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MDD123
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07 Dec 2015, 4:45 pm

SippingSpiderVenom wrote:
An interesting article on the computational expense a computer must put forward for different operations.

http://streamcomputing.eu/blog/2012-07-16/how-expensive-is-an-operation-on-a-cpu/

For our purposes:
Addition (1)
Subtraction (1)
Multiplication (4)
Division (10)
Pow (100)
Square Root (Highly variable depending on processor implementation)

So the computer would always run faster by preferring not to use powers or roots.


Interesting, exponents really slow a computer down, this is probably why log functions are so useful.


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SippingSpiderVenom
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08 Dec 2015, 10:12 am

Close, logarithms are computationally intensive, which is why logarithmic *tables* are so useful.

I didn't think 5, 5's were going to work, but I hadn't considered primorials

5!+5!+5#/5#+5#=39


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08 Dec 2015, 11:49 am

for example:
In our case 5# is the most expensive operation because it requires a primality test if it is to be generalized, however we do not need a general application in the case of 5,5's so we can compute the total and substitute the complicated math with the solution.
5#=2*3*5
becomes
5#=30

this substitution,
5#=30
Is inexpensive, because you are actually just referencing the answer.

In programming terms you would add 5#=30 to a variable rather than compute the answer every single time.


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08 Dec 2015, 12:07 pm

2=|5!+5!/5#-5-5|

1 & 3 are also incomplete.


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09 Dec 2015, 2:41 pm

|5!+5!-5!/5#-5|=1


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marshall
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10 Dec 2015, 6:42 pm

MDD123 wrote:
SippingSpiderVenom wrote:
An interesting article on the computational expense a computer must put forward for different operations.

http://streamcomputing.eu/blog/2012-07-16/how-expensive-is-an-operation-on-a-cpu/

For our purposes:
Addition (1)
Subtraction (1)
Multiplication (4)
Division (10)
Pow (100)
Square Root (Highly variable depending on processor implementation)

So the computer would always run faster by preferring not to use powers or roots.


Interesting, exponents really slow a computer down, this is probably why log functions are so useful.


I usually assume square roots are as expensive as exponential or trigonometric functions. When programming I always compare squares of distances rather than actual distances to avoid using square roots in inner loops.



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10 Dec 2015, 6:45 pm

1+2+3 = 1x2x3 = 6



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10 Dec 2015, 8:37 pm

marshall wrote:
1+2+3 = 1x2x3 = 6


6 is also a perfect number.


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10 Dec 2015, 8:42 pm

3^1318+2 is a prime number so I suppose 1318 is an interesting number.


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10 Dec 2015, 8:52 pm

The smallest number not in a sequence in the OEIS is 14,972.


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10 Dec 2015, 9:35 pm

I'm still a big fan of zero

http://yaleglobal.yale.edu/about/zero.jsp

5#/(5+5+5-5)=3

5#=30
5+5=10
5-5=0
All of these zeros disappear, why? Because they are nothing! It's like the ninja of numbers.
(5+5-5-5)/5=0
and it makes all these fives vanish as well.


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11 Dec 2015, 6:10 pm

5 is the only prime palindrome with a zero in the middle surrounded by ones in binary.

5 in base 2 is 101.


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13 Dec 2015, 8:51 am

Rudin wrote:
9474=9^4+4^4+7^4+4^4


9474 is a narcissistic number then.


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20 Dec 2015, 9:59 pm

16 (currently my second favorite number)

It's the only known number where x^y = y^x

Image



Rudin
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21 Dec 2015, 9:04 am

ReticentJaeger wrote:
16 (currently my second favorite number)

It's the only known number where x^y = y^x

Image


Where x does not equal y though.


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21 Dec 2015, 9:38 am

Rudin wrote:
ReticentJaeger wrote:
16 (currently my second favorite number)

It's the only known number where x^y = y^x

Image


Where x does not equal y though.