$(25$pts$)$ Consider the function

$f(x)=\sqrt[\phantom{2}]{1-x^2}-\sqrt[\phantom{2}]{1+x^2}$

We want to compute it accurately in the IEEE single precision standard $(,t,e_{\text{m}\text{i}\text{n}},e_{\text{m}\text{a}\text{x}})=$

$(2,24,-126,128).$

C$)$ Argue why your algorithm can produce a better result than computing with the original

expression.