# Questions tagged [floating-point]

Mathematical questions concerning floating point numbers, a finite approximation of the real numbers used in computing.

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### How inaccurate are floating point numbers? [closed]

I'm trying to understand the inaccuracies with floating point notation using ChatGPT. I had ChatGPT try out some fractions. I wanted to know what the difference was between the exact number, and how ...
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### Algebraic Structures involving 𝙽𝚊𝙽 (absorbing element).

IEEE 754 floating point numbers contain the concept of 𝙽𝚊𝙽 (not a number), which "dominates" arithmetical operations ($+,-,⋅,÷$ will return ...
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### Solve $10^{10^z} = 10^{10^x}+10^{10^y}$ for $z$ with floating point accuracy

In the following equation $$10^{10^z} = 10^{10^x}+10^{10^y}$$ I want to find an algorithm that computes $z$ in a floating point accurate manner given any values of $x$ and $y$ (e.g. $x=y=2000$). The ...
1 vote
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### How to transform this expression to a numerically stable form?

I have this function $$f(x, t)=\frac{\left(1+x\right)^{1-t}-1}{1-t}$$ Where $x \ge 0$ and $t \ge 0$. I want to use it in neural network, and thus need it to be differentiable. While it has a ...
1 vote
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### Proof that $\epsilon_{mach} \leq \frac{1}{2} b^{1-n}$

I have a question about the proof of the following statement: For each set of machine numbers $F(b, n, E_{min}, E_{max})$ with $E_{min} < E_{max}$ the following inequality holds: \$\epsilon_{mach} \...
1 vote
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### Why does TI-84 show scientific notation for zeros sometimes but not others?

When graphing a function and then going through the process to calculate the zeroes (left bound, right bound, guess), is there a reason that sometimes it shows y = 0, but there are other times when it ...
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