Re: SetDelayed and Evaluate

*To*: mathgroup at smc.vnet.net*Subject*: [mg104487] Re: SetDelayed and Evaluate*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Sun, 1 Nov 2009 17:55:07 -0500 (EST)

On 11/1/09 at 4:02 AM, insomnia.berlin at gmail.com (Peter) wrote: >after years of experience with Mathematica I've got a simple (?) >problem: >When answering to a question on the student support forum (http:// >forums.wolfram.com/student-support/topics/21448/) I tried fo myself >the folowing variants: >f[z_?NumericQ]:=Compile[{{x,_Real}},x-x^2][z]; >g[z_?NumericQ]:=Evaluate[Compile[{{x,_Real}},x-x^2]][z]; >and got the following results: >In[6]:= Timing[Do[NMaximize[f[x],x],{1000}]] >Out[6]= {35.871,Null} >In[7]:= Timing[Do[NMaximize[g[x],x],{1000}]] >Out[7]= {35.962,Null} >~1 ms per NMaximize is OK, because there are background-processes >running. >But I expect f to compile x-x^2 at every call to f and g to compile >once on time of definition. Therefore I expected g to be >significantly faster than f. I don't understand why you expect different f and g to behave differently. In both cases you use SetDelayed. So, in both cases the stuff to the right gets evaluated on every call which includes the Evaluate statement. I would expect there to be additional overhead as a result of adding Evaluate to the definition of g. And while it is tempting to interpret your timing results as supporting my expectation, there is also the possibility the timing difference is simply due to measurement uncertainties. The difference looks too small to be certain it is significant. Also, if the goal is to improve execution speed note: In[3]:= f[z_?NumericQ] := Compile[{{x, _Real}}, x - x^2][z] In[4]:= Timing[Do[NMaximize[f[x], x], {100}]] Out[4]= {8.39542,Null} In[5]:= g[x_?NumericQ] := x - x^2 In[6]:= Timing[Do[NMaximize[g[x], x], {100}]] Out[6]= {5.5667,Null} In[7]:= h[x_] := x - x^2 In[8]:= Timing[Do[NMaximize[h[x], x], {100}]] Out[8]= {4.95141,Null} Not surprisingly, the less work you require the less time it takes. I don't see any obvious way to use Compile to improve execution speed here. If you use SetDelayed, the Compile operation is done on every call. If instead you define: y[x_] = Compile[{{x, _Real}}, x - x^2] and then try NMaximize you will get an error since y[x] is no longer an expression NMaximize can work with. =46inally, it is worth noting the timing difference between y[x] and h[x]: In[9]:= Timing[Total@Table[y[RandomReal[]], {1000000}]] Out[9]= {2.89152,166741.} In[10]:= Timing[Total@Table[h[RandomReal[]], {1000000}]] Out[10]= {2.48571,166678.} The compiled version actually seems a bit slower on my system. My experience with Mathematica is Compile is more trouble than it is worth and seldom provides significant improvement on well written Mathematica code.

**Re: Problem with Screen Environment**

**Re: Re: Dotted Plots**

**Re: SetDelayed and Evaluate**

**Re: How to calculate a union**