approach numbers using limited number of positive exponents

approach.py

import math
import itertools
from operator import mul
from functools import reduce

def approx(freq, exponents):
    resulting_list = []
    maxvals = [ list(range(0, math.ceil(math.log(freq, exp)))) for exp in exponents]
    print("maxvals = ", maxvals)
    cartesian_product = itertools.product(*maxvals)
    cartesian_prod_list = []
    for idx, element in enumerate(cartesian_product):
        #print ("element = ", element)
        produced_freq = reduce(mul, [math.pow(exponents[i], element[i]) for i in range(len(exponents))])
        #print ("produced freq = ", produced_freq, element)
        diff = math.fabs(freq-produced_freq)
        #print ("diff between desired and produced: ", diff)
        energy = reduce(mul, [e+1 for e in element])
        #print ("product of (exponents+1): ", energy)
        resulting_list.append([diff, energy, idx])
        cartesian_prod_list.append(element)

    result = sorted(resulting_list, key=lambda el : (el[0], el[1]))

    # print best result
    #print(result[0])
    print(cartesian_prod_list[result[0][2]])
    total = 1
    for idx, exponent in enumerate(cartesian_prod_list[result[0][2]]):
        total = total * (math.pow(exponents[idx], exponent))
    print ("desired: ", freq, " reached: ", total, "diff: ", math.fabs(total-freq), "diff[%]: ", math.fabs(total-freq)/freq*100)

if __name__=="__main__":
    approx(440, [2,3,5,7,11,13,17,19,23])