Mathematica Stack Exchange is a question and answer site for users of Mathematica. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

There are multiple ways to convert an expression to machine precision, for example:

In[1]:= a = Sqrt[2]
Out[1]= Sqrt[2]

In[2]:= {1.a, 1`a, N@a, SetPrecision[a,MachinePrecision]}
Out[2]= {1.41421,1.41421,1.41421,1.41421}

In[3]:= Precision /@ %
Out[3]= {MachinePrecision,MachinePrecision,MachinePrecision,MachinePrecision}

My question is whether or not these methods are absolutely equivalent. Is it just a matter of personal taste which one to use, or are there examples where they behave differently?

share|improve this question
You can also use Developer`ToPackedArray[{1, Sqrt[2], 3, 4}, Real] to create machine precision numbers. – user21 Jun 28 '12 at 17:35
up vote 11 down vote accepted

In terms of speed N and SetPrecision can be expected to be faster as they do not involve an unnecessary multiplication. (Conversely 2` * a would be better than N[2 * a] because the latter does exact multiplication before the conversion.)

1. a and 1` a can be considered identical because they represent the same input. Personally I have taken to using the latter form for entering machine-precision integers because the syntax better reminds me of the purpose.

One can see that N and SetPrecision[#, MachinePrecision] & are, if not equivalent, closely related. Observe:

N[thing] := 17.5

{HoldPattern[N[thing, {MachinePrecision, MachinePrecision}]] :> 17.5}



SetPrecision[thing, MachinePrecision]


The fact that NValues output is given from SetPrecision indicates to me that it is using a common mechanism.

On-the-fly conversion does not use NValues:

1. thing

2` + thing
1. thing

2. + thing

Here is another demonstrable difference between N/SetPrecision and multiplication by 1.:

N[ Exp[1000] ]                            // Precision

SetPrecision[Exp[1000], MachinePrecision] // Precision

1. Exp[1000]                              // Precision


share|improve this answer
N also does some caching or am I mistaken? – Ajasja Jun 28 '12 at 11:10
@Ajasja I don't know, but I'll see what I can find. – Mr.Wizard Jun 28 '12 at 11:18
Here is the relevant example – Ajasja Jun 28 '12 at 12:34
@Ajasja that kind of caching is not specific to N. Try: 1`1000000 Pi; // Timing twice. – Mr.Wizard Jun 28 '12 at 12:52
@Mr.Wizard, thanks. I like the idea of using the backtick form as a reminder of the purpose. I think it looks a bit neater than 1. too (I always want to add a zero after the decimal point even though I know it isn't necessary) – Simon Woods Jul 1 '12 at 21:29

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.