Problem $7.$ Performance $(10$pts$)$

A designer wants to improve the overall performance of a given machine with respect to a target benchmark suite and is

considering an enhancement X that applies to $50\%$ of the original dynamically$-$executed instructions, and speeds each of

them up by a factor of $3.$ The designer$$s manager has some concerns about the complexity and the cost$-$effectiveness of

X and suggests that the designer should consider an alternative enhancement Y$.$ Enhancement Y$,$ if applied only to some

$($as yet unknown$)$ fraction of the original dynamically$-$executed instructions, would make them only $75\%$ faster.

Determine what percentage of all dynamically$-$executed instructions should be optimized using enhancement Y in order

to achieve the same overall speedup as obtained using enhancement X$.$