Uniswap math

The slope of the line segment connecting these points is the (negative) average price that the trade is executed at:

Expression 14: "y" equals negative "p" Subscript, "e" "x" "e" "c" "u" "t" "i" "o" "n" , Baseline "x" plus "y" Subscript, "s" "t" "a" "r" "t" , Baseline plus "y" Subscript, "e" "n" "d" , Baseline left brace, "x" Subscript, "l" "o" "w" , Baseline less than or equal to "x" less than or equal to "x" Subscript, "h" "i" "g" "h" , Baseline , right brace

For infinitesimally small trades, the price is the slope of the tangent line at that point.

Expression 16: "y" equals negative "p" Subscript, "s" "t" "a" "r" "t" , Baseline times "x" plus 2 "y" Subscript, "s" "t" "a" "r" "t" , Baseline

Expression 17: "y" equals negative "p" Subscript, "e" "n" "d" , Baseline "x" plus 2 "y" Subscript, "e" "n" "d" , Baseline

Calculations

Other labels

Execution price: ${p_executiontruncated} left parenthesis, StartFraction, "x" Subscript, "e" "n" "d" , Baseline minus "x" Subscript, "s" "t" "a" "r" "t" , Baseline Over 2 , EndFraction plus "x" Subscript, "s" "t" "a" "r" "t" , Baseline , StartFraction, "y" Subscript, "e" "n" "d" , Baseline minus "y" Subscript, "s" "t" "a" "r" "t" , Baseline Over 2 , EndFraction plus "y" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis

Étiquette:

equals

left parenthesis, 116.8 9 8 5 8 8 , 116.7 0 0 7 9 , right parenthesis

X in: ${x_{in}} left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline plus StartFraction, "x" Subscript, "i" "n" , Baseline Over 2 , EndFraction , "y" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis

Étiquette:

equals

left parenthesis, 116.8 9 8 1 7 5 , 177 , right parenthesis

X out: ${x_{out}} left parenthesis, "x" Subscript, "s" "t" "a" "r" "t" , Baseline minus StartFraction, "x" Subscript, "o" "u" "t" , Baseline Over 2 , EndFraction , "y" Subscript, "s" "t" "a" "r" "t" , Baseline , right parenthesis

Étiquette:

indéfini

Y in: ${y_{in}} left parenthesis, "x" Subscript, "e" "n" "d" , Baseline , "y" Subscript, "s" "t" "a" "r" "t" , Baseline plus StartFraction, "y" Subscript, "i" "n" , Baseline Over 2 , EndFraction , right parenthesis

Étiquette:

indéfini

Y out: ${y_{out}} left parenthesis, "x" Subscript, "e" "n" "d" , Baseline , "y" Subscript, "s" "t" "a" "r" "t" , Baseline minus StartFraction, "y" Subscript, "o" "u" "t" , Baseline Over 2 , EndFraction , right parenthesis

Étiquette:

equals

left parenthesis, 177.3 , 116.7 0 1 , right parenthesis

Expression 51:

Expression 52:

propulsé par

Start price: 3.132

End price: 0.318

Execution price: 0.998

X in: 120.802

Y out: 120.598