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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

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

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

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 49.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.42 \cdot 10^{-236}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-124}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.05 \cdot 10^{-85}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.42e-236)
   (- x)
   (if (<= y 3e-124)
     1.0
     (if (<= y 2.05e-85) (- x) (if (<= y 1.0) 1.0 (- y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.42e-236) {
		tmp = -x;
	} else if (y <= 3e-124) {
		tmp = 1.0;
	} else if (y <= 2.05e-85) {
		tmp = -x;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.42d-236)) then
        tmp = -x
    else if (y <= 3d-124) then
        tmp = 1.0d0
    else if (y <= 2.05d-85) then
        tmp = -x
    else if (y <= 1.0d0) then
        tmp = 1.0d0
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.42e-236) {
		tmp = -x;
	} else if (y <= 3e-124) {
		tmp = 1.0;
	} else if (y <= 2.05e-85) {
		tmp = -x;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.42e-236:
		tmp = -x
	elif y <= 3e-124:
		tmp = 1.0
	elif y <= 2.05e-85:
		tmp = -x
	elif y <= 1.0:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.42e-236)
		tmp = Float64(-x);
	elseif (y <= 3e-124)
		tmp = 1.0;
	elseif (y <= 2.05e-85)
		tmp = Float64(-x);
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.42e-236)
		tmp = -x;
	elseif (y <= 3e-124)
		tmp = 1.0;
	elseif (y <= 2.05e-85)
		tmp = -x;
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.42e-236], (-x), If[LessEqual[y, 3e-124], 1.0, If[LessEqual[y, 2.05e-85], (-x), If[LessEqual[y, 1.0], 1.0, (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.41999999999999996e-236 or 3e-124 < y < 2.04999999999999997e-85

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 37.2%

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

      1. neg-mul-1 37.2%

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

   5. Simplified 37.2%

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

   if -1.41999999999999996e-236 < y < 3e-124 or 2.04999999999999997e-85 < y < 1

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--r+ 99.9%

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

      3. div-sub 99.9%

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

   5. Simplified 99.9%

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

   6. Taylor expanded in y around 0 98.2%

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

   7. Taylor expanded in x around 0 54.1%

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

   if 1 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 71.8%

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

      1. neg-mul-1 71.8%

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

   5. Simplified 71.8%

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

Alternative 3: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 0.00031:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 0.00031) (- 1.0 x) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 0.00031) {
		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 <= 0.00031d0) 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 <= 0.00031) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 0.00031:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 0.00031)
		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 <= 0.00031)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 0.00031], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.1e-4

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.2%

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

   if 3.1e-4 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 73.7%

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

Alternative 4: 74.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 9000000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 9000000.0) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 9000000.0) {
		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 <= 9000000.0d0) 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 <= 9000000.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 9000000.0:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 9000000.0)
		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 <= 9000000.0)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 9000000.0], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 9e6

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 71.6%

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

   if 9e6 < y

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 72.5%

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

      1. neg-mul-1 72.5%

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

   5. Simplified 72.5%

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

Alternative 5: 43.7% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 56.6%

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

      1. neg-mul-1 56.6%

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

   5. Simplified 56.6%

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

   if -1 < x

   1. Initial program 100.0%

      \[\left(1 - x\right) - y \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 87.6%

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

      1. +-commutative 87.6%

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

      2. associate--r+ 87.6%

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

      3. div-sub 87.6%

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

   5. Simplified 87.6%

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

   6. Taylor expanded in y around 0 61.4%

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

   7. Taylor expanded in x around 0 32.4%

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

Alternative 6: 26.7% 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. Add Preprocessing

3. Taylor expanded in x around inf 90.7%

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

   1. +-commutative 90.7%

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

   2. associate--r+ 90.7%

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

   3. div-sub 90.7%

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

5. Simplified 90.7%

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

6. Taylor expanded in y around 0 60.5%

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

7. Taylor expanded in x around 0 25.3%

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

Reproduce

herbie shell --seed 2024089 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))