import math
from math import sqrt as math_sqrt

x = 81
%timeit math_sqrt(x)
%timeit math.sqrt(x)

x = 988
assert(math_sqrt(x) == x**0.5)
print('both functions produce similar results')

from math import pow as math_pow

x = 3.3
n = 4
assert(math_pow(x, n) == pow(x, n) == x**n)
print('All functions produce similar results')

import timeit

test_sqrt = [12345.54321, 54756, 23423422, 999999999999999]

timings_sqrt = {'math_module':[], 'arithmetic':[]}

for x in test_sqrt:
    timings_sqrt['math_module'].append(min(timeit.Timer('math_sqrt(x)', 
                      'from __main__ import x, math_sqrt')
                              .repeat(repeat=100, number=1000)))
    timings_sqrt['arithmetic'].append(min(timeit.Timer('x**0.5', 
                      'from __main__ import x')
                              .repeat(repeat=100, number=1000)))

import timeit

test_pow = list(range(1,13))
funcs_pow = ['math_module', 'inbuilt', 'arithmetic']

timings_pow = {f:[] for f in funcs_pow}

for n in test_pow:
    timings_pow['math_module'].append(min(timeit.Timer('math_pow(n, n)', 
                      'from __main__ import n, math_pow')
                              .repeat(repeat=100, number=1000)))
    timings_pow['inbuilt'].append(min(timeit.Timer('pow(n, n)', 
                      'from __main__ import n')
                              .repeat(repeat=100, number=1000)))
    timings_pow['arithmetic'].append(min(timeit.Timer('n**n', 
                      'from __main__ import n')
                              .repeat(repeat=100, number=1000)))   

import platform
import multiprocessing

def print_sysinfo():
    print('\nsystem   :', platform.system())
    print('release  :', platform.release())
    print('machine  :', platform.machine())
    print('processor:', platform.processor())
    print('interpreter:', platform.architecture()[0])
    print('CPU count  :', multiprocessing.cpu_count())

    print('\nPython version', platform.python_version())
    print('compiler', platform.python_compiler())
    print('\n\n')

%matplotlib inline

import matplotlib.pyplot as plt

def plot_figures(): 
    
    fig = plt.figure(figsize=(8,4))
    plt.plot(range(len(test_sqrt)), timings_sqrt['math_module'], 
              alpha=0.5, label='math.sqrt(x)', marker='o', lw=2)
    plt.plot(range(len(test_sqrt)), timings_sqrt['arithmetic'], 
              alpha=0.5, label='x**0.5', marker='o', lw=2)
    plt.legend(loc='upper left')
    plt.xticks(range(len(test_sqrt)), ['$\sqrt{%s}$'%(x) for x in test_sqrt])
    plt.grid()
    plt.ylabel('time in milliseconds')
        
    plt.show()
    
    fig = plt.figure(figsize=(8,4))
    plt.plot(range(len(test_pow)), timings_pow['math_module'], 
              alpha=0.5, label='math.pow(x, n)', marker='o', lw=2)
    plt.plot(range(len(test_pow)), timings_pow['inbuilt'], 
              alpha=0.5, label='pow(x, n)', marker='o', lw=2)
    plt.plot(range(len(test_pow)), timings_pow['arithmetic'], 
              alpha=0.5, label='x**n', marker='o', lw=2)
    plt.legend(loc='upper left')
    plt.xticks(range(len(test_pow)), ['$%s^{%s}$'%(x, x) for x in test_pow])
    plt.grid()
    plt.ylabel('time in milliseconds')
    

print_sysinfo()
plot_figures()

(81+2j)**0.5

import cmath
cmath.sqrt(81+2j)

import math
math.sqrt(81+2j)