For questions on the use of machine-precision real numbers (also known as floats), the numbers that can be directly manipulated through the underlying numerical capabilities of your computer system.

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31
votes
2answers
2k views

Meaning of backtick in floating-point literal

If I compute, say, 1/3//N, Mathematica displays 0.333333 as the result. When I copy that output to use elsewhere, the paste ...
27
votes
1answer
681 views

Is there a difference between Divide[a,b] and a/b?

In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ...
21
votes
7answers
789 views

Elegant high precision `log1p`?

Sometimes it is hard to understand how numerical expressions are evaluated. I remember reading claims by Wolfram on how smart the Kernel is to evaluate expressions trees numerically by recognizing ...
19
votes
2answers
613 views

Different floating-point numbers equal?

Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *) Let's make sure they're different with ...
18
votes
1answer
902 views

Quadruple-precision (128 bit) arithmetic

Is it possible to force Mathematica to perform computations with hardware supported quadruple-precision? The following test suggest, that all of the computations with fixed precision, different than <...
15
votes
4answers
2k views

Numerical underflow for a scaled error function

I calculate scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
15
votes
2answers
205 views

CompiledFunction returns machine numbers smaller than $MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
14
votes
4answers
298 views

Does Mathematica have an equivalent of C's nextafter?

In C (and many other programming languages), there is a function double nextafter(double x, double y) which takes two (IEEE 754) floating-point numbers and ...
11
votes
2answers
572 views
11
votes
1answer
115 views

Abnormal behavior of RealDigits[x]

In the Details of the document of RealDigits writes the following line: RealDigits[x] normally returns a list of digits of ...
10
votes
2answers
477 views

Does Mathematica have an equivalent of Python's float.as_integer_ratio?

The Python programming language has a float.as_integer_ratio(x) function which exactly converts an IEEE 754 floating-point number into a numerator/denominator pair ...
10
votes
1answer
265 views

Plot of $\sin(x^x)$ is missing from $x=143$

When plotting the graph of $\sin(x^x)$ I noticed that there is no plot from about $x=143$. I don't suppose there is a purely mathematical explanation for this? So, why is there no graph in ...
10
votes
2answers
747 views

Why is Mathematica destroying this graph?

Here I have a picture of a function I graphed: reg[x_,y_]:=(x^2+y^2)Cos[4ArcTan[y/x]]; Plot3D[reg[x,y],{x,-2,2},{y,-2,2},AxesLabel->Automatic] And here is ...
10
votes
1answer
196 views

Compilation of Total with compensated summation

I sometimes obtain an unexpected error when trying to call a compiled version of Total with compensated summation turned on. More specifically I define ...
10
votes
3answers
738 views

Mathematica Plot: Inconsistency when plotting large values

I am working with a function in Mathematica and I am getting some inconsistencies when I plot it. As I really need to understand were this comes from I would appreciate any help. I am working with a ...
9
votes
2answers
457 views

DeleteDuplicates[] does not work as expected on floating point values

Here is my simple example, and in this case function DeleteDuplicates does not work as expected. I want to FindRoot of my ...
8
votes
3answers
430 views
8
votes
2answers
459 views

Precision differences

I run this sum and get the symbolic answer below : Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}] $2 - \frac{\pi^2}{6}$ I look up the sequence on OEIS and ...
8
votes
1answer
116 views

Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
7
votes
2answers
382 views

Dealing with numbers too large for machine precision in Graphics

Graphics only supports machine precision numbers (i.e. number that can be converted to machine precision). Take for example ...
7
votes
1answer
143 views

Using Differences on data: trouble with floats and doubles

Consider the following data set (after I have run FullForm), which is imported from a file (stored typically as 10.040): ...
6
votes
4answers
1k views

Mathematica Precision

How can I set the output precision of the following statement to 10 decimal places? I was looking through the documentation, and for some reason, all I could find was ...
6
votes
1answer
262 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
6
votes
1answer
123 views

Issues with $MachineEpsilon

I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ...
6
votes
1answer
115 views

Machine precision infinity

Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
6
votes
1answer
153 views

Bug in ListPlot?

I want to check if this is a bug before I email WR about it. I can't get ListPlot[] to make scatter plots over a very small area: ...
5
votes
6answers
2k views

Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do?

The Mandelbrot set is defined by complex numbers such as $z=z^2+c$ where $z_0=0$ for the initial point and $c\in\mathbb C$. The numbers grow very fast in the iteration. ...
5
votes
1answer
1k views

Infinite expression 1/0. encountered - caused by precision?

Planck's law dependent on frequency rho is as follows: B[T_, h_, rho_, k_, c_] := (2 h rho^3)/c^2 1/(Exp[h rho/(T k)] - 1) As you can see, the denominator can ...
5
votes
1answer
85 views

Can Someone Please Explain Internal`$SameQTolerance?

If I input Internal`$SameQTolerance (* output = 0.30103 *) which is the approximation of Log[10,2], or ...
5
votes
1answer
373 views

Accurately evaluating the hypergeometric function

As part of another problem, I am working to evaluate hypergeometric functions such as Hypergeometric2F1[1, 1, n, -1] for large $n$. I am hoping to obtain at ...
5
votes
1answer
108 views

Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
5
votes
1answer
101 views

How can I make 1+$MachineEpsilon not look like 1?

I undarstand that 1+$MachineEpsilon is actually not equal 1. However, it persists to look like it was equal ...
5
votes
0answers
52 views

Can I force Mathematica to use machine precision? [duplicate]

Some built-in functions (like Exp) give an arbitrary precision result, even when the argument is a machine precision number. Example: ...
4
votes
2answers
354 views

How to make the computer consider two numbers equal up to a certain precision

My problem is that I have a matrix A and the computer says is not Hermitian (self-adjoint). Then I check which elements make A ...
4
votes
1answer
354 views

How to calculate accurate answer in Mathematica?

I accidentally discovered for myself, that Mathematica outputs inaccurate answer. For instance, if I take $\sin(2 \cdot \pi \cdot 0.5) = 0 $, then in Mathematica it is: But if I calculate it on ...
4
votes
2answers
289 views

Floating point addition not associative

Can anybody explain the following behavior? x = 0.2 + (0.3 + 0.1); y = (0.2 + 0.3) + 0.1; x == y (* -> True *) But actually the variables do not exactly ...
4
votes
1answer
63 views

A simple syntax does not work

The code below does not work. Can anyone tell me why? Thanks! ...
4
votes
2answers
1k views

Precision of number not maintained when saved via Export

Assume that the output of my calculation is a and is a number such as: a = 100.1252135246354847; ...
3
votes
1answer
217 views

Why to do parentheses change the results of a calculation?

I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 <...
3
votes
1answer
142 views

Machine-Precision and Arbitrary Precision [closed]

What is meant by a machine number in the Mathematica documentation? What is the difference between machine-precision and fixed-point precision? What is arbitrary precision?
3
votes
1answer
459 views

Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
3
votes
1answer
51 views

My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
3
votes
1answer
64 views

ConvexHullMesh fails with small numbers

When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors: ...
3
votes
2answers
152 views

Machine precision near zero: not fulfilled?

I am puzzled by the behavior of Mathematica machine precision with numbers approaching zero. This manifests itself, e.g., with FixedPoint and the like. In the examples below I will use the following "...
3
votes
2answers
69 views

Make mathematica “forget” numbers beyond the precision goal

I need Mathematica to remember only things upto two decimal places. I'm currently using the unwieldy Floor[x*100]/100 which works but is there a better way to ...
3
votes
2answers
162 views

WorkingPrecision causes issue in the NIntegrate

I really can't figure out why my code sometimes is not working. My integrals involve two variables (k and kz). The integration ...
3
votes
1answer
60 views

MachinePrecision versus $MachinePrecision in NDSolve

I'd like to understand why one of these inputs gives me an error and the other doesn't: ...
3
votes
0answers
101 views

Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
2
votes
2answers
159 views

Long run time for older code that ran fast in older versions

The following code block is in Trott's Guidebook for Programming. The associated notebook says that this and a few other routines ran in a matter of seconds. I killed it after half an hour. I am ...
2
votes
4answers
183 views

Precision problem with numerical solution of a differential equation

I want solve $$ 2\sqrt{|\gamma|}x = \int_{1}^{t} dy \sqrt{\frac{1+2|\gamma_2|y}{y^2(1-y)}} $$ where $0<t\leq $1. I'm using a for cycle to evaluate t, calculate the integral and the assign the $x$. ...