(*^

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Karl.ma
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$Version 
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Timing[N[Sin[1/2],2500]][[1]]
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Timing[N[Pi,10001]][[1]]  
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Timing[10001!][[1]]
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 First[Timing[Eigenvalues[Table[Random[],{200},{200}]]]] 
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f[x_]:= 4x-4x^2;
Timing[ Nest[f,0.6,5000]][[1]]
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f[x_]:= BesselJ[0,x];
Timing[Nest[f,0.6,2500]][[1]]
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kdv[q_]:=  D[q,t] - 1/4 D[q,{x,3}]-3/2 q D[q,x]
q3:= (-5*E^((11*t)/8)-45*E^(2*x)-18*E^((11*t)/16+x) +
     162*E^((3*t)/2+2*x)-188*E^((13*t)/16+3*x)+
     162*E^(t/8 + 4*x) - 45*E^((13*t)/8 + 4*x) -
     18*E^((15*t)/16 + 5*x) - 5*E^(t/4 + 6*x))/
     (8*(-E^((11*t)/16)+3*E^x-3*E^((13*t)/16+2*x) +
      E^(t/8 + 3*x))^2)
Timing[Simplify[kdv[q3]]]
^*)