# 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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### What's the smallest positive real allowed in mathematica?

This question may be a bit strange, but in this question, one of the answers suggests substituting some negatives values in a matrix by the smallest positive real number allowed. So, I was wondering ...
329 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 ...
109 views

### Simple division with high precision in Mathematica [closed]

I want to do a simple division i.e. 0.70524/0.51824 . What I want is to find the result of the roundation of this division for precision from 1 to 19 decimal digits....
141 views

### Numerical precision problem

I have this simple code: ep = 1 - 80000000000 (-(199999/200000) + 1/E^(1/200000)) ep // N -8.27404*10^-8 ...
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### Copy-paste with annoying trailing 0s

When one copies an output containing machine-precision numbers to a input, many trailing 0s appears. For example : Evaluate the following expression : ...
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 ...
90 views

### equal expressions give different numerical result

I have two expressions, and they are really equal: ...
497 views

### How do I convert an inexact number smaller than $MinMachineNumber to machine-precision? I was trying to convert some arbitrary-precision numbers to machine-precision numbers using N[myNumber,MachinePrecision]. But, although my test number did lose some ... 1 vote 1 answer 50 views ### How to choose elements of a matrix with internally generated variables and rank them with real coefficients I have a Code (a long one), part of it is below. The following piece basically multiplies an adjacency matrix with a vector of equilibrium values. Then tries to pick non-zero elements to be used in ... 2 votes 1 answer 158 views ### Working Precision warnings for ParametricPlot I wish to plot a series of parametric curves for the following function called poly that has five parameters (Γ, ... 15 votes 4 answers 671 views ### Terrible accuracy of DawsonF DawsonF[30.] returns 0. The correct value is 0.016676... At least it prints a warning message, ... 8 votes 3 answers 6k views ### Machine precision near zero: not fulfilled? I am puzzled by the behavior of Mathematica machine precision with numbers approaching zero. This manifests itself, e.g., with FixedPoint and the like. In the ... 5 votes 2 answers 584 views ### Why does N not upgrade precision? [duplicate] Precision[N[1.0, 20]] Precision[N[1, 20]] MachinePrecision 20. It would be so much more intuitive and less error prone, if <... 9 votes 1 answer 249 views ### Plot3D discrepancy between MMA 10 and 11.3 - possible small numbers issue I'm having some troubles with the following code I wrote in MMA 10 some time ago: ... 4 votes 1 answer 148 views ### Machine Epsilon is not equal to$MachineEpsilon [duplicate]

I try to wrap my head around machine precision calculations in Mathematica (11.2, Linux). I do not understand the following behavior: ...
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### 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 ...
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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 ...
1 vote
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### 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 ...
103 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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### 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 ...
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 ...
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For machine-precision numbers, Mathematica uses a tolerance for comparisons, so that 1.-$MachineEpsilon==1. However, Floor does ... 2 votes 1 answer 155 views ### Showing what happens with a number beyond machineprecision I want to play around a bit in Mathematica to understand how floating-point precision, rounding and truncation actually works. I understand that Machineprecision is$2^{-52}$. First of all I would ... 8 votes 1 answer 987 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:". ... 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 ... 4 votes 1 answer 249 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 & ...
1 vote
205 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 ...
962 views

### How to use Working Precision to get good result and plot?

I have a function f(x) which I would like to see going up for very low values of x: from an asymptotic study, I expect it to go to Infinity for low x; however, I can see an elbow and many oscillations....
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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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### Precision improvement for solution of the simplest low-pass filter

I solved the most basic low-pass filter using NDSolve in Mathematica and LTSpice. The solution provided by Mathematica seems to lack precision. I tried to deal with WorkingPrecision but I didn't ...
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### Unexpected behavior from CoordinateBoundingBoxArray with Into[1] and 0.41

I want to get the four corners of a Cuboid. This usually works: CoordinateBoundingBoxArray[{-{1., 1.}, {1., 1.}}, Into@1] gives ...
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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 ...
300 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 ...
1 vote
154 views

### MemberQ[{0.01, 0.05}, (0.01*9*2)/9/2] returns False

Multiplying and dividing by the same stuff seems to alter the value. Quite curiously, if the value you start from is large enough (greater than 0.05 in my case) you do not see the problem. Any idea ...
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### 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 ...
821 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 ...
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### 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, ...
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### Precision of integers vs. Precision of floating numbers

It seems that Mathematica can handle very big integers accurately, but cannot do the same for floating numbers. See the following code: ...
135 views

### How to use a higher precision?

Below is my code. If I set W to $10^{55}$, it breaks down and the result is wrong. What do I need to do to use W as large as $10^{200}$? ...
881 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 ...
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### 'eps' equivalent in Mathematica

In MATLAB, there is a function named eps. eps Spacing of floating point numbers. D = eps(X), is the positive distance from ABS(X) to the next larger in ...
814 views

### Why does 1 - Exp[-10.0^12] cause an out-of-memory error?

I would like to understand why evaluation of the expression 1 - Exp[-10.0^12] causes an out-of-memory error and how can I prevent such errors when calculating ...
1 vote
290 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 ...
1 vote
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### Chop intermediate results of NDSolve after each step [closed]

Using NDSolve for a set of three ordinary differential equations, I ran into the problem that intermediate results quickly develop negligible imaginary parts. I get ...
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. ...
315 views

### Precision problem with numerical solution of a differential equation

I want solve $$2\sqrt{|\gamma|}x = \int_{1}^{t} dy \sqrt{\frac{1+2|\gamma_2|y}{y^2(1-y)}}$$ where $0<t\leq$1. I'm using a for cycle to evaluate t, calculate the integral and the assign the $x$. ...