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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def precompile(ex, signature=(), context={}):
 """Compile the expression to an intermediate form. """

    types = dict(signature)
    input_order = [name for (name, type_) in signature]

    if isinstance(ex, (str, unicode)):
        ex = stringToExpression(ex, types, context)

    # the AST is like the expression, but the node objects don't have
    # any odd interpretations

    ast = expressionToAST(ex)

    if ex.astType != 'op':
        ast = ASTNode('op', value='copy', astKind=ex.astKind, children=(ast,))

    ast = typeCompileAst(ast)

    aliases = collapseDuplicateSubtrees(ast)

    assignLeafRegisters(ast.allOf('raw'), Immediate)
    assignLeafRegisters(ast.allOf('variable', 'constant'), Register)
    assignBranchRegisters(ast.allOf('op'), Register)

    # assign registers for aliases
    for a in aliases:
        a.reg = a.value.reg

    input_order = getInputOrder(ast, input_order)
    constants_order, constants = getConstants(ast)

    if isReduction(ast):
        ast.reg.temporary = False

    optimizeTemporariesAllocation(ast)

    ast.reg.temporary = False
    r_output = 0
    ast.reg.n = 0

    r_inputs = r_output + 1
    r_constants = setOrderedRegisterNumbers(input_order, r_inputs)
    r_temps = setOrderedRegisterNumbers(constants_order, r_constants)
    r_end, tempsig = setRegisterNumbersForTemporaries(ast, r_temps)

    threeAddrProgram = convertASTtoThreeAddrForm(ast)
    input_names = tuple([a.value for a in input_order])
    signature = ''.join(type_to_typecode[types.get(x, default_type)]
                        for x in input_names)
    return threeAddrProgram, signature, tempsig, constants, input_names