# 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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### Small positive machine number calculation in Mathematica 11.3

In Mathematica version < 11.3, any positive Machine‐Precision Numbers exceeding the range [$MinMachineNumber,$MaxMachineNumber...
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126 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 ...
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144 views

### Is it possible to get the original number from DecimalForm?

Bug introduced in 5.2 or earlier and persisting through 12.2 [CASE:4315787] Wrong behavior of NumberForm (DecimalForm outputs ...
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227 views

### Classification problem using SVM methods

I am running SVM on mathematica and I a used this code with classes: ...
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49 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 ...
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155 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 ...
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2k views

### Set Global Maximum Precision

I'm sure this has been asked before, but I've looked around and can't figure it out: How do I set a global maximum precision for a notebook (or in general, globally)? I have a large notebook in ...
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204 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 ...
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52 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 ...
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55 views

### 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 ...
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37 views

### 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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170 views

### Machine Learning Predict Precision

I have this code p = Predict[{1 -> 123456789123456789, 3 -> 987654321987654321}] values are big, more than 15 digits (standard machine precision). when I ...
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224 views

### Printing Precision of Machine Numbers

Is Mathematica making the print precision rounding judgment more stringent based on whether or not the number is above or below the rounding target? If so, why? In my real case, I have many numbers ...
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236 views

### Treating a bad conditioned covariance matrix

I am trying to detect outliers in a big dataset using the Mahalanobys distance method. To calculate the Mahalanobys distance for a given vector $x$ from a mean vector $\mu$ you have to compute the ...
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65 views

### Which operations preserve digit precision?

Imagine I had to use numbers with a 600 precision digits. Do all mathematical operations, like +,-,...
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33 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 ...
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30 views

### How to avoid machine underflow for plotting and integrating?

I am trying to integrate the following integrand, which I have plotted: ...
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### 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: ...
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38 views

### Inconsistent and oscillatory behavior with formula

I have the following code ...
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66 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 ...
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### 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 ...
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57 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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178 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 ...
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87 views

### Getting max precision limit overflow for a very simple calculation

I've never seen this error on such a simple calculation. Does anybody know how to fix this annoying error?
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60 views

### ListLinePlot gives the correct values but N doesn't

I have solved a set of 6 differential equations with DSolve. When I use the table command and produce the results of one of the equations given by DSolve, the ListLinePlot command gives me the correct ...
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42 views

### Unpredictable behavior of numerical error

A comparison of float calculation and exact expression for NumberForm[0.3^2 - (3/10)^2, 18] gives an exact zero for $0.3$. However, ...