import time

N=10**6
M=20

def square0(x):
    return x*x

def square1(x):
    def dummy(y):
        return y*y
    return x*x
    
def square2(x):
    def dummy1(y):
        return y*y
    def dummy2(y):
        return y*y
    return x*x

def square5(x):
    def dummy1(y):
        return y*y
    def dummy2(y):
        return y*y
    def dummy3(y):
        return y*y
    def dummy4(y):
        return y*y
    def dummy5(y):
        return y*y
    return x*x
    
test01_first=True
test02_first=True
test03_first=True
test04_first=True
   
for  j in range(M):
    start=time.time()
    s=0
    for i in range(N):
        s+=square0(i)
    end=time.time()
    test01_time=end-start
    if test01_first:
        test01_sum=test01_time
        test01_sqs=0
        test01_approx=test01_time
        test01_cnt=1
        test01_first=False
    else:
        test01_sum+=test01_time
        test01_sqs+=(test01_time-test01_approx)**2
        test01_cnt+=1

    start=time.time()
    s=0
    for i in range(N):
        s+=square1(i)
    end=time.time()
    test02_time=end-start
    if test02_first:
        test02_sum=test02_time
        test02_sqs=0
        test02_approx=test02_time
        test02_cnt=1
        test02_first=False
    else:
        test02_sum+=test02_time
        test02_sqs+=(test02_time-test02_approx)**2
        test02_cnt+=1

    start=time.time()
    s=0
    for i in range(N):
        s+=square2(i)
    end=time.time()
    test03_time=end-start
    if test03_first:
        test03_sum=test03_time
        test03_sqs=0
        test03_approx=test03_time
        test03_cnt=1
        test03_first=False
    else:
        test03_sum+=test03_time
        test03_sqs+=(test03_time-test03_approx)**2
        test03_cnt+=1

    start=time.time()
    s=0
    for i in range(N):
        s+=square5(i)
    end=time.time()
    test04_time=end-start
    if test04_first:
        test04_sum=test04_time
        test04_sqs=0
        test04_approx=test04_time
        test04_cnt=1
        test04_first=False
    else:
        test04_sum+=test04_time
        test04_sqs+=(test04_time-test04_approx)**2
        test04_cnt+=1
        
test01_avg=test01_sum/test01_cnt
test02_avg=test02_sum/test02_cnt
test03_avg=test03_sum/test03_cnt
test04_avg=test04_sum/test04_cnt
test01_std=((test01_sqs-(test01_sum-test01_cnt*test01_approx)**2/test01_cnt)/(test01_cnt-1))**.5
test02_std=((test02_sqs-(test02_sum-test02_cnt*test02_approx)**2/test02_cnt)/(test02_cnt-1))**.5
test03_std=((test03_sqs-(test03_sum-test03_cnt*test03_approx)**2/test03_cnt)/(test03_cnt-1))**.5
test04_std=((test04_sqs-(test04_sum-test04_cnt*test04_approx)**2/test04_cnt)/(test04_cnt-1))**.5
print("m = mean, s = standard deviation, m0 = mean of first testcase")
print("[m-3s,m+3s] is a 0.997 confidence interval if normal distributed")
print()
print("square?","{0:5} {1:7} {2:5} [{3:5},{4:5}]".format("m","s","m/m0","m-3s","m+3s"))
print("square0","{0:5.3f} {1:7.5f} {2:5.3f} [{3:5.3f},{4:5.3f}]".format(test01_avg,test01_std,test01_avg/test01_avg,test01_avg-3*test01_std,test01_avg+3*test01_std))
print("square1","{0:5.3f} {1:7.5f} {2:5.3f} [{3:5.3f},{4:5.3f}]".format(test02_avg,test02_std,test02_avg/test01_avg,test02_avg-3*test02_std,test02_avg+3*test02_std))
print("square2","{0:5.3f} {1:7.5f} {2:5.3f} [{3:5.3f},{4:5.3f}]".format(test03_avg,test03_std,test03_avg/test01_avg,test03_avg-3*test03_std,test03_avg+3*test03_std))
print("square5","{0:5.3f} {1:7.5f} {2:5.3f} [{3:5.3f},{4:5.3f}]".format(test04_avg,test04_std,test04_avg/test01_avg,test04_avg-3*test04_std,test04_avg+3*test04_std))