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Table 8:

Sample expression from ITEA for the Concrete data set limited to a maximum of 5 terms and with coefficients rounded to the third decimal place. The RMSE value on the test set for this expression is 6.74. We omitted the partial derivative of x2 since it does not appear on the generated expression.

FunctionExpression
f(x) -0.003·|x3·x6·x7|-11.762·log(x0-2·x5·x62·x7-1)+5.790 
 ·tanh(x02·x3·x42·x5-2·x7-1)-0.288·x3+0.000·(x1·x32·x62)+156.242 
fx0 23.525·logx5·x62x03·x7x5·x62x02·x7+11.579·tanhx0·x3·x42x52·x7coshx02·x3·x42x52·x72 
fx1 0.000·x32·x62 
fx3 -0.003·x6·x72·x3·x6·x732+5.79·tanhx02·x42x52·x7coshx02·x3·x42x52·x72+0.0·x1·x3·x62 
fx4 11.579·tanhx02·x3·x4x52·x7coshx02·x3·x42x52·x72 
fx5 -11.762·logx62x02·x7x5·x62x02·x7+-11.579·tanhx02·x3·x42x53·x7coshx02·x3·x42x52·x72 
fx6 -0.003·x3·x72·x3·x6·x732+-23.525·logx5·x6x02·x7x5·x62x02·x7+0.0·x1·x32·x6 
fx7 -0.003·x3·x62·x3·x6·x732+11.762·logx5·x62x02·x72x5·x62x02·x7+-5.79·tanhx02·x3·x42x52·x72coshx02·x3·x42x52·x72 
FunctionExpression
f(x) -0.003·|x3·x6·x7|-11.762·log(x0-2·x5·x62·x7-1)+5.790 
 ·tanh(x02·x3·x42·x5-2·x7-1)-0.288·x3+0.000·(x1·x32·x62)+156.242 
fx0 23.525·logx5·x62x03·x7x5·x62x02·x7+11.579·tanhx0·x3·x42x52·x7coshx02·x3·x42x52·x72 
fx1 0.000·x32·x62 
fx3 -0.003·x6·x72·x3·x6·x732+5.79·tanhx02·x42x52·x7coshx02·x3·x42x52·x72+0.0·x1·x3·x62 
fx4 11.579·tanhx02·x3·x4x52·x7coshx02·x3·x42x52·x72 
fx5 -11.762·logx62x02·x7x5·x62x02·x7+-11.579·tanhx02·x3·x42x53·x7coshx02·x3·x42x52·x72 
fx6 -0.003·x3·x72·x3·x6·x732+-23.525·logx5·x6x02·x7x5·x62x02·x7+0.0·x1·x32·x6 
fx7 -0.003·x3·x62·x3·x6·x732+11.762·logx5·x62x02·x72x5·x62x02·x7+-5.79·tanhx02·x3·x42x52·x72coshx02·x3·x42x52·x72 
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