# 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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### 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 ...
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### 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 ...
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### Dr. StrangeNumbers or: How I Learned to Stop Worrying and Love Floating Point Arithmetic

The following is the program. ...
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### Numerical underflow for a scaled error function

I calculate a scaled error function defined as f[x_] := Erfc[x]*Exp[x^2] but it can not calculate f[30000.]. ...
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### DeleteDuplicates[] does not work as expected on floating point values

Here is my simple example, and in this case function DeleteDuplicates does not work as expected. I want to FindRoot of my ...
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### 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 ...
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### Is there a difference between Divide[a,b] and a/b?

In this comment it was asserted that Divide[a,b] and a/b are different, though the documentation indicates that they are the ...
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### Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
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### Underflow error General::munfl from E^x instead of Exp[x]

In contrast to earlier versions, Mathematica 11.3 and 12.0 generate lots of underflow errors from my code, e.g. ...
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### 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 ...
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### Precision differences

I run this sum and get the symbolic answer below : Sum[ (1/(k^2 - k) - 1/k^2), {k, 2, Infinity}] $2 - \frac{\pi^2}{6}$ I look up the sequence on OEIS and ...
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### Rounding problems inside InputField

The community needs to determine if this is behavior is a bug or not. – Mr.Wizard Consider the following InputField ...
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### Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### Machine Epsilon

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

How can I set the output precision of the following statement to 10 decimal places? I was looking through the documentation, and for some reason, all I could find was ...
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I stumbled over the following weird behavior when comparing floating-point numbers close to 1.0: qq = 1.0 + 60.0 $MachineEpsilon; and then ... • 281 6 votes 4 answers 3k views ### Making a calculation with high precision I would like to make the following calculation: 1/Sqrt[1 - (150^2 10^(-4))/(9 10^16.)] - 1 Mathematica 8 returns 0. The result is obviously not 0, but my ... • 1,003 4 votes 0 answers 177 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 ... • 61.7k 4 votes 2 answers 3k views ### Precision of number not maintained when saved via Export Assume that the output of my calculation is a and is a number such as: a = 100.1252135246354847; ... • 5,341 3 votes 1 answer 283 views ### Why to do parentheses change the results of a calculation? I'm getting results that are sensitive to where I place parentheses with respect to operations that are associative1 (and should thus be insensitive to such placement). For example, if I define2 <... • 12.8k 2 votes 1 answer 1k 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 ... • 3,854 2 votes 1 answer 295 views ### How to stop Mathematica from turning .02 into 0.019999999999999997` [closed] ... 2 votes 1 answer 183 views ### Efficient Round edition with different rounding direction As pointed out in this post, Mathematica has a special version of Round that Round rounds numbers of the form x.5 toward the nearest even integer. A comment by ... • 17.1k 0 votes 1 answer 101 views ### Why this very simple problem turns to "Indeterminate"? Why the following calculation gives Indeterminate value? ... • 639 0 votes 2 answers 243 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 ... • 817 30 votes 2 answers 4k views ### 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 ... • 457 17 votes 2 answers 346 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 ...
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### 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 ...
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### 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]: ...
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### Dealing with numbers too large for machine precision in Graphics

Graphics only supports machine precision numbers (i.e. number that can be converted to machine precision). Take for example ...
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### Really understanding precision

I've been reading the documentation in Mathematica about precision, namely: Exact and Approximate Results Arbitrary-Precision Numbers Arbitrary-Precision Calculations Machine-Precision Numbers ...
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### Using Differences on data: trouble with floats and doubles

Consider the following data set (after I have run FullForm), which is imported from a file (stored typically as 10.040): ...
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### 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: ...
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### How do I convert an inexact number smaller than $MinMachineNumber to machine-precision? I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ... • 7,142 6 votes 1 answer 290 views ### ConvexHullMesh fails with small numbers When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors: ... • 1,067 5 votes 1 answer 453 views ### MachinePrecision versus$MachinePrecision in NDSolve

I'd like to understand why one of these inputs gives me an error and the other doesn't: ...
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### Compilation, square roots, and integers

After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ...
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