# 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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### 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 ...
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### 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 ...
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### 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 ...
533 views

### Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
61 views

### Understanding Working Precision - two example equations

I am trying to understand how WorkingPrecision works, and in general how very small/large numbers are to be handled. Let me preface I probably do not have ...
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### Conflicting output provided by N[…]

I am trying to evaluate an expression : (-((I (k2 - k1) (-1 + E^(2 I (k2 - k1) \[Pi])))/(-1 + (k2 - k1)^2))) /. {k1 -> 2, k2 -> 7} This gives ...
39 views

### Dealing with General::munfl errors

Edit: So, while trying to figure out a minimal exmaple, I found out that my main problem was actually unrelated to this and it just happened to be that giant pile of warnings and error messages coming ...
180 views

### How can I suppress the warning “precision may be lost”?

When I import data from a .dat file, V11.3 emits the message: is too small to represent as a normalized machine number; precision may be lost. How can I close the ...
81 views

### Equality for floats

Suppose I have two floats (e.g. {x,y} = RandomReal[{0,1},2]). Might there be a situation where all three comparisons evaluate to ...
46 views

### Numerical precision - simulating an unstable equilibrium

I was playing around with NDSolve and the following ODE s = NDSolve[{y''[x] == -Sin[y[x]], y == \[Pi], y' == 0 }, y, {x, 0, 120}] The equation and the ...
90 views

### DeleteCases with a case as float?

Might the DeleteCases have issues in matching when the list is of floats (machine precision numbers)? E.g. in this code it might fail to match correctly because ...
86 views

### Number definition and approximation

I run these lines: a = 0.833 SetPrecision[a, 20] and this is the output: 0.833 0.83299999999999996270 I expected to ...
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### Set Underflow precision in Mathematica 12 same as version 11.x [duplicate]

It seems like Mathematica version 12 sets arbitrary underflow precision depending on the function, but I would like the underflow precision to be same as what was for previous version of Mathematica ...
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### FindRoot giving error in Mathematica version 12

I was using the same code in previous version of Mathematica but unfortunately I had to update Mathematica to version 12 because I upgraded MacOS to Catalina. Now when I run my code, I get this error ...
121 views

### How does Mathematica evaluate N[π, 30] == π?

I want to know how N[π, 30] == π works. The result is True. I wonder whether the exact number ...
307 views

### How to detect underflow/overflow (post 11.3)?

This old trick used to work before 11.3: SetSystemOptions["CheckMachineUnderflow" -> True] But no longer... so how can we explicitly check for this in v12+?? ...
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### Changing machine precision notebook-wide leads to peculiarities

For a project of mine it is preferrable to set notebook precision globally. I have done so by using the answer in Global precision setting. The idea is to dynamically create a ...
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### Allow Mathematica to solve the differential equations with larger than 16 digits parameters

Consider the system of differential equations ...
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### Why is Mathematica's default precision only 16 digits? [closed]

I was performing some basic computations when I noticed that NumberForm[N[Zeta], {100, 100}] yields ...
712 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 ...
60 views

### why some parts of my curve are removed or wiped

When I try to draw the next code I get a curve with missing parts, as shown in the picture. I do not know if it is an precision problem in the Mathematica program or is some data not calculated. Or is ...
55 views

### Preventing Mathematica from considering small values to be equal to zero [duplicate]

In my calculations I have a variable (say z) which can be an argument of Log, say, z Log[z]. ...
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### Why this very simple problem turns to “Indeterminate”?

Why the following calculation gives Indeterminate value? ...
50 views

### How to resolve underflow occurrences?

I am solving a second order differential equation described by odey below. For the asymptotics, I have the following code which will be used as initial conditions for NDSolve. ...
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### Truncate a number in mathematica

I want to truncate a simple number to n decimal digits. For example, 2/3. I used f[x_, n_] := N[IntegerPart[x 10^n]/10^n] but I get ...
56 views

### How to get the correct result in a simple operation in Mathematica

I have the following values for x[[i]], y[[i]] and A[[i,j]]: ...
143 views

### What's the smallest positive real allowed in mathematica?

This question may be a bit strange, but in this question, one of the answers suggests substituting some negatives values in a matrix by the smallest positive real number allowed. So, I was wondering ...
147 views

### Plot a function with very small values, close to zero

I want to plot a function with very small values, close to zero, but even though the limit is -3/2 as x->0, I can't get any ...
48 views

### Simple division with high precision in Mathematica [closed]

I want to do a simple division i.e. 0.70524/0.51824 . What I want is to find the result of the roundation of this division for precision from 1 to 19 decimal digits....