Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 5

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

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

Python

def code(x, y):
	return (1.0 - x) - y

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

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

Python

def code(x, y):
	return (1.0 - x) - y

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (1.0d0 - x) - y
end function

Java

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

Python

def code(x, y):
	return (1.0 - x) - y

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]

2. Final simplification 100.0%

   \[\leadsto \left(1 - x\right) - y \]

Alternative 2: 84.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq -2 \cdot 10^{+161}:\\ \;\;\;\;-x\\ \mathbf{elif}\;1 - x \leq -2 \cdot 10^{+92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;1 - x \leq -4000000000 \lor \neg \left(1 - x \leq 2\right):\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- 1.0 x) -2e+161)
   (- x)
   (if (<= (- 1.0 x) -2e+92)
     (- y)
     (if (or (<= (- 1.0 x) -4000000000.0) (not (<= (- 1.0 x) 2.0)))
       (- 1.0 x)
       (- 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= -2e+161) {
		tmp = -x;
	} else if ((1.0 - x) <= -2e+92) {
		tmp = -y;
	} else if (((1.0 - x) <= -4000000000.0) || !((1.0 - x) <= 2.0)) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((1.0d0 - x) <= (-2d+161)) then
        tmp = -x
    else if ((1.0d0 - x) <= (-2d+92)) then
        tmp = -y
    else if (((1.0d0 - x) <= (-4000000000.0d0)) .or. (.not. ((1.0d0 - x) <= 2.0d0))) then
        tmp = 1.0d0 - x
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= -2e+161) {
		tmp = -x;
	} else if ((1.0 - x) <= -2e+92) {
		tmp = -y;
	} else if (((1.0 - x) <= -4000000000.0) || !((1.0 - x) <= 2.0)) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (1.0 - x) <= -2e+161:
		tmp = -x
	elif (1.0 - x) <= -2e+92:
		tmp = -y
	elif ((1.0 - x) <= -4000000000.0) or not ((1.0 - x) <= 2.0):
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - x) <= -2e+161)
		tmp = Float64(-x);
	elseif (Float64(1.0 - x) <= -2e+92)
		tmp = Float64(-y);
	elseif ((Float64(1.0 - x) <= -4000000000.0) || !(Float64(1.0 - x) <= 2.0))
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((1.0 - x) <= -2e+161)
		tmp = -x;
	elseif ((1.0 - x) <= -2e+92)
		tmp = -y;
	elseif (((1.0 - x) <= -4000000000.0) || ~(((1.0 - x) <= 2.0)))
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(1.0 - x), $MachinePrecision], -2e+161], (-x), If[LessEqual[N[(1.0 - x), $MachinePrecision], -2e+92], (-y), If[Or[LessEqual[N[(1.0 - x), $MachinePrecision], -4000000000.0], N[Not[LessEqual[N[(1.0 - x), $MachinePrecision], 2.0]], $MachinePrecision]], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if (-.f64 1 x) < -2.0000000000000001e161

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around inf 89.1%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 89.1%

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

   4. Simplified 89.1%

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

   if -2.0000000000000001e161 < (-.f64 1 x) < -2.0000000000000001e92

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around inf 75.0%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. neg-mul-1 75.0%

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

   4. Simplified 75.0%

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

   if -2.0000000000000001e92 < (-.f64 1 x) < -4e9 or 2 < (-.f64 1 x)

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around 0 75.2%

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

   if -4e9 < (-.f64 1 x) < 2

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{1 - y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq -2 \cdot 10^{+161}:\\ \;\;\;\;-x\\ \mathbf{elif}\;1 - x \leq -2 \cdot 10^{+92}:\\ \;\;\;\;-y\\ \mathbf{elif}\;1 - x \leq -4000000000 \lor \neg \left(1 - x \leq 2\right):\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2400000 \lor \neg \left(y \leq 3350\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2400000.0) (not (<= y 3350.0))) (- y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2400000.0) || !(y <= 3350.0)) {
		tmp = -y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2400000.0d0)) .or. (.not. (y <= 3350.0d0))) then
        tmp = -y
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2400000.0) || !(y <= 3350.0)) {
		tmp = -y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2400000.0) or not (y <= 3350.0):
		tmp = -y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2400000.0) || !(y <= 3350.0))
		tmp = Float64(-y);
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2400000.0) || ~((y <= 3350.0)))
		tmp = -y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2400000.0], N[Not[LessEqual[y, 3350.0]], $MachinePrecision]], (-y), N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4e6 or 3350 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. neg-mul-1 72.8%

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

   4. Simplified 72.8%

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

   if -2.4e6 < y < 3350

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around 0 99.1%

      \[\leadsto \color{blue}{1 - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2400000 \lor \neg \left(y \leq 3350\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 4: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -10000000 \lor \neg \left(y \leq 19500\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -10000000.0) (not (<= y 19500.0))) (- y) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -10000000.0) || !(y <= 19500.0)) {
		tmp = -y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-10000000.0d0)) .or. (.not. (y <= 19500.0d0))) then
        tmp = -y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -10000000.0) || !(y <= 19500.0)) {
		tmp = -y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -10000000.0) or not (y <= 19500.0):
		tmp = -y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -10000000.0) || !(y <= 19500.0))
		tmp = Float64(-y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -10000000.0) || ~((y <= 19500.0)))
		tmp = -y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -10000000.0], N[Not[LessEqual[y, 19500.0]], $MachinePrecision]], (-y), (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -1e7 or 19500 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in y around inf 72.8%

      \[\leadsto \color{blue}{-1 \cdot y} \]
   3. Step-by-step derivation

      1. neg-mul-1 72.8%

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

   4. Simplified 72.8%

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

   if -1e7 < y < 19500

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]

   2. Taylor expanded in x around inf 46.2%

      \[\leadsto \color{blue}{-1 \cdot x} \]
   3. Step-by-step derivation

      1. neg-mul-1 46.2%

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

   4. Simplified 46.2%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -10000000 \lor \neg \left(y \leq 19500\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 38.4% accurate, 2.5× 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 Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]

2. Taylor expanded in x around inf 36.5%

   \[\leadsto \color{blue}{-1 \cdot x} \]
3. Step-by-step derivation

   1. neg-mul-1 36.5%

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

4. Simplified 36.5%

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

5. Final simplification 36.5%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023305 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))