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

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