Article: Increasing the D Compiler Speed by Over 75%

[JS]

On Thursday, 25 July 2013 at 21:27:47 UTC, Walter Bright wrote:
> On 7/25/2013 11:49 AM, Dmitry S wrote:
>> I am also confused by the numbers. What I see at the end of 
>> the article is
>> "21.56 seconds, and the latest development version does it in 
>> 12.19", which is
>> really a 43% improvement. (Which is really great too.)
>
> 21.56/12.19 is 1.77, i.e. a >75% improvement in speed.
>
> A reduction in time would be the reciprocal of that.


Actually, it is a 43% speed improvement. 0.43*21.56 = 9.27s


So if it is 43% faster, it means it's reduced the time by 9.27s 
or, 21.56 - 9.27 = 12.28 seconds total.

Now, if we started at 12.28 seconds and it jumped to 21.56 then 
it would be 21.56/12.19 = 1.77 ==> 77% longer.

21.56/12.19 != 12.19/21.56.

The order matters.

To make it obvious. Suppose the running time is 20 seconds. You 
optimize it, it is 100% **faster**(= 1.0*20 = 20s seconds), then 
it takes 0 seconds(20 - 20).

Suppose the running time is 20 seconds, you screw it up, it takes 
40 seconds, now it is 100% slower(1.0*20 = 20, and 20 + 20 = 40).

In both cases there is a difference of 20 seconds BUT they mean 
very different things.

A 20% increase is not calculated the same as a 20% decrease.

That is,

(A - B)/A != (A - B)/B.

The LHS is relative to A and the RHS is relative to B.

So

(21.56 - 12.19)/21.56 = 9.37/21.56 = 43%

or

1 - 12.19/21.56 = 1 - 0.57 = 0.43

To make the numbers simple,

20 second original, 10 second new.

How much faster is the new version? it is 10 seconds faster, or 
in percent, 1 - 10/20 = 0.5% (BUT if we started with 10 seconds 
then it would be increase of 100%)

The numbers are very close to the original, but not very close to 
75%.


Basically you are calculating the percentage as if you slowed 
down the program... but it is not the same.

Another example will suffice:

Suppose you have 1000$. You lose 10% of it, or 100$. You now have 
900$. You gain 10% of it, or 90$. You now have 990$! (Where did 
the 10$ go?)

This is why the stock market and economy is much worse than 2007 
even though the numbers look the same. Easier: Suppose you have 
1000$ loose 99% then gain 99%, you have only (1000*0.01)*1.99 = 
10*1.99 = 19.9... no where near your original amount. (Even 
though the DIJA isn't a percentage this issue does creep into the 
calculation due to inflation and other factors)