UNARIES = ["-%s", "e(%s)", "arctan(%s)"]
BINARIES = ["%s + %s", "%s - %s", "%s * %s", "%s / %s", "%s ^ %s"]

PROB_PARENTHESES = 0.3
PROB_BINARY = 0.8

def generate_expressions(scope, num_exp, num_ops):
    scope = list(scope)
    for _ in range(num_ops):
        if random() < PROB_BINARY:
            op = choice(BINARIES)
            args = None
            while not args or ('/' in op and args[1] == '0'):
                args = (choice(scope), choice(scope))


            ex = op % args 
            if random() < PROB_PARENTHESES:
                ex = "(%s)" % ex
            scope.append(ex)
        else:
            scope.append(choice(UNARIES) % choice(scope))
    return scope[-num_exp:]

for x in generate_expressions(["0", "1", "2", "10", "100", "x"], 1000, 100):
    print('"' + x + '"')

for x in generate_expressions(["0", "1", "2", "10", "100", "x"], 100, 100):
    pprint(parse('diff(' + x + ', x)'))