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So if the following function is evaluated with the floating-point arithmetic, we get poor results for certain range of values of $x$. Therefore, I need to provide an alternate function that can be used for those values of $x$. The function is: $$f(x)=e^x-1$$ So how would I make an alternate expression or function for this. The range of this function is $y\gt -1$, $y\in\mathbb{R}$. So would I use the Taylor series for this....?

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    Have you learned anything from the comments and answers to your other question that would help you with this? http://math.stackexchange.com/questions/108678/alternate-expression-for-the-following-function2012-02-13
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    i do understand that...but this is a slightly different function....and Conjugate would not work for this...So I am thinking Taylor series would work.2012-02-13
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    When you say does not work for certain values of $x$, you should also tell which ones and what exactly you mean by 'does not work'! Also, you write $f$, but talk about $y$.2012-02-13
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    "Conjugate" was not suggested for your other problem, either. What about the ideas that *were* suggested for your other problem? Did you try them for this one? Are you actually trying to learn something, or are you just getting people to do your homework for you?2012-02-13
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    The advanced HP calculators (48, 49, 50) have built in functions for exp(x)-1 and ln(1+x) for exactly this reason: improved accuracy around x = 0.2012-02-13
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    @marty: Not just calculators. Good compilers often provide for [$\exp\,x-1$ (`expm1()`)](http://software.intel.com/sites/products/documentation/studio/composer/en-us/2011/compiler_c/cref_cls/common/cppref_math_expo.htm#expm1) and [$\log(1+x)$ (`log1p()`)](http://software.intel.com/sites/products/documentation/studio/composer/en-us/2011/compiler_c/cref_cls/common/cppref_math_expo.htm#log1p) functions.2012-02-13
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    @ Gerry Myerson.....I never mentioned Conjugate here..... did you even read the post....2012-02-13
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    Yes, I read the post, and I also read your comment: "...and Conjugate would not work for this..." so, yes, you sure as heck did mention "Conjugate" here.2012-02-14

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