In[95]:= $Version Out[95]= "12.0.0 for Mac OS X x86 (64-bit) (February 25, 2019)" In[76]:= InverseFunction@InverseFunction // FunctionExpand Out[76]= InverseFunction[InverseFunction] Shouldn't this just be Identity? E.g., In[81]:= InverseFunction@InverseFunction@Tan Out[81]= Tan But In[82]:= (InverseFunction@InverseFunction)@Tan Out[82]= InverseFunction[InverseFunction][Tan] (Hang onto your hat:) In[83]:= %[\[Pi]/4] Out[83]= -2 (24 \[Pi] + ArcTan[4/\[Pi] + Sqrt[16 + \[Pi]^2]/\[Pi]]) !!! AKA (ries) Out[90]= -49 \[Pi] + ArcCos[4/Sqrt[16 + \[Pi]^2]] In[91]:= FullSimplify[% - %83] Out[91]= -(\[Pi]/2) - ArcTan[4/\[Pi]] + 2 ArcTan[(4 + Sqrt[16 + \[Pi]^2])/\[Pi]] Another bug! In[92]:= Sign@% During evaluation of In[92]:= N::meprec: Internal precision limit $MaxExtraPrecision = 50.` reached while evaluating -(\[Pi]/2)-ArcTan[4/\[Pi]]+2 ArcTan[(4+Sqrt[16+Power[<<2>>]])/\[Pi]]. Out[92]= Sign[-(\[Pi]/2) - ArcTan[4/\[Pi]] + 2 ArcTan[(4 + Sqrt[16 + \[Pi]^2])/\[Pi]]] —Bill