Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3

Percentage Accurate: 97.6% → 100.0%

Time: 7.3s

Alternatives: 5

Speedup: 1.7×

• 21.1% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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 * y) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot y + z \cdot \left(1 - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ (* x y) (* z (- 1.0 y))))

C

double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - 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 * y) + (z * (1.0d0 - y))
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) + (z * (1.0 - y));
}

Python

def code(x, y, z):
	return (x * y) + (z * (1.0 - y))

Julia

function code(x, y, z)
	return Float64(Float64(x * y) + Float64(z * Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) + (z * (1.0 - y));
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x - z, z\right) \end{array} \]

FPCore

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

C

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

Julia

function code(x, y, z)
	return fma(y, Float64(x - z), z)
end

Wolfram

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

Derivation

1. Initial program 96.9%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{x \cdot y + z \cdot \left(1 - y\right)} \]
4. Step-by-step derivation

   1. distribute-rgt-out-- N/A

      \[\leadsto x \cdot y + \color{blue}{\left(1 \cdot z - y \cdot z\right)} \]

   2. unsub-neg N/A

      \[\leadsto x \cdot y + \color{blue}{\left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right)} \]

   3. *-lft-identity N/A

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

   4. mul-1-neg N/A

      \[\leadsto x \cdot y + \left(z + \color{blue}{-1 \cdot \left(y \cdot z\right)}\right) \]

   5. +-commutative N/A

      \[\leadsto x \cdot y + \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + z\right)} \]

   6. associate-+l+ N/A

      \[\leadsto \color{blue}{\left(x \cdot y + -1 \cdot \left(y \cdot z\right)\right) + z} \]

   7. *-commutative N/A

      \[\leadsto \left(\color{blue}{y \cdot x} + -1 \cdot \left(y \cdot z\right)\right) + z \]

   8. mul-1-neg N/A

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

   9. distribute-rgt-neg-in N/A

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

   10. mul-1-neg N/A

       \[\leadsto \left(y \cdot x + y \cdot \color{blue}{\left(-1 \cdot z\right)}\right) + z \]

   11. distribute-lft-in N/A

       \[\leadsto \color{blue}{y \cdot \left(x + -1 \cdot z\right)} + z \]

   12. +-commutative N/A

       \[\leadsto y \cdot \color{blue}{\left(-1 \cdot z + x\right)} + z \]

   13. mul-1-neg N/A

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

   14. remove-double-neg N/A

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

   15. mul-1-neg N/A

       \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot x}\right)\right)\right) + z \]

   16. distribute-neg-in N/A

       \[\leadsto y \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z + -1 \cdot x\right)\right)\right)} + z \]

   17. accelerator-lowering-fma.f64 N/A

       \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{neg}\left(\left(z + -1 \cdot x\right)\right), z\right)} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, z\right)} \]
6. Add Preprocessing

Alternative 2: 86.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(0 - y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.5e-72)
   (fma y x z)
   (if (<= x 7.3e-65) (fma (- 0.0 y) z z) (fma y x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.5e-72) {
		tmp = fma(y, x, z);
	} else if (x <= 7.3e-65) {
		tmp = fma((0.0 - y), z, z);
	} else {
		tmp = fma(y, x, z);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.5e-72)
		tmp = fma(y, x, z);
	elseif (x <= 7.3e-65)
		tmp = fma(Float64(0.0 - y), z, z);
	else
		tmp = fma(y, x, z);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.5e-72], N[(y * x + z), $MachinePrecision], If[LessEqual[x, 7.3e-65], N[(N[(0.0 - y), $MachinePrecision] * z + z), $MachinePrecision], N[(y * x + z), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -3.5e-72 or 7.2999999999999998e-65 < x

   1. Initial program 95.1%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Simplified 87.7%

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

      1. *-commutative N/A

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

      2. accelerator-lowering-fma.f64 87.7

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

   7. Applied egg-rr 87.7%

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

   if -3.5e-72 < x < 7.2999999999999998e-65

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{x \cdot y + z \cdot \left(1 - y\right)} \]
   4. Step-by-step derivation

      1. distribute-rgt-out-- N/A

         \[\leadsto x \cdot y + \color{blue}{\left(1 \cdot z - y \cdot z\right)} \]

      2. unsub-neg N/A

         \[\leadsto x \cdot y + \color{blue}{\left(1 \cdot z + \left(\mathsf{neg}\left(y \cdot z\right)\right)\right)} \]

      3. *-lft-identity N/A

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

      4. mul-1-neg N/A

         \[\leadsto x \cdot y + \left(z + \color{blue}{-1 \cdot \left(y \cdot z\right)}\right) \]

      5. +-commutative N/A

         \[\leadsto x \cdot y + \color{blue}{\left(-1 \cdot \left(y \cdot z\right) + z\right)} \]

      6. associate-+l+ N/A

         \[\leadsto \color{blue}{\left(x \cdot y + -1 \cdot \left(y \cdot z\right)\right) + z} \]

      7. *-commutative N/A

         \[\leadsto \left(\color{blue}{y \cdot x} + -1 \cdot \left(y \cdot z\right)\right) + z \]

      8. mul-1-neg N/A

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

      9. distribute-rgt-neg-in N/A

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

      10. mul-1-neg N/A

          \[\leadsto \left(y \cdot x + y \cdot \color{blue}{\left(-1 \cdot z\right)}\right) + z \]

      11. distribute-lft-in N/A

          \[\leadsto \color{blue}{y \cdot \left(x + -1 \cdot z\right)} + z \]

      12. +-commutative N/A

          \[\leadsto y \cdot \color{blue}{\left(-1 \cdot z + x\right)} + z \]

      13. mul-1-neg N/A

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

      14. remove-double-neg N/A

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

      15. mul-1-neg N/A

          \[\leadsto y \cdot \left(\left(\mathsf{neg}\left(z\right)\right) + \left(\mathsf{neg}\left(\color{blue}{-1 \cdot x}\right)\right)\right) + z \]

      16. distribute-neg-in N/A

          \[\leadsto y \cdot \color{blue}{\left(\mathsf{neg}\left(\left(z + -1 \cdot x\right)\right)\right)} + z \]

      17. accelerator-lowering-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(y, \mathsf{neg}\left(\left(z + -1 \cdot x\right)\right), z\right)} \]

   5. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x - z, z\right)} \]
   6. Step-by-step derivation

      1. sub-neg N/A

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

      2. distribute-lft-in N/A

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

      3. associate-+l+ N/A

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

      4. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, y \cdot \left(\mathsf{neg}\left(z\right)\right) + z\right)} \]

      5. accelerator-lowering-fma.f64 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \color{blue}{\mathsf{fma}\left(y, \mathsf{neg}\left(z\right), z\right)}\right) \]

      6. neg-sub0 N/A

         \[\leadsto \mathsf{fma}\left(y, x, \mathsf{fma}\left(y, \color{blue}{0 - z}, z\right)\right) \]

      7. --lowering--.f64 100.0

         \[\leadsto \mathsf{fma}\left(y, x, \mathsf{fma}\left(y, \color{blue}{0 - z}, z\right)\right) \]

   7. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, \mathsf{fma}\left(y, 0 - z, z\right)\right)} \]
   8. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(y \cdot x + y \cdot \left(0 - z\right)\right) + z} \]

      2. +-commutative N/A

         \[\leadsto \color{blue}{\left(y \cdot \left(0 - z\right) + y \cdot x\right)} + z \]

      3. associate-+r+ N/A

         \[\leadsto \color{blue}{y \cdot \left(0 - z\right) + \left(y \cdot x + z\right)} \]

      4. sub0-neg N/A

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

      5. distribute-rgt-neg-out N/A

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

      6. distribute-lft-neg-in N/A

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

      7. accelerator-lowering-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{neg}\left(y\right), z, y \cdot x + z\right)} \]

      8. neg-lowering-neg.f64 N/A

         \[\leadsto \mathsf{fma}\left(\color{blue}{\mathsf{neg}\left(y\right)}, z, y \cdot x + z\right) \]

      9. accelerator-lowering-fma.f64 100.0

         \[\leadsto \mathsf{fma}\left(-y, z, \color{blue}{\mathsf{fma}\left(y, x, z\right)}\right) \]

   9. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-y, z, \mathsf{fma}\left(y, x, z\right)\right)} \]

   10. Taylor expanded in y around 0

       \[\leadsto \mathsf{fma}\left(\mathsf{neg}\left(y\right), z, \color{blue}{z}\right) \]
   11. Step-by-step derivation

   12. Simplified 85.9%

       \[\leadsto \mathsf{fma}\left(-y, z, \color{blue}{z}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.5 \cdot 10^{-72}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \mathbf{elif}\;x \leq 7.3 \cdot 10^{-65}:\\ \;\;\;\;\mathsf{fma}\left(0 - y, z, z\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y, x, z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-61}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-110}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6e-61) (* y x) (if (<= y 2e-110) z (* y x))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-61) {
		tmp = y * x;
	} else if (y <= 2e-110) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	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 <= (-6d-61)) then
        tmp = y * x
    else if (y <= 2d-110) then
        tmp = z
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e-61) {
		tmp = y * x;
	} else if (y <= 2e-110) {
		tmp = z;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6e-61:
		tmp = y * x
	elif y <= 2e-110:
		tmp = z
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6e-61)
		tmp = Float64(y * x);
	elseif (y <= 2e-110)
		tmp = z;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6e-61)
		tmp = y * x;
	elseif (y <= 2e-110)
		tmp = z;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6e-61], N[(y * x), $MachinePrecision], If[LessEqual[y, 2e-110], z, N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.00000000000000024e-61 or 2.0000000000000001e-110 < y

   1. Initial program 95.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

      1. +-rgt-identity N/A

         \[\leadsto \color{blue}{x \cdot y + 0} \]

      2. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot x} + 0 \]

      3. accelerator-lowering-fma.f64 58.4

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 0\right)} \]

   5. Simplified 58.4%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-lowering-*.f64 58.4

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

   7. Applied egg-rr 58.4%

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

   if -6.00000000000000024e-61 < y < 2.0000000000000001e-110

   1. Initial program 100.0%

      \[x \cdot y + z \cdot \left(1 - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

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

   5. Simplified 82.5%

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

Alternative 4: 76.2% accurate, 2.4× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, x, z\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 96.9%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

5. Simplified 77.8%

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

   1. *-commutative N/A

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

   2. accelerator-lowering-fma.f64 77.8

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

7. Applied egg-rr 77.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, x, z\right)} \]
8. Add Preprocessing

Alternative 5: 35.8% accurate, 17.0× 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 96.9%

   \[x \cdot y + z \cdot \left(1 - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around 0

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

5. Simplified 35.7%

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

Developer Target 1: 100.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ z - \left(z - x\right) \cdot y \end{array} \]

FPCore

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

C

double code(double x, double y, double z) {
	return z - ((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 - ((z - x) * y)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024196 
(FPCore (x y z)
  :name "Diagrams.TwoD.Segment:bezierClip from diagrams-lib-1.3.0.3"
  :precision binary64

  :alt
  (! :herbie-platform default (- z (* (- z x) y)))

  (+ (* x y) (* z (- 1.0 y))))