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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10
votes
2answers
207 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 ...
3
votes
0answers
74 views
1
vote
1answer
59 views

Wrong Limit[…] for inexact expressions

I noticed that Limit can return nonsense when using inexact parameters. In the following code, a is my (exact/inexact) ...
6
votes
1answer
148 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
1answer
93 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
96 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 ...
0
votes
0answers
34 views

Handling a matrix with components greater than machine precision

I have four quantities stemming from a 4th order differential equation. I can represent these as a vector which is a product of a 4X4 matrix $$ M=\left\{v,\frac{\partial v}{\partial x},\frac{\partial ...
8
votes
1answer
104 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 ...
3
votes
2answers
65 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 ...
1
vote
1answer
88 views

How to increase the precision to get the correct roots at the boundaries?

I want to solve an equation and Plot a graph of $\delta(\tau)$, where $0<\tau,\delta<1$. In principal $\delta(0)=1,\delta(1)=0$. However, when I solve the equation, the points near $\tau=1$ ...
15
votes
2answers
199 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 ...
1
vote
2answers
61 views

Export numeric data with preset decimal places

I have a table of pairs of numbers, each with 300 decimal places, which are all important. If saved using Export["data.dat", data] and then imported back via Import["data.dat"] - then the 300 decimal ...
0
votes
1answer
54 views

N, machine precision and expression evaluation [closed]

I should state that I am a Mathematica beginner but I checked the questions about machine vs arbitrary precision (such as: this one ) and I continue to have the following issue while trying to ...
3
votes
2answers
137 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 ...
10
votes
1answer
173 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 ...
1
vote
0answers
59 views

Odd plotting/math issue (could be a precision problem)

I've got a pretty odd error on a project I'm working on and was hoping to enlist some advice to fix it. The goal of this notebook is to show that I can eliminate the non-normalizable (blowing up part) ...
0
votes
2answers
74 views

Varying results from the Round function

My problem is simple. Consider the following. ...
11
votes
2answers
256 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 ...
3
votes
2answers
154 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 ...
21
votes
7answers
717 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 ...
1
vote
0answers
68 views

Floor inconsistent with Less for machine-precision approximate numbers

For machine-precision numbers, Mathematica uses a tolerance for comparisons, so that 1.-$MachineEpsilon==1. However, Floor does ...
5
votes
1answer
74 views

Can Someone Please Explain Internal`$SameQTolerance?

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

Precision of LinearModelFit with Polynomials

I have a Problem regarding the fit of given points with a polynomial up to the fifth degree. tableofvalues=Import["tableofvalues.csv"] My polynomial is: ...
3
votes
2answers
298 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 ...
10
votes
2answers
455 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 ...
18
votes
2answers
572 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 ...
1
vote
1answer
142 views

Why does it matter at what point I replace?

I need to find four orthogonal linear combinations of complicated functions, that vanish at four different points. I use (LK4 is defined below, but its shape should have nothing to do with my ...
0
votes
1answer
92 views

Floating point arithmetic bug caused by Table[]

I was doing something fairly ordinary and noticed something I can't, for the life of me, explain. For context, I wanted to take make a function that takes an array of data like the one below, then an ...
2
votes
0answers
63 views

Enforcing WorkingPrecision in NIntegrate

I have a very complicated 2D integral that I need to calculate repeatedly, and I'm trying to speed it up a bit, since at the moment it's taking a couple of days to complete. One thing I've noticed is ...
2
votes
2answers
335 views

NIntegrate 2D highly oscillatory function

I am trying to integrate a function, and the error I get is greater than the result. So I need to calculate ...
0
votes
0answers
26 views

why i cannot get appropriate number with my custom precision? [duplicate]

why i cannot get appropriate number with my custom precision? In[25]:= N[(1 + Exp[-30])/(1 + Exp[-29.9]), 1000] Out[25]= 1. I expect to see a few digits after ...
6
votes
1answer
105 views

Machine precision infinity

Is it possible to obtain the machine precision (double) version of Infinity? This is useful when using LibraryLink and C ...
5
votes
0answers
44 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: ...
1
vote
0answers
45 views

Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
2
votes
1answer
222 views
2
votes
4answers
173 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 $x$. ...
4
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. ...
1
vote
1answer
195 views

How to increase significant digits in Mathematica

How can I increase the number of significant digits in Mathematica? When I import a matrix, an element like 112.5276 is rounded to 112.528. I would like to increase the number of significant digits ...
1
vote
2answers
85 views

Decimal output from a simple equation

Let x= 0.0000000000000000036; y = 1 - x If i type this in Mathematica the answer of y is 1. I want the answer to be as it ...
2
votes
1answer
90 views

How to map HoldForm?

I'm trying to compare between Sqrt[3.] and Sqrt[3]. To display the result, I mapped HoldForm to display the expressions on the left hand column (code at end), but it seems like Sqrt[3.] had been ...
8
votes
1answer
108 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. ...
6
votes
1answer
223 views

Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
0
votes
1answer
59 views

Unexpected behavior of subtraction with approximate numbers [duplicate]

I'm using the Table command to generate a list of values: FullForm /@ Table[10. - x, {x, 2.7, 2.8, .1}] and I get the ...
28
votes
2answers
1k 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 ...
0
votes
1answer
377 views

How to get more accurate orthonormal eigenvectors?

I have a matrix M with real entries in MachinePrecision. I compute its eigenvectors and construct matrix ...
0
votes
2answers
139 views

The precision of the number

I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ...
4
votes
2answers
242 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 ...