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

Percentage Accurate: 100.0% → 100.0%

Time: 2.3s

Alternatives: 6

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

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

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(1.0 - Float64(x + y))
end

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]
2. Step-by-step derivation

   1. associate--l- 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 49.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1850:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-22} \lor \neg \left(x \leq -4.4 \cdot 10^{-277}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1850.0)
   (- x)
   (if (or (<= x -4.5e-22) (not (<= x -4.4e-277))) (- y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1850.0) {
		tmp = -x;
	} else if ((x <= -4.5e-22) || !(x <= -4.4e-277)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1850.0d0)) then
        tmp = -x
    else if ((x <= (-4.5d-22)) .or. (.not. (x <= (-4.4d-277)))) then
        tmp = -y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1850.0) {
		tmp = -x;
	} else if ((x <= -4.5e-22) || !(x <= -4.4e-277)) {
		tmp = -y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1850.0:
		tmp = -x
	elif (x <= -4.5e-22) or not (x <= -4.4e-277):
		tmp = -y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1850.0)
		tmp = Float64(-x);
	elseif ((x <= -4.5e-22) || !(x <= -4.4e-277))
		tmp = Float64(-y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1850.0)
		tmp = -x;
	elseif ((x <= -4.5e-22) || ~((x <= -4.4e-277)))
		tmp = -y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1850.0], (-x), If[Or[LessEqual[x, -4.5e-22], N[Not[LessEqual[x, -4.4e-277]], $MachinePrecision]], (-y), 1.0]]

Derivation

1. Split input into 3 regimes

2. if x < -1850

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.8%

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

      1. mul-1-neg 80.8%

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

   7. Simplified 80.8%

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

   if -1850 < x < -4.49999999999999987e-22 or -4.39999999999999991e-277 < x

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 41.8%

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

      1. neg-mul-1 41.8%

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

   7. Simplified 41.8%

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

   if -4.49999999999999987e-22 < x < -4.39999999999999991e-277

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 56.1%

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

   6. Taylor expanded in x around 0 56.1%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1850:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-22} \lor \neg \left(x \leq -4.4 \cdot 10^{-277}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq 2:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (- 1.0 x) 2.0) (- 1.0 y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= 2.0) {
		tmp = 1.0 - 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 ((1.0d0 - x) <= 2.0d0) then
        tmp = 1.0d0 - y
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= 2.0) {
		tmp = 1.0 - y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (1.0 - x) <= 2.0:
		tmp = 1.0 - y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - x) <= 2.0)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((1.0 - x) <= 2.0)
		tmp = 1.0 - y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(1.0 - x), $MachinePrecision], 2.0], N[(1.0 - y), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 #s(literal 1 binary64) x) < 2

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 76.8%

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

   if 2 < (-.f64 #s(literal 1 binary64) x)

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 82.4%

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

Alternative 4: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 40000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 40000.0) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 40000.0) {
		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 <= 40000.0d0) 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 <= 40000.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 40000.0:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 40000.0)
		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 <= 40000.0)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 40000.0], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 4e4

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 77.1%

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

   if 4e4 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 83.6%

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

      1. neg-mul-1 83.6%

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

   7. Simplified 83.6%

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

Alternative 5: 43.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.0029:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -0.0029) (- x) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.0029) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-0.0029d0)) then
        tmp = -x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -0.0029) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.0029:
		tmp = -x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.0029)
		tmp = Float64(-x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.0029)
		tmp = -x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.0029], (-x), 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -0.0029

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.8%

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

      1. mul-1-neg 80.8%

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

   7. Simplified 80.8%

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

   if -0.0029 < x

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Step-by-step derivation

      1. associate--l- 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 58.9%

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

   6. Taylor expanded in x around 0 36.0%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 6: 26.4% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

   \[\left(1 - x\right) - y \]
2. Step-by-step derivation

   1. associate--l- 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{1 - \left(x + y\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 64.5%

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

6. Taylor expanded in x around 0 28.7%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024180 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))