If seems to be faster than Piecewise for this specific example, but defining a separate downvalue is even faster, especially when you might be able to use a literal zero rather than PossibleZeroQ. Here are some example evaluations and timings:
In[25]:= numCalls = 10^4;
numTrials = 10;
ClearAll[myfunc1, myfunc2, myfunc3, myfunc4, myfunc5];
(* Piecewise approach *)
myfunc1[x_] := Piecewise[{{0, x == 0}}, (1 - Exp[-x^2])/x];
(* If approach *)
myfunc2[x_] := If[x == 0, 0, (1 - Exp[-x^2])/x];
(* "Separate downvalue" approach, testing for zero *)
myfunc3[_?PossibleZeroQ] = 0;
myfunc3[x_] := (1 - Exp[-x^2])/x;
(* "Separate downvalue" approach, assuming literal zero (exact or approximate) *)
myfunc4[0 | 0.] = 0;
myfunc4[x_] := (1 - Exp[-x^2])/x;
(* "Separate downvalue" approach, assuming only exact zero *)
myfunc5[0] = 0;
myfunc5[x_] := (1 - Exp[-x^2])/x;
timings =
Mean /@
Table[
First@
AbsoluteTiming@
Do[
myfunc[0],
{numCalls}]/numCalls,
{myfunc, {myfunc1, myfunc2, myfunc3, myfunc4, myfunc5}},
{numTrials}]
Out[36]= {2.6400*10^-6, 2.3000*10^-6, 2.0100*10^-6, 4.700*10^-7, 2.900*10^-7}
Hope this helps!
