# 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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2answers
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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 ...
2answers
2k 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 ...
2answers
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 ...
2answers
780 views

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

The following is the program. ...
5answers
4k views

### 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.]. ...
3answers
1k views

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

When I evalute the following expression, ...
8answers
1k views

### 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 ...
2answers
517 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. ...
1answer
1k views

### 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 ...
2answers
766 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 ...
2answers
566 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 ...
3answers
5k views

### 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 ...
4answers
543 views

### Terrible accuracy of DawsonF

DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ...
2answers
800 views

### 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 ...
1answer
236 views

1answer
615 views

### Machine Epsilon

I'm trying to evaluate the machine epsilon of my computer (see below). I wrote this: ...
6answers
3k 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. ...
1answer
536 views

### 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 ...
4answers
429 views

### 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 ...
1answer
707 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?
1answer
380 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 ...
2answers
2k views

I stumbled over the following weird behavior when comparing floating-point numbers close to 1.0: qq = 1.0 + 60.0 $MachineEpsilon; and then ... 2answers 3k views ### Precision of number not maintained when saved via Export Assume that the output of my calculation is a and is a number such as: a = 100.1252135246354847; ... 1answer 281 views ### How to stop Mathematica from turning .02 into 0.019999999999999997` [closed] ... 1answer 73 views ### Why this very simple problem turns to “Indeterminate”? Why the following calculation gives Indeterminate value? ... 2answers 217 views ### The precision of the number I have problem in Mathematica with unnecessary rounding which is caused by high precision. For example I have value a = 2.052685846*10^-1865, when I make ... 1answer 721 views ### Really understanding precision I've been reading the documentation in Mathematica about precision, namely: Exact and Approximate Results Arbitrary-Precision Numbers Arbitrary-Precision Calculations Machine-Precision Numbers ... 2answers 4k views ### Why does Mathematica results differ from C++ results within machine precision? I am trying to wrap my head around floating-point precision. Performing the following numeric operation: 275./6.*1.03692775514337 in Mathematica and C++ and ... 1answer 530 views ### What explains the inaccuracies in machine-precision 'integers' with trigonometry or powers? This Mathematica tutorial notes some strange behaviour with calculations such as Sin[10^50]: ... 1answer 240 views ### ConvexHullMesh fails with small numbers When I try to get the ConvexHullMesh of a List of points that are "small scale", I get errors: ... 2answers 316 views ### CompiledFunction returns machine numbers smaller than$MinMachineNumber

When thinking on the workaround for this LogLogPlot bug suggested by halirutan I noticed that CompiledFunction actually can ...
1answer
2k views

### 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 ...
2answers
470 views

### 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 ...
0answers
151 views

### 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: ...
4answers
390 views

I'm attempting to add $MachineEpsilon to numbers I am pulling from the domains of 3 interpolating functions. I pulled 3 numbers, and for one of these numbers adding ... 1answer 178 views ### Compilation, square roots, and integers After looking at this question, particularly this answer, I wrote my own performance test, using the two functions ... 1answer 342 views ### MachinePrecision versus$MachinePrecision in NDSolve

I'd like to understand why one of these inputs gives me an error and the other doesn't: ...
1answer
146 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
784 views

### 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 ...
1answer
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 ...
1answer
156 views

### 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): ...