The second problem involves applying our system to a trigonometric identity problem summarised in Table 2 [Ryan 98b]. The particular function examined was
, and the desired trigonometric identity was
The system was given a set of input and output pairs, and must determine the function that maps one onto the other, with the input values in the range
Other identities exist for ,
2 Cos2x - 1. If we were to include Cos as one of the terminals in our BNF grammar definition, GE would naturally produce simple Cos identities for ,
which was verified in early experiments which included Cos. These runs consistently found the target expression
and, therefore, we decided to exclude Cos from the terminal operator set. Koza included the constant 1.0 in his terminal operator set, although Genetic Programming has shown an ability to generate the constant 1.0, as has GE with expressions such as x/x. However, we included 1.0 for reasons of consistency.