print "SAGE :", numerical_approx(pi,400)
print
print "Calculation of 4 digits of PI"
# Wallis
t = cputime()
m=8477
x=2
for n in range(1,m+1):
x = x * (2*(n)*2*(n))/(((2*n)+1)*((2*n)-1))
print "Wallis 1 :", numerical_approx(x), "CPU:", cputime(t)
# Wallis 2
t = cputime()
m=8477
y=(2**(4*m))*((factorial(m))**4)
z=((factorial(2*m))**2)*(m+1/2)
x=y/z
print "Wallis 2 :",numerical_approx(x), "CPU:", cputime(t)
#Euler
t = cputime()
m=10308
x=0
for n in range(1,m):
x = x + 1/(n**2)
x = sqrt(6*x)
print "Euler :",numerical_approx(x), "CPU:", cputime(t)
#Leibniz
t = cputime()
m=10828
x=0
for n in range(0,m):
x = x + (-1)**n/(2*n+1)
x = 4*x
print "Leibniz :",numerical_approx(x), "CPU:", cputime(t)
print
print "Calculation of more digits of PI"
# Vieta
t = cputime()
m=15
x=2
for n in range(1,m):
x = 2 + sqrt(x)
x = (2**(m+1))*sqrt(2-sqrt(x))
print "Vieta :",numerical_approx(x), "CPU:", cputime(t)
print
#Ramanujan
t = cputime()
m=14
x=0
for n in range(0,m):
x = x+(factorial(4*n)*(1103+26390*n))/((factorial(n)**4)*(396**(4*n)))
x = 9801/(x*sqrt(8))
print "Ramanujan:",numerical_approx(x,400), "CPU:", cputime(t)
#Lambert
t = cputime()
m=150
x=1
for nn in range(1,m):
n = m - nn
x = (2*n-1)+(n**2)/x
x = 4/x
print "Lambert :",numerical_approx(x,400), "CPU:", cputime(t)
#BBP
t = cputime()
m=90
x=0
for n in range(0,m):
x = x+(1/(16**n))*((4/((8*n)+1))-((2/((8*n)+4))+(1/((8*n)+5))+(1/((8*n)+6))))
print "BBP :",numerical_approx(x,400), "CPU:", cputime(t)
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SAGE :
3.1415926535897932384626433832795028841971693993751058209749445923078164\
0628620899862803482534211706798214808651328230665
Calculation of 4 digits of PI
Wallis 1 : 3.14150000993513 CPU: 0.16
Wallis 2 : 3.14150000993513 CPU: 0.02
Euler : 3.14150000806581 CPU: 0.53
Leibniz : 3.14150030043151 CPU: 0.1
Calculation of more digits of PI
Vieta : 3.14159260737572 CPU: 0.01
Ramanujan:
3.1415926535897932384626433832795028841971693993751058209749445923078164\
0628620899862803482534211706798214808651372158654 CPU: 0.01
Lambert :
3.1415926535897932384626433832795028841971693993751058209749445923078164\
0628620899862803482534211706798214808651325682942 CPU: 0.0
BBP :
3.1415926535897932384626433832795028841971693993751058209749445923078164\
0628620899862803482534211706798214808651326929119 CPU: 0.0
SAGE : 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651328230665
Calculation of 4 digits of PI
Wallis 1 : 3.14150000993513 CPU: 0.16
Wallis 2 : 3.14150000993513 CPU: 0.02
Euler : 3.14150000806581 CPU: 0.53
Leibniz : 3.14150030043151 CPU: 0.1
Calculation of more digits of PI
Vieta : 3.14159260737572 CPU: 0.01
Ramanujan: 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651372158654 CPU: 0.01
Lambert : 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651325682942 CPU: 0.0
BBP : 3.14159265358979323846264338327950288419716939937510582097494459230781640628620899862803482534211706798214808651326929119 CPU: 0.0
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