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The m/s to mph conversion factor: 2.23693629

2.5 cos(26.52) = 2.23694638 (+0.00001009)

ln(9+tan(7/20 rad)) = 2.23698237859 (+0.000036)

I'd like to start a new round (not disturbing the pervious ongoing games) with the following rule:
Every player in this round (players) are only allowed to post a string of less than, let's say, 256 characters.
The string must follow a type of expression mentioned below as the Singular Expression, shorten as the S.
the S is described to be using only 6 characters, including 'i', '+', '=', ',' and the brackets ('(' and ')'), whose uses are described below.
The non-capital letter 'i' is a variable that initially has value 0, and whose resulting numeric value will determine the result of the S.
The operator plus '+' is used to add the number in it's left and right, but can have uses other than this in composite operators.
The operator copy '=' is used to copy the number in it's right to it's left, but also have uses in composite operators.
The seperator ',' is used to seperate 2 pieces of expressions.
The brackets '(<S>)' is used to describe functions. for example, if one wants a function with 2 parameters, calculates the sum of them and then return the sum, one can write:
$"<previous S>,i(,)(i)+(i+1),<after S>"
Before the first left bracket '(', there is an i (or any expression resulting a number) indicating the index of the function. For this example, if no copy expression happens before, i will be 0 and the index will be 0, too.
Between the first left bracket and the first right bracket '(<S>)', there is a seperator ',' which declares that the number of the parameters is 2. It is supposed that every function should have at least 1 parameter, so the parameter amount is the seperator amount in the brackets plus one.
After the right bracket there is an S, which has 2 pairs of brackets. In the first pair there is an i inside, and the second has 'i+1'. These 2 Ses indicates the index of the parameters, and the brackets beside them turns the index into the values of the indexed parameter.
The return value of the function is simply the value of the S after the calculation.
Note that '+' will always be calculated from left to right, and '=' will always copy from right to left, and brackets cannot be used to redefine priority.
'=' will be calculated only after the 2 sides' calculation.
I'll describe composite operators next day.

2^(7/6) = 2.2449241...

(π^e)/10 ≈ 2.24592. (+0.00099)

∜(8.1π) ≈ 2.24599468 (I hope you can see Unicode)

Ohhhhhhhhh wrote: January 27th, 2023, 11:17 am Rules about singular expression

Composite operators:
+=: a += b is equivalent to a = a + b.
++: ++a is equivalent to a = a + 1.
==: ==a is equivalent to a = -a, since you sometimes need to decrease the value.
It’s similar to C++ if you have learnt that, but not totally the same.

Finally, you’re allowed to use space to distinguish the different operators when situations like $"i+=i+++i"happens, So to get rid of the misguiding Ses.

Now I’ll start my first S:
$"i+=++i" = 4
Note that a singular expression should start with $" and end with ".

Edit #1: Fixed some mistakes in rule making.

hotdogPi wrote: January 29th, 2023, 10:37 am ∜(8.1π) ≈ 2.24599468 (I hope you can see Unicode)

2 * arcsec(e - 0.4) = 2.2496067 rad
(~0.00361202 difference)

I'll take the simple one: 9/4

(music theory fans, no, that's not what I meant, don't correct me here)

hotdogPi wrote: February 6th, 2023, 10:09 am I'll take the simple one: 9/4

(music theory fans, no, that's not what I meant, don't correct me here)

e-0.45 (2.2682818285)

BokaBB wrote: February 6th, 2023, 10:15 am e-0.45 (2.2682818285)

sqrt(51127)/(30pi+2e) is about 2.26828804104
0.00000621253 difference (5 leading 0's let's go!)

rutabaga wrote: February 6th, 2023, 11:23 am

BokaBB wrote: February 6th, 2023, 10:15 am e-0.45 (2.2682818285)

sqrt(51127)/(30pi+2e) is about 2.26828804104
0.00000621253 difference (5 leading 0's let's go!)

Woooooow... Gonna need to think...

e⁴/(4!) ≈ 2.27492292

sqrt(ln(177)) ≈ 2.2751153229

PHPBB12345 wrote: February 6th, 2023, 11:59 am sqrt(ln(177)) ≈ 2.2751153229

cube root (588817/50000) = 2.27511547939
0.0000001565 difference >:D

(6 sqrt(14) pi)/31 ≈ 2.275115488749

ln(5) * √2 ≈ 2.27608892

hotdogPi wrote: February 6th, 2023, 10:17 pm ln(5) * √2 ≈ 2.27608892

ln(31)^(2/3) ≈ 2.2761407551

PHPBB12345 wrote: February 6th, 2023, 10:48 pm

hotdogPi wrote: February 6th, 2023, 10:17 pm ln(5) * √2 ≈ 2.27608892

ln(31)^(2/3) ≈ 2.2761407551

41/18 = 2.27777... (+0.001637023)

3^(3/4) ≈ 2.27950706

hotdogPi wrote: February 7th, 2023, 1:27 pm 3^(3/4) ≈ 2.27950706

cos(3 rad)*ln(0.1) ≈ 2.279541965

PHPBB12345 wrote: February 7th, 2023, 1:49 pm

hotdogPi wrote: February 7th, 2023, 1:27 pm 3^(3/4) ≈ 2.27950706

cos(3 rad)*ln(0.1) ≈ 2.279541965

(11846^(1/3))/10 = 2.2795926224 (+0.0000506574)

rutabaga wrote: February 7th, 2023, 8:35 pm (11846^(1/3))/10 = 2.2795926224 (+0.0000506574)

sqrt(ln(2+pi))+1 ≈ 2.2795948133 (+0.0000021909)

PHPBB12345 wrote: February 8th, 2023, 4:49 am

rutabaga wrote: February 7th, 2023, 8:35 pm (11846^(1/3))/10 = 2.2795926224 (+0.0000506574)

sqrt(ln(2+pi))+1 ≈ 2.2795948133 (+0.0000021909)

log1904 - 1 = 2.27966694405 (+0.00007213075)