# inverse function – InverseFunction: Precision problem

I define a function SS(t) as an inverse function:

``````tt(S_) := 10(2Sqrt((1-S)S) +14/5 ArcTan(Sqrt(S), Sqrt(1-S)) +
2/5 ArcTanh(1/2 Sqrt((1-S)/S)));
SS = InverseFunction(tt);
N(SS(53), 60)
(* 0.200580902656825260833989366151287711207279221292307930697890 *)
``````

SS(t) works great up to t=53: it’s fast, I get a precision of 60, and I can plug it back into the original (forward) function.

PROBLEM:

Starting at t=54, it’s very slow, and the output is way wrong, complex and wrong magnitude. (It should be real and in (0.2, 0.2006)).

STUFF I TRIED:

• The forward function works well for inputs S=0.2+$$epsilon$$ ($$epsilon$$ very small, like $$10^{-10}$$), giving tt($$cdot$$) up to 80, no problem.

• \$MinPrecision=0, \$MaxPrecision=$$infty$$ (defaults).

• Increasing N($$cdot$$,60) to N($$cdot$$,100) makes no difference.

I use Mathematica 8.0.4 on MacOS, installed… 5 years ago?