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
$f(x)$ $-0.003·|x3·x6·x7|-11.762·log(x0-2·x5·x62·x7-1)+5.790$
$·tanh(x02·x3·x42·x5-2·x7-1)-0.288·x3+0.000·(x1·x32·x62)+156.242$
$∂f∂x0$ $23.525·logx5·x62x03·x7x5·x62x02·x7+11.579·tanhx0·x3·x42x52·x7coshx02·x3·x42x52·x72$
$∂f∂x1$ $0.000·x32·x62$
$∂f∂x3$ $-0.003·x6·x72·x3·x6·x732+5.79·tanhx02·x42x52·x7coshx02·x3·x42x52·x72+0.0·x1·x3·x62$
$∂f∂x4$ $11.579·tanhx02·x3·x4x52·x7coshx02·x3·x42x52·x72$
$∂f∂x5$ $-11.762·logx62x02·x7x5·x62x02·x7+-11.579·tanhx02·x3·x42x53·x7coshx02·x3·x42x52·x72$
$∂f∂x6$ $-0.003·x3·x72·x3·x6·x732+-23.525·logx5·x6x02·x7x5·x62x02·x7+0.0·x1·x32·x6$
$∂f∂x7$ $-0.003·x3·x62·x3·x6·x732+11.762·logx5·x62x02·x72x5·x62x02·x7+-5.79·tanhx02·x3·x42x52·x72coshx02·x3·x42x52·x72$
FunctionExpression
$f(x)$ $-0.003·|x3·x6·x7|-11.762·log(x0-2·x5·x62·x7-1)+5.790$
$·tanh(x02·x3·x42·x5-2·x7-1)-0.288·x3+0.000·(x1·x32·x62)+156.242$
$∂f∂x0$ $23.525·logx5·x62x03·x7x5·x62x02·x7+11.579·tanhx0·x3·x42x52·x7coshx02·x3·x42x52·x72$
$∂f∂x1$ $0.000·x32·x62$
$∂f∂x3$ $-0.003·x6·x72·x3·x6·x732+5.79·tanhx02·x42x52·x7coshx02·x3·x42x52·x72+0.0·x1·x3·x62$
$∂f∂x4$ $11.579·tanhx02·x3·x4x52·x7coshx02·x3·x42x52·x72$
$∂f∂x5$ $-11.762·logx62x02·x7x5·x62x02·x7+-11.579·tanhx02·x3·x42x53·x7coshx02·x3·x42x52·x72$
$∂f∂x6$ $-0.003·x3·x72·x3·x6·x732+-23.525·logx5·x6x02·x7x5·x62x02·x7+0.0·x1·x32·x6$
$∂f∂x7$ $-0.003·x3·x62·x3·x6·x732+11.762·logx5·x62x02·x72x5·x62x02·x7+-5.79·tanhx02·x3·x42x52·x72coshx02·x3·x42x52·x72$
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