Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B

Percentage Accurate: 99.8% → 99.8%

Time: 7.4s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot \sin y + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x * math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x * sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \sin y + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x * math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x * sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \sin y + z \cdot \cos y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x (sin y)) (* z (cos y))))

C

double code(double x, double y, double z) {
	return (x * sin(y)) + (z * cos(y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = (x * sin(y)) + (z * cos(y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * Math.sin(y)) + (z * Math.cos(y));
}

Python

def code(x, y, z):
	return (x * math.sin(y)) + (z * math.cos(y))

Julia

function code(x, y, z)
	return Float64(Float64(x * sin(y)) + Float64(z * cos(y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * sin(y)) + (z * cos(y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 73.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -150 \lor \neg \left(x \leq 4.45 \cdot 10^{+24}\right) \land \left(x \leq 4.5 \cdot 10^{+68} \lor \neg \left(x \leq 1.75 \cdot 10^{+148}\right)\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -150.0)
         (and (not (<= x 4.45e+24))
              (or (<= x 4.5e+68) (not (<= x 1.75e+148)))))
   (* x (sin y))
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -150.0) || (!(x <= 4.45e+24) && ((x <= 4.5e+68) || !(x <= 1.75e+148)))) {
		tmp = x * sin(y);
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-150.0d0)) .or. (.not. (x <= 4.45d+24)) .and. (x <= 4.5d+68) .or. (.not. (x <= 1.75d+148))) then
        tmp = x * sin(y)
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -150.0) || (!(x <= 4.45e+24) && ((x <= 4.5e+68) || !(x <= 1.75e+148)))) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -150.0) or (not (x <= 4.45e+24) and ((x <= 4.5e+68) or not (x <= 1.75e+148))):
		tmp = x * math.sin(y)
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -150.0) || (!(x <= 4.45e+24) && ((x <= 4.5e+68) || !(x <= 1.75e+148))))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -150.0) || (~((x <= 4.45e+24)) && ((x <= 4.5e+68) || ~((x <= 1.75e+148)))))
		tmp = x * sin(y);
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -150.0], And[N[Not[LessEqual[x, 4.45e+24]], $MachinePrecision], Or[LessEqual[x, 4.5e+68], N[Not[LessEqual[x, 1.75e+148]], $MachinePrecision]]]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -150 or 4.45000000000000011e24 < x < 4.5000000000000003e68 or 1.7499999999999999e148 < x

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.7%

      \[\leadsto \color{blue}{x \cdot \sin y} \]

   if -150 < x < 4.45000000000000011e24 or 4.5000000000000003e68 < x < 1.7499999999999999e148

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 82.3%

      \[\leadsto \color{blue}{z \cdot \cos y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -150 \lor \neg \left(x \leq 4.45 \cdot 10^{+24}\right) \land \left(x \leq 4.5 \cdot 10^{+68} \lor \neg \left(x \leq 1.75 \cdot 10^{+148}\right)\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.96 \cdot 10^{-103} \lor \neg \left(x \leq 1.8 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.96e-103) (not (<= x 1.8e+14)))
   (+ (* x (sin y)) z)
   (* z (cos y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.96e-103) || !(x <= 1.8e+14)) {
		tmp = (x * sin(y)) + z;
	} else {
		tmp = z * cos(y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.96d-103)) .or. (.not. (x <= 1.8d+14))) then
        tmp = (x * sin(y)) + z
    else
        tmp = z * cos(y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.96e-103) || !(x <= 1.8e+14)) {
		tmp = (x * Math.sin(y)) + z;
	} else {
		tmp = z * Math.cos(y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.96e-103) or not (x <= 1.8e+14):
		tmp = (x * math.sin(y)) + z
	else:
		tmp = z * math.cos(y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.96e-103) || !(x <= 1.8e+14))
		tmp = Float64(Float64(x * sin(y)) + z);
	else
		tmp = Float64(z * cos(y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.96e-103) || ~((x <= 1.8e+14)))
		tmp = (x * sin(y)) + z;
	else
		tmp = z * cos(y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.96e-103], N[Not[LessEqual[x, 1.8e+14]], $MachinePrecision]], N[(N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision] + z), $MachinePrecision], N[(z * N[Cos[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9600000000000001e-103 or 1.8e14 < x

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 88.4%

      \[\leadsto x \cdot \sin y + \color{blue}{z} \]

   if -1.9600000000000001e-103 < x < 1.8e14

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 87.0%

      \[\leadsto \color{blue}{z \cdot \cos y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.96 \cdot 10^{-103} \lor \neg \left(x \leq 1.8 \cdot 10^{+14}\right):\\ \;\;\;\;x \cdot \sin y + z\\ \mathbf{else}:\\ \;\;\;\;z \cdot \cos y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0152 \lor \neg \left(y \leq 0.00375\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -0.0152) (not (<= y 0.00375)))
   (* x (sin y))
   (+ z (* y (+ x (* -0.5 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0152) || !(y <= 0.00375)) {
		tmp = x * sin(y);
	} else {
		tmp = z + (y * (x + (-0.5 * (y * z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-0.0152d0)) .or. (.not. (y <= 0.00375d0))) then
        tmp = x * sin(y)
    else
        tmp = z + (y * (x + ((-0.5d0) * (y * z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -0.0152) || !(y <= 0.00375)) {
		tmp = x * Math.sin(y);
	} else {
		tmp = z + (y * (x + (-0.5 * (y * z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -0.0152) or not (y <= 0.00375):
		tmp = x * math.sin(y)
	else:
		tmp = z + (y * (x + (-0.5 * (y * z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -0.0152) || !(y <= 0.00375))
		tmp = Float64(x * sin(y));
	else
		tmp = Float64(z + Float64(y * Float64(x + Float64(-0.5 * Float64(y * z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -0.0152) || ~((y <= 0.00375)))
		tmp = x * sin(y);
	else
		tmp = z + (y * (x + (-0.5 * (y * z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -0.0152], N[Not[LessEqual[y, 0.00375]], $MachinePrecision]], N[(x * N[Sin[y], $MachinePrecision]), $MachinePrecision], N[(z + N[(y * N[(x + N[(-0.5 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.0152 or 0.0037499999999999999 < y

   1. Initial program 99.7%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 52.9%

      \[\leadsto \color{blue}{x \cdot \sin y} \]

   if -0.0152 < y < 0.0037499999999999999

   1. Initial program 100.0%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)} \]
   4. Step-by-step derivation

      1. *-commutative 100.0%

         \[\leadsto z + y \cdot \left(x + -0.5 \cdot \color{blue}{\left(z \cdot y\right)}\right) \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{z + y \cdot \left(x + -0.5 \cdot \left(z \cdot y\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.0152 \lor \neg \left(y \leq 0.00375\right):\\ \;\;\;\;x \cdot \sin y\\ \mathbf{else}:\\ \;\;\;\;z + y \cdot \left(x + -0.5 \cdot \left(y \cdot z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 39.7% accurate, 25.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.3 \cdot 10^{+83}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= x -6.3e+83) (* x y) z))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.3e+83) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-6.3d+83)) then
        tmp = x * y
    else
        tmp = z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.3e+83) {
		tmp = x * y;
	} else {
		tmp = z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.3e+83:
		tmp = x * y
	else:
		tmp = z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.3e+83)
		tmp = Float64(x * y);
	else
		tmp = z;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.3e+83)
		tmp = x * y;
	else
		tmp = z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.3e+83], N[(x * y), $MachinePrecision], z]

Derivation

1. Split input into 2 regimes

2. if x < -6.30000000000000034e83

   1. Initial program 99.9%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

      \[\leadsto \color{blue}{x \cdot \left(\sin y + \frac{z \cdot \cos y}{x}\right)} \]
   4. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto x \cdot \left(\sin y + \color{blue}{z \cdot \frac{\cos y}{x}}\right) \]

   5. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \left(\sin y + z \cdot \frac{\cos y}{x}\right)} \]

   6. Taylor expanded in y around 0 46.7%

      \[\leadsto x \cdot \color{blue}{\left(y + \frac{z}{x}\right)} \]

   7. Taylor expanded in x around inf 29.3%

      \[\leadsto \color{blue}{x \cdot y} \]

   if -6.30000000000000034e83 < x

   1. Initial program 99.8%

      \[x \cdot \sin y + z \cdot \cos y \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{z \cdot \cos y + x \cdot \sin y} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\cos y \cdot z} + x \cdot \sin y \]

      3. add-sqr-sqrt 43.3%

         \[\leadsto \cos y \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} + x \cdot \sin y \]

      4. associate-*r* 43.3%

         \[\leadsto \color{blue}{\left(\cos y \cdot \sqrt{z}\right) \cdot \sqrt{z}} + x \cdot \sin y \]

      5. fma-define 43.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{z}, \sqrt{z}, x \cdot \sin y\right)} \]

   4. Applied egg-rr 43.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{z}, \sqrt{z}, x \cdot \sin y\right)} \]

   5. Taylor expanded in y around 0 40.3%

      \[\leadsto \color{blue}{z} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 52.2% accurate, 41.4× speedup

Math

\[\begin{array}{l} \\ z + x \cdot y \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ z (* x y)))

C

double code(double x, double y, double z) {
	return z + (x * y);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z + (x * y)
end function

Java

public static double code(double x, double y, double z) {
	return z + (x * y);
}

Python

def code(x, y, z):
	return z + (x * y)

Julia

function code(x, y, z)
	return Float64(z + Float64(x * y))
end

MATLAB

function tmp = code(x, y, z)
	tmp = z + (x * y);
end

Wolfram

code[x_, y_, z_] := N[(z + N[(x * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing

3. Taylor expanded in y around 0 47.2%

   \[\leadsto \color{blue}{z + x \cdot y} \]
4. Step-by-step derivation

   1. *-commutative 47.2%

      \[\leadsto z + \color{blue}{y \cdot x} \]

5. Simplified 47.2%

   \[\leadsto \color{blue}{z + y \cdot x} \]

6. Final simplification 47.2%

   \[\leadsto z + x \cdot y \]
7. Add Preprocessing

Alternative 7: 38.5% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 z)

C

double code(double x, double y, double z) {
	return z;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z
end function

Java

public static double code(double x, double y, double z) {
	return z;
}

Python

def code(x, y, z):
	return z

Julia

function code(x, y, z)
	return z
end

MATLAB

function tmp = code(x, y, z)
	tmp = z;
end

Wolfram

code[x_, y_, z_] := z

Derivation

1. Initial program 99.8%

   \[x \cdot \sin y + z \cdot \cos y \]
2. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.8%

      \[\leadsto \color{blue}{z \cdot \cos y + x \cdot \sin y} \]

   2. *-commutative 99.8%

      \[\leadsto \color{blue}{\cos y \cdot z} + x \cdot \sin y \]

   3. add-sqr-sqrt 45.8%

      \[\leadsto \cos y \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)} + x \cdot \sin y \]

   4. associate-*r* 45.8%

      \[\leadsto \color{blue}{\left(\cos y \cdot \sqrt{z}\right) \cdot \sqrt{z}} + x \cdot \sin y \]

   5. fma-define 45.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{z}, \sqrt{z}, x \cdot \sin y\right)} \]

4. Applied egg-rr 45.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y \cdot \sqrt{z}, \sqrt{z}, x \cdot \sin y\right)} \]

5. Taylor expanded in y around 0 36.8%

   \[\leadsto \color{blue}{z} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024089 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))