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. Final simplification 100.0%

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

Alternative 2: 49.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8.5e-308) (- x) (if (<= y 1.0) 1.0 (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.5e-308) {
		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 <= 8.5d-308) 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 <= 8.5e-308) {
		tmp = -x;
	} else if (y <= 1.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.5e-308:
		tmp = -x
	elif y <= 1.0:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.5e-308)
		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 <= 8.5e-308)
		tmp = -x;
	elseif (y <= 1.0)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.5e-308], (-x), If[LessEqual[y, 1.0], 1.0, (-y)]]

Derivation

1. Split input into 3 regimes

2. if y < 8.49999999999999972e-308

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 47.5%

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

      1. neg-mul-1 47.5%

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

   5. Simplified 47.5%

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

   if 8.49999999999999972e-308 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.7%

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

   4. Taylor expanded in x around inf 82.2%

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

   5. Taylor expanded in x around 0 59.7%

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

   if 1 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.3%

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

      1. neg-mul-1 76.3%

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

   5. Simplified 76.3%

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

4. Final simplification 57.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{-308}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.8e+28) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.8e+28) {
		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 <= 3.8d+28) 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 <= 3.8e+28) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.8e+28:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.8e+28)
		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 <= 3.8e+28)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.8e+28], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3.7999999999999999e28

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.3%

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

   if 3.7999999999999999e28 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.8%

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

      1. neg-mul-1 79.8%

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

   5. Simplified 79.8%

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

4. Final simplification 77.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4.5e-24) (- 1.0 x) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.5e-24) {
		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 <= 4.5d-24) 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 <= 4.5e-24) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.5e-24:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.5e-24)
		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 <= 4.5e-24)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.5e-24], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.4999999999999997e-24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.5%

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

   if 4.4999999999999997e-24 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 77.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-24}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -0.28) (- x) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.28) {
		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 <= (-0.28d0)) 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 <= -0.28) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.28:
		tmp = -x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.28)
		tmp = Float64(-x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.28)
		tmp = -x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.28], (-x), 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -0.28000000000000003

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 70.0%

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

      1. neg-mul-1 70.0%

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

   5. Simplified 70.0%

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

   if -0.28000000000000003 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 90.0%

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

   4. Taylor expanded in x around inf 50.7%

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

   5. Taylor expanded in x around 0 32.5%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.28:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. 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 y around inf 87.1%

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

4. Taylor expanded in x around inf 50.3%

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

5. Taylor expanded in x around 0 25.1%

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

6. Final simplification 25.1%

   \[\leadsto 1 \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024115 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))