Development of a specific hardware architecture for a particular algorithm How does a technical and theoretical study of a project of implementing an algorithm on a specific hardware architecture?
Function example:
%Expresion 1:
y1 = exp (- (const1 + x) ^ 2 / ((conts2 ^ 2)),
y2 = y1 * const3

Where x is the input variable,
y2 is the output and const1, const3 const2 and are constant.
I need to determine the error you get in terms of architecture that decides to develop, for example it suppose that is not the same architecture with 11 bits for the exponent and 52 bits for mantissa.
This is the concept of error I handle:
Relative Error = (Real Data - Architecture Data) / (Real Data) * 100

I consider as 'Real Data' the ouput of my algorithm I get from Matlab  (Matlab use double precission float point, IEEE 754, 52 bits to mantisa, 11 bits for exponent, one bit fo sign ) with the expression 1 and I consider as 'Architecture Data' the ouput of my algorithm running in an particular architecture (For instance a architecture that uses 12 bits for mantisa, 5 bits for exponent and 1 bit for sign)
EDIT:
NOTE: The kind of algorithm I am refering to are all those which use matemathical functions that can be descompose in terms of addition, multiplication, subtrations and division.
Thank you!

You have several issues to consider.  First, your output format allows very many fewer output values than the double standard.  If your exponent is 2-based, your output will be of the form $\pm m*2^e$ where m has 2048 values available and e has 32 values (maybe they range from -15 to +16).  The restricted range of e means that you will underflow/overflow quite often.  If you are within range, you will still have an error as large as one part in 4096 assuming your calculation is perfect and the only error is representing the output value.
A second issue is precision of the input and error propagation.  If your input values are represented in the same format, they will be in error by up to 1 part in 4096 for the same reason.  Then when you calculate $f(x)=c_3 \exp {\frac{-(c_1+x)^2}{c_2}}$ (where I absorbed the squaring of $c_2$ into its definition) the error will propagate.  You can assess this by evaluating $\frac{\text{d}\ln f(x)}{\text{d}x}=\frac{\text{d}\ln (c_3 \exp {\frac{-(c_1+x)^2}{c_2}})}{\text{d}x}$ to get the fractional error in $f(x)$ depending on the error in $x$
All this assumes your calculation is perfect and the only problem is the accuracy of representing the data.  If not, you also need to assess the error that is inherent in the computation.
