# 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 N not upgrade precision? [duplicate]

Precision[N[1.0, 20]] Precision[N[1, 20]] MachinePrecision 20. It would be so much more intuitive and less error prone, if <...
249 views

### Plot3D discrepancy between MMA 10 and 11.3 - possible small numbers issue

I'm having some troubles with the following code I wrote in MMA 10 some time ago: ...
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### Machine Epsilon is not equal to $MachineEpsilon [duplicate] I try to wrap my head around machine precision calculations in Mathematica (11.2, Linux). I do not understand the following behavior: ... 0 votes 2 answers 77 views ### NIntegrate numerical accuracy and errors I have the following 3x3 matrix M = {{-I*ω + Γ/2, I*g1, 0}, {I*g1, -I*ω + κ1/2, I*g2}, {0, I*g2, -I*ω + κ2/2}}; Finding the eigenvalues and eigenvectors ... 1 vote 1 answer 164 views ### Performance Tuning - How can I make Mathematica to use less than certain digits number? I would like to know if there is a way to make Mathematica to use at most certain digit number. For example, Suppose I want to calculate 2*Pi. x=N[Pi] y=2*x ... 0 votes 0 answers 104 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? 5 votes 1 answer 78 views ### Precision-related error in Audio Bug introduced in 11.3 or earlier CASE:4075745 I have been experimenting with using Audio and associated functions for data acquisition using an external sound ... 4 votes 1 answer 155 views ### The algorithm behind InputForm for machine numbers There are several questions on this site about implementing fast CSV/TSV export for machine numbers without loss of precision. Recently I discovered that Export ... 4 votes 0 answers 176 views ### Is it possible to get the original number from DecimalForm? Bug introduced in 5.2 or earlier and persisting through 13.1.0 [CASE:4315787] Wrong behavior of NumberForm (DecimalForm outputs ... 21 votes 2 answers 3k views ### New General::munfl error and loss of precision The latest version 11.3.0.0 of Mathematica returns Indeterminate when evaluating Log[Exp[-800.]]. I believe this was not ... 8 votes 1 answer 991 views ### What is wrong with importing Real32 or Real64? Those who visit the chat might have seen the question of varkor. I'm posting it here in the hope that I have missed something. Assume you have a real number ... 1 vote 1 answer 66 views ### Precision Issue with Log I have the following codes. Naturally, I expect to get zero. I thought it is due to some possible issues stated as "Machine-precision inputs can give numerically wrong answers on branch cuts:". ... 8 votes 2 answers 590 views ### how to get single, and quad Precision out of Mathematica which match Fortran result by default, if a number has decimal . after it, then Mathematica will do computation using machine Precision, which on my PC (intel hardware) running windows 7 64 ... 4 votes 1 answer 250 views ### Is Mathematica, while operating within$MachinePrecision IEEE 754 compliant?

I was looking in Mathematicas documentation and could not find to which point Mathematica includes the IEEE 754 standard? It is mention it in its documentation MachinePrecision under Background & ...
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### Why does Mathematica results differ from C++ results within machine precision?

I am trying to wrap my head around floating-point precision. Performing the following numeric operation: 275./6.*1.03692775514337 in Mathematica and C++ and ...
1 vote
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### 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 ...
556 views

### What explains the inaccuracies in machine-precision 'integers' with trigonometry or powers?

This Mathematica tutorial notes some strange behaviour with calculations such as Sin[10^50]: ...
497 views

$MachineEpsilon x = 0.0000000000000001 % + 1 % - 1 As expected the final result equals zero, since x < MachineEpsilon ($2.22045\times10^{-16}$). However, if I ... 6 votes 1 answer 290 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: ... 4 votes 1 answer 75 views ### A simple syntax does not work The code below does not work. Can anyone tell me why? Thanks! ... 8 votes 1 answer 931 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? 5 votes 1 answer 444 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: ...
927 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 ...
3k views

### How do I overcome an Overflow?

I'm trying to calculate entropies for an absolutely giant system by counting states, and this means I have to use some obscenely large numbers. I'm running ...
645 views

### Mathematica Precisions vs Doubles in C/C++

I'm having a bit of an issue regarding numerical precision and I'm not sure how to deal with it. I have a certain randomly generated matrix, say $M$, that I wish to compute the eigenvalues. The ...
460 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 site ...
111 views

### My NIntegrate expression returns a wildly inaccurate value

I am trying to integrate a function using NIntegrate: ...
362 views

### How to tell Mathematica to treat all numbers (including those in decimal form) as arbitrary precision numbers

I have code that is essentially numerical. It uses functions like NDSolve and NIntegrate. But in most interesting cases, the ...
395 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 ...