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

The following is the program. ...
1k 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 ...
1k views

### 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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### 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.]. ...
1k views

### Very different results from evaluating same expression with different precisions

When I evalute the following expression, ...
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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 ...
551 views

### 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 ...
403 views

### 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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### 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 ...
716 views

### 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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### 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 <...
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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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### 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 C's nextafter?

In C (and many other programming languages), there is a function double nextafter(double x, double y) which takes two (IEEE 754) floating-point numbers and ...
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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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### Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
369 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 ...
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Let's define two different numbers. x = 1. y = 1. + 2^-52 (* equivalently, 1 + $MachineEpsilon *) Let's make sure they're different with ... 6answers 2k views ### Why is this Mandelbrot set's implementation infeasible: takes a massive amount of time to do? The Mandelbrot set is defined by complex numbers such as$z=z^2+c$where$z_0=0$for the initial point and$c\in\mathbb C$. The numbers grow very fast in the iteration. ... 3answers 866 views ### Mathematica Plot: Inconsistency when plotting large values I am working with a function in Mathematica and I am getting some inconsistencies when I plot it. As I really need to understand were this comes from I would appreciate any help. I am working with a ... 1answer 181 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: ... 4answers 2k views ### 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 ... 4answers 2k 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 ... 0answers 122 views ### Is it possible to get the original number from DecimalForm? Bug introduced in 5.2 or earlier and persisting through 12.0 [CASE:4315787] Wrong behavior of NumberForm (DecimalForm outputs ... 1answer 254 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 <... 1answer 838 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 ... 1answer 534 views ### Machine Epsilon I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ... 2answers 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; ... 1answer 278 views ### How to stop Mathematica from turning .02 into 0.019999999999999997` [closed] ... 2answers 203 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 ... 1answer 64 views ### Why this very simple problem turns to “Indeterminate”? Why the following calculation gives Indeterminate value? ... 2answers 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 ... 1answer 662 views ### 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 ... 1answer 211 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: ... 1answer 520 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]: ... 2answers 285 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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### Adding precision for the calculation of a function

I have some function $f(x)$ I wish to evaluate, which is yielding divide-by-zero errors for sufficiently large inputs. How do I increase the precision with which this function is evaluated in order ...
319 views

I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ... 1answer 164 views ### Compilation, square roots, and integers After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ... 1answer 138 views ### The algorithm behind InputForm for machine numbers There are several questions on this site about implementing fast CSV/TSV export for machine numbers without loss of precision. Recently I discovered that Export ... 1answer 281 views ### MachinePrecision versus$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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### Could the PrecisionGoal for NDSolve be a negative number?

The help of Mathematica doesn't say so much about the PrecisionGoal for NDSolve, and I never considered much about it even after ...
135 views

### 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 ...