June 2018 Update
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agm(A,G,A) :- abs(A-G) < 1.0e-15, !.
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agm(A,G,Res) :- A1 is (A+G)/2.0, G1 is sqrt(A*G),!, agm(A1,G1,Res).
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?- agm(1,1/sqrt(2),Res).
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Res = 0.8472130847939792.
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