Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.9% → 99.0%

Time: 5.2s

Alternatives: 4

Speedup: 0.5×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-66} \lor \neg \left(y \leq 5.2 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{2}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2e-66) (not (<= y 5.2e-116)))
   (* x (* 2.0 (/ y (- x y))))
   (* y (* x (/ 2.0 (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2e-66) || !(y <= 5.2e-116)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * (x * (2.0 / (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2d-66)) .or. (.not. (y <= 5.2d-116))) then
        tmp = x * (2.0d0 * (y / (x - y)))
    else
        tmp = y * (x * (2.0d0 / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2e-66) || !(y <= 5.2e-116)) {
		tmp = x * (2.0 * (y / (x - y)));
	} else {
		tmp = y * (x * (2.0 / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2e-66) or not (y <= 5.2e-116):
		tmp = x * (2.0 * (y / (x - y)))
	else:
		tmp = y * (x * (2.0 / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2e-66) || !(y <= 5.2e-116))
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	else
		tmp = Float64(y * Float64(x * Float64(2.0 / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2e-66) || ~((y <= 5.2e-116)))
		tmp = x * (2.0 * (y / (x - y)));
	else
		tmp = y * (x * (2.0 / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2e-66], N[Not[LessEqual[y, 5.2e-116]], $MachinePrecision]], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x * N[(2.0 / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2e-66 or 5.2000000000000001e-116 < y

   1. Initial program 80.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   if -2e-66 < y < 5.2000000000000001e-116

   1. Initial program 74.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*l* 74.6%

         \[\leadsto \frac{\color{blue}{x \cdot \left(2 \cdot y\right)}}{x - y} \]

      2. associate-*r/ 69.9%

         \[\leadsto \color{blue}{x \cdot \frac{2 \cdot y}{x - y}} \]

      3. associate-*l/ 69.7%

         \[\leadsto x \cdot \color{blue}{\left(\frac{2}{x - y} \cdot y\right)} \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(x \cdot \frac{2}{x - y}\right) \cdot y} \]

   4. Applied egg-rr 99.7%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-66} \lor \neg \left(y \leq 5.2 \cdot 10^{-116}\right):\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{2}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+91} \lor \neg \left(x \leq 1.45 \cdot 10^{-51}\right) \land \left(x \leq 1.96 \cdot 10^{+43} \lor \neg \left(x \leq 1.9 \cdot 10^{+82}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.6e+91)
         (and (not (<= x 1.45e-51)) (or (<= x 1.96e+43) (not (<= x 1.9e+82)))))
   (* y 2.0)
   (* x -2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.6e+91) || (!(x <= 1.45e-51) && ((x <= 1.96e+43) || !(x <= 1.9e+82)))) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-4.6d+91)) .or. (.not. (x <= 1.45d-51)) .and. (x <= 1.96d+43) .or. (.not. (x <= 1.9d+82))) then
        tmp = y * 2.0d0
    else
        tmp = x * (-2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.6e+91) || (!(x <= 1.45e-51) && ((x <= 1.96e+43) || !(x <= 1.9e+82)))) {
		tmp = y * 2.0;
	} else {
		tmp = x * -2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.6e+91) or (not (x <= 1.45e-51) and ((x <= 1.96e+43) or not (x <= 1.9e+82))):
		tmp = y * 2.0
	else:
		tmp = x * -2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.6e+91) || (!(x <= 1.45e-51) && ((x <= 1.96e+43) || !(x <= 1.9e+82))))
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * -2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.6e+91) || (~((x <= 1.45e-51)) && ((x <= 1.96e+43) || ~((x <= 1.9e+82)))))
		tmp = y * 2.0;
	else
		tmp = x * -2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.6e+91], And[N[Not[LessEqual[x, 1.45e-51]], $MachinePrecision], Or[LessEqual[x, 1.96e+43], N[Not[LessEqual[x, 1.9e+82]], $MachinePrecision]]]], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.59999999999999982e91 or 1.44999999999999986e-51 < x < 1.9600000000000001e43 or 1.90000000000000017e82 < x

   1. Initial program 71.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 80.6%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 80.6%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 80.6%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 81.6%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 81.6%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 81.6%

      \[\leadsto \color{blue}{y \cdot 2} \]

   if -4.59999999999999982e91 < x < 1.44999999999999986e-51 or 1.9600000000000001e43 < x < 1.90000000000000017e82

   1. Initial program 83.4%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 83.2%

         \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]

      2. associate-/l* 83.0%

         \[\leadsto \color{blue}{\left(x \cdot \frac{2}{x - y}\right)} \cdot y \]

      3. associate-*l* 98.5%

         \[\leadsto \color{blue}{x \cdot \left(\frac{2}{x - y} \cdot y\right)} \]

      4. *-commutative 98.5%

         \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{2}{x - y}\right)} \]

   3. Simplified 98.5%

      \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{2}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 81.5%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+91} \lor \neg \left(x \leq 1.45 \cdot 10^{-51}\right) \land \left(x \leq 1.96 \cdot 10^{+43} \lor \neg \left(x \leq 1.9 \cdot 10^{+82}\right)\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot -2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+174} \lor \neg \left(x \leq 2.3 \cdot 10^{+174}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.5e+174) (not (<= x 2.3e+174)))
   (* y 2.0)
   (* x (* 2.0 (/ y (- x y))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.5e+174) || !(x <= 2.3e+174)) {
		tmp = y * 2.0;
	} else {
		tmp = x * (2.0 * (y / (x - 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 <= (-5.5d+174)) .or. (.not. (x <= 2.3d+174))) then
        tmp = y * 2.0d0
    else
        tmp = x * (2.0d0 * (y / (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.5e+174) || !(x <= 2.3e+174)) {
		tmp = y * 2.0;
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.5e+174) or not (x <= 2.3e+174):
		tmp = y * 2.0
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.5e+174) || !(x <= 2.3e+174))
		tmp = Float64(y * 2.0);
	else
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.5e+174) || ~((x <= 2.3e+174)))
		tmp = y * 2.0;
	else
		tmp = x * (2.0 * (y / (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.5e+174], N[Not[LessEqual[x, 2.3e+174]], $MachinePrecision]], N[(y * 2.0), $MachinePrecision], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.4999999999999998e174 or 2.2999999999999998e174 < x

   1. Initial program 58.0%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 64.2%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 64.2%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 64.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 97.8%

      \[\leadsto \color{blue}{2 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 97.8%

         \[\leadsto \color{blue}{y \cdot 2} \]

   7. Simplified 97.8%

      \[\leadsto \color{blue}{y \cdot 2} \]

   if -5.4999999999999998e174 < x < 2.2999999999999998e174

   1. Initial program 83.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-/l* 98.1%

         \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]

      2. associate-*l* 98.1%

         \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
   4. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+174} \lor \neg \left(x \leq 2.3 \cdot 10^{+174}\right):\\ \;\;\;\;y \cdot 2\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x -2.0))

C

double code(double x, double y) {
	return x * -2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (-2.0d0)
end function

Java

public static double code(double x, double y) {
	return x * -2.0;
}

Python

def code(x, y):
	return x * -2.0

Julia

function code(x, y)
	return Float64(x * -2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x * -2.0;
end

Wolfram

code[x_, y_] := N[(x * -2.0), $MachinePrecision]

Derivation

1. Initial program 78.6%

   \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
2. Step-by-step derivation

   1. associate-*l/ 89.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]

   2. associate-/l* 89.6%

      \[\leadsto \color{blue}{\left(x \cdot \frac{2}{x - y}\right)} \cdot y \]

   3. associate-*l* 91.2%

      \[\leadsto \color{blue}{x \cdot \left(\frac{2}{x - y} \cdot y\right)} \]

   4. *-commutative 91.2%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{2}{x - y}\right)} \]

3. Simplified 91.2%

   \[\leadsto \color{blue}{x \cdot \left(y \cdot \frac{2}{x - y}\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 56.7%

   \[\leadsto x \cdot \color{blue}{-2} \]

6. Final simplification 56.7%

   \[\leadsto x \cdot -2 \]
7. Add Preprocessing

Developer target: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024066 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

  (/ (* (* x 2.0) y) (- x y)))