Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 7

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, 1 - x, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y (- 1.0 x) x))

C

double code(double x, double y) {
	return fma(y, (1.0 - x), x);
}

Julia

function code(x, y)
	return fma(y, Float64(1.0 - x), x)
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]

2. Taylor expanded in x around 0 100.0%

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

   1. sub-neg 100.0%

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

   2. +-commutative 100.0%

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

   3. distribute-lft1-in 100.0%

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

   4. *-commutative 100.0%

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

   5. associate-+l+ 100.0%

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

   6. distribute-rgt-neg-out 100.0%

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

   7. sub-neg 100.0%

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

   8. *-lft-identity 100.0%

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

   9. distribute-rgt-out-- 100.0%

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

   10. *-commutative 100.0%

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

   11. *-commutative 100.0%

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

   12. fma-def 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, 1 - x, x\right) \]

Alternative 2: 60.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(-x\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-75}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3750000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62} \lor \neg \left(y \leq 3.5 \cdot 10^{+83}\right) \land \left(y \leq 1.1 \cdot 10^{+210} \lor \neg \left(y \leq 1.46 \cdot 10^{+248}\right)\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (- x))))
   (if (<= y -1.0)
     t_0
     (if (<= y 4.8e-120)
       x
       (if (<= y 1.2e-75)
         y
         (if (<= y 1.48e-52)
           x
           (if (<= y 3750000000.0)
             y
             (if (or (<= y 5e+62)
                     (and (not (<= y 3.5e+83))
                          (or (<= y 1.1e+210) (not (<= y 1.46e+248)))))
               t_0
               y))))))))

C

double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 4.8e-120) {
		tmp = x;
	} else if (y <= 1.2e-75) {
		tmp = y;
	} else if (y <= 1.48e-52) {
		tmp = x;
	} else if (y <= 3750000000.0) {
		tmp = y;
	} else if ((y <= 5e+62) || (!(y <= 3.5e+83) && ((y <= 1.1e+210) || !(y <= 1.46e+248)))) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * -x
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 4.8d-120) then
        tmp = x
    else if (y <= 1.2d-75) then
        tmp = y
    else if (y <= 1.48d-52) then
        tmp = x
    else if (y <= 3750000000.0d0) then
        tmp = y
    else if ((y <= 5d+62) .or. (.not. (y <= 3.5d+83)) .and. (y <= 1.1d+210) .or. (.not. (y <= 1.46d+248))) then
        tmp = t_0
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * -x;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 4.8e-120) {
		tmp = x;
	} else if (y <= 1.2e-75) {
		tmp = y;
	} else if (y <= 1.48e-52) {
		tmp = x;
	} else if (y <= 3750000000.0) {
		tmp = y;
	} else if ((y <= 5e+62) || (!(y <= 3.5e+83) && ((y <= 1.1e+210) || !(y <= 1.46e+248)))) {
		tmp = t_0;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * -x
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 4.8e-120:
		tmp = x
	elif y <= 1.2e-75:
		tmp = y
	elif y <= 1.48e-52:
		tmp = x
	elif y <= 3750000000.0:
		tmp = y
	elif (y <= 5e+62) or (not (y <= 3.5e+83) and ((y <= 1.1e+210) or not (y <= 1.46e+248))):
		tmp = t_0
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(-x))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 4.8e-120)
		tmp = x;
	elseif (y <= 1.2e-75)
		tmp = y;
	elseif (y <= 1.48e-52)
		tmp = x;
	elseif (y <= 3750000000.0)
		tmp = y;
	elseif ((y <= 5e+62) || (!(y <= 3.5e+83) && ((y <= 1.1e+210) || !(y <= 1.46e+248))))
		tmp = t_0;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * -x;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 4.8e-120)
		tmp = x;
	elseif (y <= 1.2e-75)
		tmp = y;
	elseif (y <= 1.48e-52)
		tmp = x;
	elseif (y <= 3750000000.0)
		tmp = y;
	elseif ((y <= 5e+62) || (~((y <= 3.5e+83)) && ((y <= 1.1e+210) || ~((y <= 1.46e+248)))))
		tmp = t_0;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * (-x)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 4.8e-120], x, If[LessEqual[y, 1.2e-75], y, If[LessEqual[y, 1.48e-52], x, If[LessEqual[y, 3750000000.0], y, If[Or[LessEqual[y, 5e+62], And[N[Not[LessEqual[y, 3.5e+83]], $MachinePrecision], Or[LessEqual[y, 1.1e+210], N[Not[LessEqual[y, 1.46e+248]], $MachinePrecision]]]], t$95$0, y]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.75e9 < y < 5.00000000000000029e62 or 3.49999999999999977e83 < y < 1.09999999999999993e210 or 1.46e248 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in x around inf 60.7%

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

   3. Taylor expanded in y around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-out 60.0%

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

   5. Simplified 60.0%

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

   if -1 < y < 4.7999999999999999e-120 or 1.2000000000000001e-75 < y < 1.47999999999999993e-52

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in y around 0 78.8%

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

   if 4.7999999999999999e-120 < y < 1.2000000000000001e-75 or 1.47999999999999993e-52 < y < 3.75e9 or 5.00000000000000029e62 < y < 3.49999999999999977e83 or 1.09999999999999993e210 < y < 1.46e248

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in x around 0 62.1%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{-120}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-75}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-52}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3750000000:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+62} \lor \neg \left(y \leq 3.5 \cdot 10^{+83}\right) \land \left(y \leq 1.1 \cdot 10^{+210} \lor \neg \left(y \leq 1.46 \cdot 10^{+248}\right)\right):\\ \;\;\;\;y \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 84.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-132} \lor \neg \left(x \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4e-132) (not (<= x 1.4e-18))) (* x (- 1.0 y)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4e-132) || !(x <= 1.4e-18)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4d-132)) .or. (.not. (x <= 1.4d-18))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4e-132) || !(x <= 1.4e-18)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4e-132) or not (x <= 1.4e-18):
		tmp = x * (1.0 - y)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4e-132) || !(x <= 1.4e-18))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4e-132) || ~((x <= 1.4e-18)))
		tmp = x * (1.0 - y);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4e-132], N[Not[LessEqual[x, 1.4e-18]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e-132 or 1.40000000000000006e-18 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in x around inf 89.3%

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

   if -3.9999999999999999e-132 < x < 1.40000000000000006e-18

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in x around 0 79.2%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-132} \lor \neg \left(x \leq 1.4 \cdot 10^{-18}\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 4: 72.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4e-132) (* x (- 1.0 y)) (- y (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e-132) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4d-132)) then
        tmp = x * (1.0d0 - y)
    else
        tmp = y - (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4e-132) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y - (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e-132:
		tmp = x * (1.0 - y)
	else:
		tmp = y - (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e-132)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y - Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e-132)
		tmp = x * (1.0 - y);
	else
		tmp = y - (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e-132], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y - N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e-132

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in x around inf 84.9%

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

   if -3.9999999999999999e-132 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in y around inf 71.4%

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

      1. distribute-lft-out-- 71.4%

         \[\leadsto \color{blue}{y \cdot 1 - y \cdot x} \]

      2. *-rgt-identity 71.4%

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

   4. Simplified 71.4%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-132}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y - y \cdot x\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]

2. Final simplification 100.0%

   \[\leadsto \left(y + x\right) - y \cdot x \]

Alternative 6: 47.7% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -4e-132) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4e-132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-4d-132)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4e-132) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4e-132:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4e-132)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4e-132)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4e-132], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -3.9999999999999999e-132

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in y around 0 48.6%

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

   if -3.9999999999999999e-132 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]

   2. Taylor expanded in x around 0 48.7%

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

4. Final simplification 48.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{-132}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 38.8% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]

2. Taylor expanded in y around 0 37.8%

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

3. Final simplification 37.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))