Re: A Problem with Simplify

*To*: mathgroup at smc.vnet.net*Subject*: [mg87513] Re: A Problem with Simplify*From*: Alexey Popkov <popkov at gmail.com>*Date*: Sat, 12 Apr 2008 06:56:28 -0400 (EDT)*References*: <ftkb7f$a9m$1@smc.vnet.net> <200804110542.BAA04641@smc.vnet.net>

On 11 =C1=D0=D2, 14:00, Andrzej Kozlowski <a... at mimuw.edu.pl> wrote: > On 11 Apr 2008, at 14:42, Alexey Popkov wrote: > > > Recently I also have found another strange bug in Simplfy (not so > > dangerous): > > FullSimplify[Sin[x]*Cos[x]] > > gives Sin[x]*Cos[x] instead Sin[2*x]/2. The workaround is > > FullSimplify[2*Sin[x]*Cos[x]]/2 > > This is not a bug! > > In[7]:= LeafCount[Sin[x]*Cos[x]] > Out[7]= 5 > > In[8]:= LeafCount[Sin[2*x]/2] > Out[8]= 8 > > In other words, Sin[x] Cos[x] is considered simpler by Simplify than =9A > Sin[2*x]/2, that's all. Indeed: > > In[9]:= Simplify[Sin[2*x]/2] > Out[9]= Cos[x]*Sin[x] > > If you want Simplify to return Sin[2*x]/2 use a different complexity =9A > functions: > > =9A Simplify[Sin[x]*Cos[x], ComplexityFunction -> > =9A =9A =9A (LeafCount[#1] + 10*Count[#1, _Cos, > =9A =9A =9A =9A =9A =9A =9A =9AInfinity] & )] > =9A (1/2)*Sin[2*x] This is very useful example for me. Thank you. Now it is clear.

**References**:**Re: A Problem with Simplify***From:*Alexey Popkov <popkov@gmail.com>