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agm:=proc(n)
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local a:=1,g:=evalf(sqrt(1/2)),s:=0,p:=4,i;
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for i to n do
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a,g:=(a+g)/2,sqrt(a*g);
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s+=p*(a*a-g*g);
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p+=p
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od;
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4*a*a/(1-s)
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end:
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Digits:=100000:
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d:=agm(16)-evalf(Pi):
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evalf[10](d);
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# 4.280696926e-89415
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