ArcCoth[x] + ArcSinh[y] == ArcCoth[(I (-1)^Floor[1/2 - Arg[(I y + (I Sqrt[y^2 + 1])/x)/Sqrt[1 - 1/x^2]]/ Pi] (y/x + Sqrt[y^2 + 1]))/(Sqrt[1 - 1/x^2] Sqrt[1 - (y/x + Sqrt[y^2 + 1])^2/(1 - 1/x^2)])] - (1/2) Pi I ((-1)^(Floor[1/2 - Arg[(I y + (I Sqrt[y^2 + 1])/x)/Sqrt[1 - 1/x^2]]/Pi] + Floor[1/2 - Arg[1 - 1/x^2]/(2 Pi) + Arg[-(y/x) - Sqrt[1 + y^2]]/Pi]) + 2 (1 + (-1)^Floor[1/2 - Arg[(I y + (I Sqrt[y^2 + 1])/x)/Sqrt[1 - 1/x^2]]/ Pi]) Floor[(Arg[(I - I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[y^2 + 1] - y])/(2 Pi)] + (-1)^Floor[1/2 - Arg[(I y + (I Sqrt[y^2 + 1])/x)/Sqrt[1 - 1/x^2]]/Pi] - 2 (-1 + (-1)^Floor[1/2 - Arg[(I y + (I Sqrt[y^2 + 1])/x)/Sqrt[1 - 1/x^2]]/ Pi]) Floor[1/2 - (Arg[(I - I/x)/Sqrt[1 - 1/x^2]] + Arg[Sqrt[y^2 + 1] - y])/(2 Pi)])

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