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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
In the IEEE standard the base is binary, i.e. =, and normalization is used.The IEEE standard stores the sign, exponent, and significand in separate fields of a floating point word, each of which has a fixed width (number of bits).
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
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Provided the data are strictly positive, a better measure of relative accuracy can be obtained based on the log of the accuracy ratio: log(F t / A t) This measure is easier to analyze statistically and has valuable symmetry and unbiasedness properties.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
where is the instance, [] the expectation value, is a class into which an instance is classified, (|) is the conditional probability of label for instance , and () is the 0–1 loss function: L ( x , y ) = 1 − δ x , y = { 0 if x = y 1 if x ≠ y {\displaystyle L(x,y)=1-\delta _{x,y}={\begin{cases}0&{\text{if }}x=y\\1&{\text{if }}x\neq y\end ...
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