# Questions tagged [machine-precision]

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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### How to modify the given codes (NIntegrate of Boole) to get the most accurate result possible?

I have five conditions con1 to con5 over the two-dimensional domain $t,u\in[o,2\pi]$. I want to compute this area $(con1 \cap con2 )\cup(con3 \cap con4 \cap con5)$ numerically. I try the two codes ...
1 vote
50 views

### How to modify NIntegrate code below so that it gives the most accurate/reliable numerical result?

Imagine that I have two conditions con1 and con2 over the two-dimensional domain $x,y\in[-2,2]$. I want to compute the area of the union of these two conditions i.e. the region $(con1 )\cup(con2)$. I ...
343 views

### Table does not give expected result with 30 but right with 40

I want Mathematica to generate a table, but I am very confused by its behaviour. tab = Table[i, {i, 6.311, 6.312, 0.001}] Now I get the desired result, namely {6....
426 views

When I do: ...
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...
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### Is there any alternative for conditional plot that gives a more precise result in a shorter time?

I have the given function $Func$ and want to have a plot of those domains where $-3\leq Func\leq 3$ in precise details. I am using ...
1 vote
68 views

### How to handle "too small to represent as a normalized machine number" when plotting a figure [duplicate]

I am trying to plot a figure by the following codes: Plot[(27 2^((-2 + a)/(-1 + a)) 5^(a/(-1 + a)) 7^(1/(1 - a)) a^2)/((-1 + a) (4 + 9 a)), {a, 1.001, 3}] ...
1 vote
246 views

### How to prevent Mathematica from rounding some PDF values to 0?

Dear Mathematica community, I'm having a problem with the PDF function for the hypoexponential distribution. Specifically, Mathematica returns 0 as soon as the value is very small. Below is an example:...
69 views

### How to avoid General::munfl errors?

Let's have a look at a following system of equations: ...
158 views

### Floating point precision and speed [closed]

I am attempting to understand how to speed up the evaluation of numerical expression. Specifically, following the first point of this blog, Mathematica is much quicker dealing with floating-point ...
305 views

### IntegerPart - is this a known bug?

I'm working in Mathematica 13.0 and I type a=0.00001; IntegerPart[a/a] and well, the output is 0. Try with almost any other value of ...
152 views

### Adding numbers with defined precision produces incorrect result

I've tracked a bug in my code down to the problem of adding two numbers together, with the left argument having machine precision, e.g by 3 . The issue is, if ...
1 vote
54 views

### Issue with some floating-point errors and not others

Not looking for a solution necessarily, but just trying to understand why this issue occurrs. I have a 'Do' loop which iterates some algorithm over values of a parameter 'x' with range {x,0,1,0.1} and ...
152 views

### How to handle very numbers that are "too small to represent as a normalized machine number"?

I will preface this by saying that I am not very familiar with Mathematica whatsoever. That is why I am asking this here even though I have found a few forum posts that might provide the solution to ...
1k views

### Error "is too small to represent as a normalized machine number; precision \ may be lost " for small values in Plot

I'm trying to plot two curves but I'm having issues with the lower end of the range: ...
122 views

### Spurious poles in a gain plot (due to machine precision or complex numbers?)

I have the following plot that I like to make. It details the gain of an amplifier. ...
347 views

### Real number equality (==) not working: what's the least-overcomplicated solution?

I'm running a program that evaluates equalities after I substitute all symbols for numbers. The equalities on floats are giving me trouble. My program is reaching a point where something like the ...
140 views

### FixedPoint not working, despite quick convergence of sequence [closed]

Trying the computation below, with Mathematica 13.0.0, I am not getting a result returned. FixedPoint[Cos, 0.85] This appears in the 3rd edition of "...
1 vote
117 views

### Exponential fit precision lost

I have a data: ...
51 views

### How to set up precision by default?

I have a table computing many numbers with large precision. Because of this, probably, Mathematica consumes a lot of RAM. Is it possible to restrict the precision in any calculations by default (...
1 vote
45 views

### KernelMixtureDistribution error message about precision

I want to use KernelMixtureDistribution to deal with a large amount of data points. For example, the following codes shows how I use it: ...
42 views

### Why is the N function giving me the wrong result when using WolframScript? [duplicate]

I am using wolframscript.exe to learn mathematica and I would expect the following code to return 0.7071: ...
1 vote
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1 vote
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### How does WorkingPrecision in NDSolve handle MachinePrecision?

I'm wondering why the following code NDSolve[{y''[t] + y[t] == 0, y == 1., y' == 0}, y, {t, 0, 10}, WorkingPrecision -> 6] throws the error/warning, that ...
1 vote
43 views

### ContourPlot3D with small domain produces glitchy mess

I'm able to plot some graphs over small domains, but not others. For example, this works just fine: ...
171 views

### Simplify for precision

I have an a set of equations to solve — details irrelevant — the result of which will be converted into PostScript, a 1980s printer-control language the only floating precision of which is single. ...
39 views

### General::munfl - Precision lost in LinearModelFit

I am new to mathematica so I am confused regarding the loss of precision in LinearModelFit. In building a linear model with uora (1 or 2) and encodeSeverity (1,2 or 3) ...
220 views

### How to deal with too small numbers

When dealing with a code that produces too small numbers (in a complicated way) like 0.33691 4.015757066049965*10^-330 I get the following warning General::munfl: ...
50 views

### Solving a determinant to get non-zero roots in a heat transfer problem

I am trying to solve a mathematical model of a heat transfer problem. As an intermediate step there is a characteristic equation in the form of a determinant, which needs to be solved for variable <...
87 views

### How to change Machine Precision digits to meet the tolerances

I am trying to solve for Tcm and Mag by solving nonlinear equations using FindRoot command using following code: ...
1 vote
46 views

### Are pixels machine numbers? [closed]

Mathematica allows one to work with the information that is behind a photo. For example, the command ImageData generates a list containing the “pixels” (which will it be a number from $0$ to $1$ if no ...
67 views

### Problem with the Rank of a matrix after a FindRoot

I am solving a boundary problem defined by a set of four-component vectorial functions. Without going into many details, I have two functions on the left and two on the right of an interface. The ...
1 vote
85 views

### How to increase the value of MinMachineNumber to avoid overflow error?

I have a complicated function called f2[re] ...
83 views

### How to copy and paste numbers with "" mark and use them in calculations, without using N or setting precision every time

Suppose we have run a calculation and get a number like 2.758952615889003 If we then copy-paste this number and do a calculation like ...
106 views

### Generalizing technique to handle General::munfl error?

In contrast to earlier versions of Mathematica, in versions 11.3 and later Mathematica no longer switches to arbitrary precision when it detects a MachineNumber underflow. While this behavior is ...
87 views

### Too small to represent and Chop in inaccessible algorithm

Overview I want to apply a specified Chop function to every step in an function call in Mathematica (in my case LegendreP), ...
27 views

### Different sensitivies from LinearSolve and Eigenvalues. How to conciliate them?

I use the following functions to receive a matrix, and make it symmetric positive definite: ...
1k views

### General:: Exp[-717.401] is too small to represent as a normalized machine number; precision may be lost

I am solving pde. For the post processing bvp, there is solution given in output which is the solution from mathematica version 10.0.1. Output from above in mathematica 10.0.1 is, But when the similar ...
55 views

### Avoid MachinePrecision numbers in Message

Can I change the output of Message to not show MachinePrecision numbers? E.g. ...
1 vote
198 views

### Can I change the default behavior so that "0.1" is interpreted as "1/10" automatically?

Consider the function f[a_] := NIntegrate[Sqrt[a + Log[x]], {x, 1, 10}, WorkingPrecision -> 30]. With this definition, I cannot call ...
1 vote
108 views

### Machine-precision numbers cause loss of precision

I am trying to use the Mod function as follows. Table[ Nest[Mod[2 #, 1] &, FractionalPart[Pi], n], {n, 100}] // N ...
679 views

### How can I compute Erf of large numbers to more precision?

I would like to compute Erf[80/3] to enough precision to know the order of magnitude of 1 - Erf[80/3] How can I do that? I ...
153 views

### Why does precision decrease after increasing PrecisionGoal and WorkingPrecision on this integral?

I am trying to calculate a messy double-integral to many digits of precision. As shown below, the precision seems to increase reliably as WorkingPrecision goes from ...
227 views

### How to improve working precision?

I'm trying to fit the array data as follow: NonlinearModelFit[ data, s*t^r + (A/(w*(Pi/2)^0.5))*Exp[-2*((t - u)/w)^2], {s, r, A, w, u}, t]; But when ...
1 vote
68 views

### How to get the output for the following code involving differentiation and integration?

I need to evaluate the following Mathematica code to get a numerical value as my output. But during compilation I get the error message NumericalMathFixedPrecisionEvaluate::precbd: Requested ...