Assume for a given processor the CPI $($cycles per instruction$)$ are as follows:

arithmetic instructions is $1$

load$/$store instructions is $10$

branch instructions is $3$

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Assume a program has the following instruction breakdowns:

$500$ million arithmetic instructions

$300$ million load$/$store instructions

$100$ million branch instructions.

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$5\mathrm{.}1$ Suppose that new, more powerful arithmetic instructions are added to the instruction set. On average, using these more powerful arithmetic instructions, the number of arithmetic instructions needed to execute a program is reduced by $25\%$ with the impact that clock cycle time is now increased by $10\%.$

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Is this a good design choice? Why?$(2$ points$)$

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$5\mathrm{.}2$ Suppose that we find a way to double the performance of arithmetic instructions. What is the overall speedup of our machine? What if we find a way to improve the performance of arithmetic instructions by $10$ times?$(4$ points$)$