count iterations/recursive calls to a function that repeatedly evaluates the digit product of a base 10 number representation

digitprod.py

from functools import reduce
from operator import mul

# For DRYness's sake, we'll write digitprod here. We have to rull our own prod, since
# Python doesn't have one, but will take Trey Hunner's advice and use operator.mul, which
# gives * a name so we can avoid a lambda.
def digitprod(n):
    return reduce(mul, (int(c) for c in str(n)), 1)
    
# Now for the real action. We repeatedly evaluate the "digit product" of the base 10
# representation of a number and want to know how many iterations it takes to get to
# converge to a one-digit number. The real goal might well be how to instrument
# recursive functions in general--perhaps someone's already done it. We got distracted
# and did recursion elimination as well as instrumenting the code.

# iterative version
def dpreduce(n):
    count = 0
    while n > 9:
        count += 1
        n = digitprod(n)
    return count

# recursive version
def dpreduce2(n, count = 0):
    return count if n < 10 else dpreduce2(digitprod(n), count + 1)

# Ultimately, I should instruct myself in the ways of hypothesis and write test code.