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

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

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: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+41}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3e+15) (- y) (if (<= y 6.8e+41) (- 1.0 x) (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3e+15) {
		tmp = -y;
	} else if (y <= 6.8e+41) {
		tmp = 1.0 - 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 (y <= (-3d+15)) then
        tmp = -y
    else if (y <= 6.8d+41) then
        tmp = 1.0d0 - x
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3e+15) {
		tmp = -y;
	} else if (y <= 6.8e+41) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3e+15:
		tmp = -y
	elif y <= 6.8e+41:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3e+15)
		tmp = Float64(-y);
	elseif (y <= 6.8e+41)
		tmp = Float64(1.0 - x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3e+15)
		tmp = -y;
	elseif (y <= 6.8e+41)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3e+15], (-y), If[LessEqual[y, 6.8e+41], N[(1.0 - x), $MachinePrecision], (-y)]]

Derivation

1. Split input into 2 regimes

2. if y < -3e15 or 6.79999999999999996e41 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   4. Simplified 79.1%

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

   if -3e15 < y < 6.79999999999999996e41

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+41}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 87.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+40}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+15) (- 1.0 y) (if (<= y 3e+40) (- 1.0 x) (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = 1.0 - y;
	} else if (y <= 3e+40) {
		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 (y <= (-4.2d+15)) then
        tmp = 1.0d0 - y
    else if (y <= 3d+40) 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 (y <= -4.2e+15) {
		tmp = 1.0 - y;
	} else if (y <= 3e+40) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+15:
		tmp = 1.0 - y
	elif y <= 3e+40:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = Float64(1.0 - y);
	elseif (y <= 3e+40)
		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 (y <= -4.2e+15)
		tmp = 1.0 - y;
	elseif (y <= 3e+40)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+15], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 3e+40], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e15 or 3.0000000000000002e40 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.1%

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

   if -4.2e15 < y < 3.0000000000000002e40

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.2%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+40}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 4: 62.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+38}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.4e+15) (- y) (if (<= y 3.1e+38) (- x) (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.4e+15) {
		tmp = -y;
	} else if (y <= 3.1e+38) {
		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 (y <= (-8.4d+15)) then
        tmp = -y
    else if (y <= 3.1d+38) then
        tmp = -x
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.4e+15) {
		tmp = -y;
	} else if (y <= 3.1e+38) {
		tmp = -x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.4e+15:
		tmp = -y
	elif y <= 3.1e+38:
		tmp = -x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.4e+15)
		tmp = Float64(-y);
	elseif (y <= 3.1e+38)
		tmp = Float64(-x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.4e+15)
		tmp = -y;
	elseif (y <= 3.1e+38)
		tmp = -x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.4e+15], (-y), If[LessEqual[y, 3.1e+38], (-x), (-y)]]

Derivation

1. Split input into 2 regimes

2. if y < -8.4e15 or 3.10000000000000018e38 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   4. Simplified 79.1%

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

   if -8.4e15 < y < 3.10000000000000018e38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 49.5%

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

      1. neg-mul-1 49.5%

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

   4. Simplified 49.5%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.4 \cdot 10^{+15}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+38}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5: 37.0% 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 36.4%

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

   1. neg-mul-1 36.4%

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

4. Simplified 36.4%

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

5. Final simplification 36.4%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))