh,(,x,) 1440 | sin,(,x,+,x,+,x,) 1441 | x,+,c,+,x,+,x,+,x,+,x,+,x 1442 | x,+,c,+,sin,(,x,) 1443 | sin,(,x,+,x,),+,x 1444 | tanh,(,x,),+,c,+,c 1445 | sin,(,sin,(,tanh,(,x,),),) 1446 | tanh,(,x,+,x,+,x,) 1447 | tanh,(,x,) 1448 | tanh,(,x,),+,tanh,(,x,),+,c 1449 | tanh,(,x,),+,tanh,(,x,) 1450 | sin,(,x,+,x,+,sin,(,x,),) 1451 | x,+,x,+,x,+,x,+,x 1452 | sin,(,x,+,x,+,c,) 1453 | tanh,(,x,) 1454 | sin,(,x,),+,tanh,(,x,+,c,) 1455 | x,+,x,+,tanh,(,x,),+,c 1456 | tanh,(,sin,(,x,),+,tanh,(,x,),) 1457 | x,+,x,+,c 1458 | tanh,(,x,+,c,) 1459 | x,+,x,+,sin,(,x,),+,tanh,(,tanh,(,x,),) 1460 | tanh,(,tanh,(,x,),),+,sin,(,tanh,(,x,),) 1461 | x,+,c,+,tanh,(,x,) 1462 | sin,(,x,+,c,+,sin,(,x,),) 1463 | sin,(,sin,(,x,),) 1464 | x,+,x,+,c,+,x 1465 | sin,(,x,+,c,+,x,) 1466 | tanh,(,sin,(,x,),+,x,+,c,) 1467 | x,+,c 1468 | tanh,(,x,+,x,+,c,) 1469 | tanh,(,x,+,c,),+,sin,(,x,) 1470 | tanh,(,x,) 1471 | x,+,x 1472 | x,+,x 1473 | sin,(,sin,(,x,),),+,c 1474 | tanh,(,tanh,(,x,),) 1475 | x,+,x,+,x,+,x,+,sin,(,x,+,x,) 1476 | tanh,(,x,),+,x,+,sin,(,x,),+,sin,(,x,) 1477 | tanh,(,sin,(,x,),),+,x,+,x 1478 | x,+,x 1479 | x,+,c 1480 | sin,(,sin,(,sin,(,x,),),) 1481 | tanh,(,x,),+,x 1482 | tanh,(,x,+,x,+,x,) 1483 | sin,(,sin,(,x,),),+,x 1484 | x,+,c,+,c 1485 | x,+,x,+,x,+,sin,(,x,) 1486 | tanh,(,sin,(,x,),),+,c 1487 | sin,(,x,),+,x,+,c,+,x 1488 | tanh,(,tanh,(,x,),+,x,) 1489 | sin,(,x,) 1490 | tanh,(,x,) 1491 | tanh,(,x,) 1492 | tanh,(,x,+,x,),+,c 1493 | tanh,(,tanh,(,x,+,c,),) 1494 | sin,(,x,+,x,+,sin,(,x,),) 1495 | sin,(,x,) 1496 | x,+,c 1497 | x,+,x,+,c,+,tanh,(,x,+,x,) 1498 | sin,(,sin,(,sin,(,x,),),) 1499 | x,+,c,+,c 1500 | tanh,(,sin,(,x,),),+,tanh,(,tanh,(,x,),) 1501 | -------------------------------------------------------------------------------- /data_loader.py: -------------------------------------------------------------------------------- 1 | import csv 2 | import numpy as np 3 | # load in data from file 4 | 5 | def create_dictionaries(equation_strings): 6 | dictionary = {} 7 | reverse_dictionary = {} 8 | index = 0 9 | for equation in equation_strings: 10 | for element in equation: 11 | if element not in dictionary.keys(): 12 | dictionary[element] = index 13 | reverse_dictionary[index] = element 14 | index += 1 15 | return dictionary, reverse_dictionary 16 | 17 | def eq_strings_to_one_hot(equation_strings, dictionary): 18 | one_hot_list = [] 19 | for eq_str in equation_strings: 20 | M = len(eq_str) 21 | N = len(dictionary)+1 22 | one_hot = np.zeros((M,N)) 23 | for eq_index, eq_element in enumerate(eq_str): 24 | one_hot_index = dictionary[eq_element] 25 | one_hot[eq_index,one_hot_index] = 1 26 | one_hot_list.append(one_hot) 27 | return one_hot_list 28 | 29 | def load_data(fname_phi,fname_eq): 30 | 31 | equation_strings = [] 32 | with open(fname_eq, 'rb') as csvfile: 33 | reader = csv.reader(csvfile, delimiter='\n') 34 | for row in reader: 35 | equation_strings.append(row[0].split(',')+['']) 36 | phi_list = [] 37 | with open(fname_phi, 'rb') as csvfile: 38 | reader = csv.reader(csvfile, delimiter='\n') 39 | for row in reader: 40 | phi = row[0].split(',') 41 | phi_list.append([float(p) for p in phi]) 42 | 43 | dictionary, reverse_dictionary = create_dictionaries(equation_strings) 44 | one_hot_list = eq_strings_to_one_hot(equation_strings, dictionary) 45 | num_classes = len(dictionary)+1 46 | num_training = len(equation_strings) 47 | max_len_equation = max([len(e) for e in equation_strings]) 48 | return phi_list, equation_strings, one_hot_list, dictionary, reverse_dictionary 49 | -------------------------------------------------------------------------------- /encoder.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Accelerating Symbolic Regression with Deep Learning 3 | By Tyler Hughes, Siddharth Buddhiraju and Rituraj 4 | For CS 221, Fall 2017-2018 5 | 6 | Provides helper function for fitting the x,y points and 7 | extracting features. 8 | ''' 9 | 10 | from NN import NN 11 | import numpy as np 12 | 13 | def feature_fit(x_list,y_list,layer_sizes, activations, N_epochs=10, learning_rate = 1.0, threshold = 1e-3, lambda_reg=0.0): 14 | # given x,y pairs, construct the neural network, fit the data, and return the feature vector, including the normalization parameters 15 | N = len(x_list) 16 | y_norm = np.array(y_list) 17 | neural_net = NN(layer_sizes, activations) 18 | #neural_net.derivative_check(m=5, epsilon=1e-4, verbose=False) 19 | inputs = np.reshape(np.array(x_list),(len(x_list),1)).T 20 | Js = [] 21 | for i in range(N_epochs): 22 | A = neural_net.forward_prop(inputs) 23 | dAdZ = 1 24 | J = 1/2.0*np.sum(np.power(A-y_norm,2))/N 25 | Js.append(J) 26 | dJdZ = -(A-y_norm)*dAdZ 27 | neural_net.back_prop(dJdZ) 28 | neural_net.update_weights(learning_rate=learning_rate,lambda_reg=lambda_reg) 29 | if J < threshold: 30 | break 31 | feature_vec = neural_net.flatten_parameters() 32 | return feature_vec, J -------------------------------------------------------------------------------- /equation_tree.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Accelerating Symbolic Regression with Deep Learning 3 | By Tyler Hughes, Siddharth Buddhiraju and Rituraj 4 | For CS 221, Fall 2017-2018 5 | 6 | Basic equation tree class used for storing equations and 7 | performing basic operations on them. 8 | ''' 9 | 10 | from numpy.random import random 11 | 12 | # implements an equation tree class 13 | class Node: 14 | def __init__(self): 15 | self.val = None # value of node, corresponding to the value up to that node when x is entered and constants are specified 16 | self.name = None # name of node 17 | self.eq_class = None # class of node 18 | self.anon_fn = None # anonomous function of node 19 | self.nextL = None # left child (specified for operator only, None for constant and function) 20 | self.nextR = None # right child (specified for operator and function, None for constant) 21 | self.string_rep = '' # string represntation (unused) 22 | 23 | class EquationTree: 24 | 25 | def __init__(self): 26 | # create head node on initialization 27 | self.head = Node() 28 | 29 | def __str__(self): 30 | # print(tree) just gives empty string (may be implemented later for printing out trees) 31 | return '' 32 | 33 | def print_expanded_tree(self): 34 | # recursively prints an expanded tree. Uses indentation for structure 35 | def recurse(node,spacing): 36 | if node.val is not None: 37 | print(spacing+node.name+'='+str(node.val)) 38 | else: 39 | print(spacing+node.name) 40 | if node.nextL is not None: 41 | recurse(node.nextL,spacing+' ') 42 | if node.nextR is not None: 43 | recurse(node.nextR,spacing+' ') 44 | recurse(self.head,'') 45 | 46 | def fix_constants(self,const_range): 47 | # fits all constants (besides x) in tree randomly with values between constant_range[0] and constant_range[1] 48 | node = self.head 49 | def recurse(node): 50 | if node.eq_class == 'const' and node.name != 'x': 51 | node.val = const_range[0]+(const_range[1]-const_range[0])*random() 52 | if node.nextL is not None: 53 | recurse(node.nextL) 54 | if node.nextR is not None: 55 | recurse(node.nextR) 56 | recurse(node) 57 | 58 | def evaluate(self,x): 59 | # get a y value from the equation given an x value, recursively evaluates each node up from the leaves 60 | node = self.head 61 | def get_value(node): 62 | if node.eq_class == 'const': 63 | return node.val 64 | if node.eq_class == 'var': 65 | if node.name == 'x': 66 | return x 67 | if node.eq_class == 'fn': 68 | return node.anon_fn(get_value(node.nextR)) 69 | if node.eq_class == 'op': 70 | return node.anon_fn(get_value(node.nextL),get_value(node.nextR)) 71 | return get_value(node) 72 | 73 | 74 | def flatten(self): 75 | # sets the string representation of the head node (tree.string_rep is equal to the equation string now) 76 | # returns a list of the equation elements (including parentheses) of the tree 77 | def get_string(node): 78 | if node is None: 79 | return '' 80 | if node.eq_class == 'const' or node.eq_class == 'var': 81 | return node.name 82 | elif node.eq_class == 'fn': 83 | return node.name +'('+ get_string(node.nextR) +')' 84 | else: 85 | return '('+ get_string(node.nextL) +')' + node.name +'('+ get_string(node.nextR) +')' 86 | def get_list(node): 87 | if node is None: 88 | return [''] 89 | if node.eq_class == 'const' or node.eq_class == 'var': 90 | return [node.name] 91 | elif node.eq_class == 'fn': 92 | return [node.name]+['(']+ get_list(node.nextR) +[')'] 93 | else: 94 | return get_list(node.nextL) + [node.name] + get_list(node.nextR) 95 | 96 | self.string_rep = get_string(self.head) 97 | return get_list(self.head) 98 | -------------------------------------------------------------------------------- /fitter.py: -------------------------------------------------------------------------------- 1 | import math 2 | import random 3 | 4 | unary_list = ['sin','cos','tan'] 5 | binary_list = ['+','*'] 6 | def evalstr(fnstring, constant_list, x): 7 | fnstring = fnstring.replace(" ","") 8 | tmp = fnstring 9 | out = '' 10 | cnt = 0 11 | c = 0 12 | while cnt < len(fnstring): 13 | prog = 0 14 | for i in range(len(unary_list)): 15 | if tmp.startswith(unary_list[i]+'('): 16 | cnt += len(unary_list[i]) 17 | out = out + 'math.' + unary_list[i] 18 | tmp = tmp[len(unary_list[i]):] 19 | prog = 1 20 | break 21 | if prog == 1 : 22 | continue 23 | if tmp.startswith('x'): 24 | out = out + str(x) 25 | tmp = tmp[1:] 26 | cnt += 1 27 | continue 28 | elif tmp.startswith('c'): 29 | out = out + str(constant_list[c]) 30 | tmp = tmp[1:] 31 | cnt += 1 32 | c += 1 33 | continue 34 | else : 35 | out = out + fnstring[cnt] 36 | tmp = tmp[1:] 37 | cnt += 1 38 | #print eval(out) 39 | return eval(out) 40 | 41 | def numc(fnstring): 42 | tmp = fnstring 43 | cnt = 0 44 | c = 0 45 | while cnt < len(fnstring): 46 | prog = 0 47 | for i in range(len(unary_list)): 48 | if tmp.startswith(unary_list[i]+'('): 49 | cnt += len(unary_list[i]) 50 | tmp = tmp[len(unary_list[i]):] 51 | prog = 1 52 | break 53 | if prog == 1 : 54 | continue 55 | if tmp.startswith('x'): 56 | tmp = tmp[1:] 57 | cnt += 1 58 | continue 59 | elif tmp.startswith('c'): 60 | tmp = tmp[1:] 61 | cnt += 1 62 | c += 1 63 | continue 64 | else : 65 | tmp = tmp[1:] 66 | cnt += 1 67 | return c 68 | 69 | def errorsum(fnstring,constant_list,x,y): 70 | err = 0.0 71 | for i in range(len(x)): 72 | err += (evalstr(fnstring,constant_list,x[i])-y[i])**2 73 | return err 74 | 75 | def regression(fnstring, x, y, tol=0.01, eta = 0.001, dx = 0.001): 76 | constant_list = [] 77 | for i in range(numc(fnstring)): 78 | constant_list.append(0) 79 | err = errorsum(fnstring, constant_list,x,y) 80 | c = numc(fnstring) 81 | print c 82 | while err > tol : 83 | for i in range(c): 84 | tmp_list = list(constant_list) 85 | tmp_list[i] += dx 86 | grad = (errorsum(fnstring, tmp_list,x,y) - err)/dx 87 | constant_list[i] -= eta*grad 88 | err = errorsum(fnstring, constant_list,x,y) 89 | print err 90 | return err, constant_list 91 | 92 | x = [] 93 | y = [] 94 | for i in range(100): 95 | x.append(i*math.pi/100) 96 | y.append(math.sin(x[i]*0.45)+math.cos(x[i])) 97 | err, constant_list = regression('sin(x*c)+cos(x*c)',x,y) 98 | print err, constant_list 99 | #print evalstr('sin(x+1)+tan(c)',[1],1) 100 | #print numc('sin(c)+tan(c)+cos(c)') 101 | -------------------------------------------------------------------------------- /generate_examples.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Accelerating Symbolic Regression with Deep Learning 3 | By Tyler Hughes, Siddharth Buddhiraju and Rituraj 4 | For CS 221, Fall 2017-2018 5 | 6 | Script to generate datasets to be stored in ./data/ 7 | ''' 8 | 9 | import numpy as np 10 | import csv 11 | import dill # needed for pickling lambda expressions 12 | import pickle # comes pre-installed 13 | 14 | from generate_examples_helper import generate_training_examples 15 | 16 | # stores the allowable function elements, 17 | # first element is the name of the function element 18 | # second is the class (must be one of {'fn','op','const'} for function, operator, and constant 19 | # third is lambda expression for computing the element, return True for constants 20 | allowed = [('sin','fn',lambda x: np.sin(x)), 21 | #('cos','fn',lambda x: np.cos(x)), 22 | ('x','var',lambda _:True), 23 | ('+','op',lambda x,y: x+y), 24 | #('*','op',lambda x,y: x*y), 25 | ('tanh','fn',lambda x: np.tanh(x)), 26 | ('c','const',lambda _: True)] 27 | #('b','const',lambda _: True), 28 | #('log','fn',lambda x: np.log(np.abs(x)))] 29 | #('cosh','fn',lambda x: np.cosh(x))] 30 | 31 | # parameters for fitting to the datapoints 32 | const_range = [-5,5] # when determining constants, sample randomly in this range 33 | x_range = [-1,1] # when sampling x points, sample randomly in this range 34 | N_points = 50 # number of x,y pairs to generate in training examples 35 | N_epochs = 1000 # number of training epochs for neural network fitting of x,y pairs 36 | tree_depth = 4 # max equation tree depth (depth of 0 is x,c by default, depth of 1 could be sin(x), cos(c), c, etc.) 37 | learning_rate = .1 # neural network learning rate 38 | layer_sizes = [1,4,1] # layer sizes in neural network, first must be 1, last must be 1, middle layers can change size or add more 39 | activations = ['tanh','linear'] # NN activations, list must be 1 less in length than above layer sizes. Stick to pattern of tanh, tanh, ... tanh, sigmoid 40 | N_training = 1500 # number of training steps for the NN fit. 41 | 42 | print('generating %s training examples up to tree depth of %s...'%(N_training,tree_depth)) 43 | # this generates random equations, randomly sets constants, generates the x,y pairs, fits them to neural network and returns feature vectors 44 | input_features, input_vectors, input_trees, losses = generate_training_examples(N_training, 45 | allowed,tree_depth=tree_depth,const_range=const_range,x_range=x_range,N_points=N_points, 46 | layer_sizes=layer_sizes,activations=activations, 47 | N_epochs=N_epochs,learning_rate=learning_rate,verbose=False,uniquify=False,lambda_reg=.01) 48 | # input features: list of feature vectors (flattened weights and biases from NN) 49 | # input vectors: list of list of one_hot vector corresponding to the equations generated. 50 | # input trees: list of tree structures corresponding to the equations 51 | # losses: list of losses for each of the NN fits (to see if the fitting was accurate enough) 52 | # y_list: ignore, y points corresponding to x points generated from sampling. 53 | 54 | # write the equation strings and feature vectors to files in the data/ directory 55 | print(' started with %s training examples'%N_training) 56 | N_training = len(input_features) # need to account for the fact that we removed duplicated training examples 57 | print(' have %s training examples if removing duplicates'%N_training) 58 | print('saving data to files...') 59 | g = open('data/desired_equation_components_d'+str(tree_depth)+'.txt', 'w') 60 | for i in range(N_training): 61 | eq_tree = input_trees[i] 62 | eq_string = eq_tree.flatten() 63 | g.write(','.join(eq_string)+'\n') # python will convert \n to os.linesep 64 | g.close() 65 | np.savetxt("data/encoded_states_d"+str(tree_depth)+".txt", np.array(input_features), delimiter=",") 66 | pickle.dump(input_trees, open( "data/equation_trees_d"+str(tree_depth)+".p", "wb" ) ) 67 | pickle.dump(allowed, open( "data/allowed_d"+str(tree_depth)+".p", "wb" ) ) 68 | -------------------------------------------------------------------------------- /generate_examples_helper.py: -------------------------------------------------------------------------------- 1 | ''' 2 | Accelerating Symbolic Regression with Deep Learning 3 | By Tyler Hughes, Siddharth Buddhiraju and Rituraj 4 | For CS 221, Fall 2017-2018 5 | 6 | Helper functions for generating dataset 7 | ''' 8 | 9 | import numpy as np 10 | from numpy.random import randint, random 11 | from equation_tree import * 12 | from NN import * 13 | from encoder import * 14 | import sys 15 | 16 | def generate_random_tree(allowed, depth=3): 17 | # generates a random equation tree to some depth 18 | 19 | # separate allowed dictionary into separate classes 20 | constants = [(name,eq_class,anon_fn) for (name,eq_class,anon_fn) in allowed if eq_class == 'const'] 21 | variables = [(name,eq_class,anon_fn) for (name,eq_class,anon_fn) in allowed if eq_class == 'var'] 22 | functions = [(name,eq_class,anon_fn) for (name,eq_class,anon_fn) in allowed if eq_class == 'fn'] 23 | operators = [(name,eq_class,anon_fn) for (name,eq_class,anon_fn) in allowed if eq_class == 'op'] 24 | 25 | def get_constant(not_allowed): 26 | # returns a random constant 27 | if not_allowed == 'const': 28 | end_nodes = variables 29 | else: 30 | end_nodes = constants + variables 31 | return end_nodes[randint(len(end_nodes))] 32 | 33 | def get_obj(not_allowed): 34 | # returns a random equation element 35 | if 'const' in not_allowed and 'var' in not_allowed: 36 | grouped = [functions,operators] 37 | group_pick = grouped[randint(2)] 38 | 39 | elif not_allowed == 'const': 40 | grouped = [variables, functions, operators] 41 | group_pick = grouped[randint(3)] 42 | else: 43 | grouped = [variables, constants, functions, operators] 44 | group_pick = grouped[randint(4)] 45 | 46 | return group_pick[randint(len(group_pick))] 47 | # first samples randomly from constants, functions, and operators 48 | # then samples randomly from this class 49 | # this makes it so that adding a lot of one class does not bias the equations to have more elements from that class 50 | 51 | 52 | # recursive function to add a layer to the equation tree based on the class 53 | def add_layer(node,depth,not_allowed): 54 | # if we're at the max depth, it must be a constant, because they have no children 55 | if depth == 1: 56 | (name,eq_class,anon_fn) = get_constant(not_allowed) 57 | # otherwise, it can be anything 58 | else: 59 | name,eq_class,anon_fn = get_obj(not_allowed) 60 | node.name = name 61 | node.eq_class = eq_class 62 | # if it's a function, add one child recursively 63 | if eq_class == 'fn': 64 | node.anon_fn = anon_fn 65 | node.nextR = Node() 66 | add_layer(node.nextR,depth-1,'const') 67 | # if it's an operator, add two children recursively 68 | elif eq_class == 'op': 69 | node.anon_fn = anon_fn 70 | node.nextL = Node() 71 | node.nextR = Node() 72 | class_1 = add_layer(node.nextL,depth-1,'const') 73 | class_2 = add_layer(node.nextR,depth-1,'') 74 | 75 | if class_1 in ['const','var'] and class_2 == 'fn': 76 | node.nextL, node.nextR = node.nextR, node.nextL 77 | 78 | 79 | return eq_class 80 | 81 | # get new equation tree object and recursively add layers to tree 82 | tree = EquationTree() 83 | #add_layer(tree.head, depth,'') ##use this if only 'x' and 'c' are acceptable 84 | 85 | add_layer(tree.head, depth,['const','var']) 86 | # this disallows examples that are only 'x' or only 'c' to allow training 87 | # on more complex examples. 88 | return tree 89 | 90 | def generate_example_list(tree,const_range,x_range,N_points): 91 | # generates x y sampling points from an equation tree 92 | # fixes the constants randomly beween range 93 | tree.fix_constants(const_range) 94 | N_points = 100 95 | # randomly sample x and evaluate tree for y points 96 | x_list = x_range[0] + random(N_points)*(x_range[1]-x_range[0]) 97 | y_list = [] 98 | for i in range(N_points): 99 | y_list.append(tree.evaluate(x_list[i])) 100 | return x_list, y_list 101 | 102 | def create_index_map(allowed): 103 | # give a unique index to each equation element, add parentheses too 104 | index_map = {allowed[i][0]:i+3 for i in range(len(allowed))} 105 | index_map['('] = 1 106 | index_map[')'] = 2 107 | return index_map 108 | 109 | def operator_list_to_one_hot(operator_list,index_map): 110 | # with a list of operators, generate one hot numpy array 111 | N = len(index_map) 112 | M = len(operator_list) 113 | one_hot = np.zeros((N,M)) 114 | for i in range(M): 115 | name = operator_list[i] 116 | index = index_map[name] 117 | one_hot[index-1,i] = 1 118 | return one_hot 119 | 120 | def generate_training_examples(N_training,allowed,tree_depth=6,const_range=[-5,5],x_range=[-5,5],N_points=100, 121 | layer_sizes=[1,10,10,1],activations=['tanh','tanh','sigmoid'], N_epochs=100,learning_rate=1,verbose=False,uniquify=True,lambda_reg=0.0): 122 | # function called by main to get all training examples at once 123 | # set up important elements 124 | input_features = [] 125 | input_trees = [] 126 | input_vectors = [] 127 | losses = [] 128 | index_map = create_index_map(allowed) 129 | seen_equations = set() 130 | print("") 131 | # loop through number of training examples desired 132 | for train_i in range(N_training): 133 | # generate a random equation and get tree 134 | tree = generate_random_tree(allowed, depth=tree_depth) 135 | # get the corresponding operator name list 136 | operator_list = tree.flatten() 137 | # convert this to one hot representation 138 | eq_string = ''.join(operator_list) 139 | sys.stdout.write("\r working on %s/%s: generating tree for equation: %s " % (train_i+1,N_training, eq_string)) 140 | sys.stdout.flush() 141 | one_hot = operator_list_to_one_hot(operator_list,index_map) 142 | # generate x,y points from the equation 143 | x_list, y_list = generate_example_list(tree,const_range,x_range,N_points) 144 | # fit the NN to the x,y points and get the feature vector and loss 145 | phi,loss = feature_fit(x_list,y_list,layer_sizes,activations,N_epochs=N_epochs,learning_rate=learning_rate,lambda_reg=lambda_reg) 146 | # only add if equation is unique 147 | if uniquify: 148 | if tree.string_rep not in seen_equations: 149 | seen_equations.add(tree.string_rep) 150 | if verbose: 151 | print(train_i,loss) 152 | input_vectors.append(one_hot) 153 | input_trees.append(tree) 154 | losses.append(loss) 155 | input_features.append(phi) 156 | else: 157 | seen_equations.add(tree.string_rep) 158 | if verbose: 159 | print(train_i,loss) 160 | input_vectors.append(one_hot) 161 | input_trees.append(tree) 162 | losses.append(loss) 163 | input_features.append(phi) 164 | return input_features, input_vectors, input_trees, losses 165 | 166 | 167 | def process_IO_for_keras(input_features,input_vectors,N_training,allowed): 168 | # Ignore, I was using this to get data into keras but it is no longer needed. 169 | L_feature = len(input_features[0]) 170 | L_max_eq = max([a.shape[1] for a in input_vectors]) 171 | L_eq_identifier = len(allowed)+2 172 | 173 | resized_input_vectors = [] 174 | for a in input_vectors: 175 | num_needed = L_max_eq-a.shape[1] 176 | if num_needed > 0: 177 | new_array = np.zeros((L_eq_identifier,num_needed)) 178 | resized_input_vectors.append((np.concatenate((a,new_array),axis=1))) 179 | else: 180 | resized_input_vectors.append(a) 181 | 182 | inputs = [] 183 | for i in range(N_training): 184 | phi = np.reshape(np.array(input_features[i]),(L_feature,1)) 185 | one_hots = resized_input_vectors[i] 186 | extra_needed = L_feature-L_eq_identifier 187 | padding = np.zeros((extra_needed,one_hots.shape[1])) 188 | one_hots = np.concatenate((one_hots,padding),axis=0) 189 | inputs.append(np.concatenate((phi,one_hots),axis=1).T) 190 | #inputs is a list of numpy arrays, [input dimension x number in sequence] 191 | input_x = L_max_eq+1 # input size dimension 192 | input_y = L_feature # number in sequence 193 | 194 | outputs = [] 195 | for i in range(N_training): 196 | input_array = inputs[i] 197 | output_array = np.zeros((input_x,input_y)) 198 | output_array[:-1,:] = input_array[1:,:] 199 | outputs.append(output_array) 200 | 201 | return np.array(inputs),np.array(outputs) 202 | -------------------------------------------------------------------------------- /plot_data/tree_saveLosses_d0.txt: -------------------------------------------------------------------------------- 1 | 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-------------------------------------------------------------------------------- /plot_data/tree_saveLosses_d1.txt: -------------------------------------------------------------------------------- 1 | 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