Apply simplification rule for special functions

I am defining two custom functions in Sympy called phi

and phi

. I know that Phi(x)+Phi(-x) == 1

. How do you provide Sympy with this simplification rule? Can I specify this in the class definition?

Here's what I've done so far:

from sympy import Function


class phi(Function):

    nargs = 1

    def fdiff(self, argindex=1):
        if argindex == 1:
            return -1*self.args[0]*phi(self.args[0])
        else:
            raise ArgumentIndexError(self, argindex)

    @classmethod
    def eval(cls, arg):
        # The function is even, so try to pull out factors of -1
        if arg.could_extract_minus_sign():
            return cls(-arg)


class Phi(Function):

    nargs = 1

    def fdiff(self, argindex=1):
        if argindex == 1:
            return phi(self.args[0])
        else:
            raise ArgumentIndexError(self, argindex)

      

        
        
        
      

    

For the curious, phi

and phi

are Gaussian PDF and CDF, respectively. They are implemented in sympy.stats

. But, in my case, it is easier to interpret the results in terms of phi

and phi

.