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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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. Final simplification 100.0%

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

Alternative 2: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-44}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-277}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-261}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.4e-6)
   (- x)
   (if (<= x -1.1e-44)
     (- y)
     (if (<= x 2.05e-277)
       1.0
       (if (<= x 7e-261) (- y) (if (<= x 1.05e-188) 1.0 (- y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.4e-6) {
		tmp = -x;
	} else if (x <= -1.1e-44) {
		tmp = -y;
	} else if (x <= 2.05e-277) {
		tmp = 1.0;
	} else if (x <= 7e-261) {
		tmp = -y;
	} else if (x <= 1.05e-188) {
		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 (x <= (-5.4d-6)) then
        tmp = -x
    else if (x <= (-1.1d-44)) then
        tmp = -y
    else if (x <= 2.05d-277) then
        tmp = 1.0d0
    else if (x <= 7d-261) then
        tmp = -y
    else if (x <= 1.05d-188) 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 (x <= -5.4e-6) {
		tmp = -x;
	} else if (x <= -1.1e-44) {
		tmp = -y;
	} else if (x <= 2.05e-277) {
		tmp = 1.0;
	} else if (x <= 7e-261) {
		tmp = -y;
	} else if (x <= 1.05e-188) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.4e-6:
		tmp = -x
	elif x <= -1.1e-44:
		tmp = -y
	elif x <= 2.05e-277:
		tmp = 1.0
	elif x <= 7e-261:
		tmp = -y
	elif x <= 1.05e-188:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.4e-6)
		tmp = Float64(-x);
	elseif (x <= -1.1e-44)
		tmp = Float64(-y);
	elseif (x <= 2.05e-277)
		tmp = 1.0;
	elseif (x <= 7e-261)
		tmp = Float64(-y);
	elseif (x <= 1.05e-188)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.4e-6)
		tmp = -x;
	elseif (x <= -1.1e-44)
		tmp = -y;
	elseif (x <= 2.05e-277)
		tmp = 1.0;
	elseif (x <= 7e-261)
		tmp = -y;
	elseif (x <= 1.05e-188)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.4e-6], (-x), If[LessEqual[x, -1.1e-44], (-y), If[LessEqual[x, 2.05e-277], 1.0, If[LessEqual[x, 7e-261], (-y), If[LessEqual[x, 1.05e-188], 1.0, (-y)]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.39999999999999997e-6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.1%

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

      1. neg-mul-1 79.1%

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

   4. Simplified 79.1%

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

   if -5.39999999999999997e-6 < x < -1.10000000000000006e-44 or 2.04999999999999994e-277 < x < 6.9999999999999995e-261 or 1.05e-188 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 46.5%

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

      1. neg-mul-1 46.5%

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

   4. Simplified 46.5%

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

   if -1.10000000000000006e-44 < x < 2.04999999999999994e-277 or 6.9999999999999995e-261 < x < 1.05e-188

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. flip-- 78.0%

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

      3. metadata-eval 78.0%

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

   3. Applied egg-rr 78.0%

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

      1. +-commutative 78.0%

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

      2. +-commutative 78.0%

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

      3. associate-+r+ 78.0%

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

   5. Simplified 78.0%

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

   6. Taylor expanded in y around 0 57.0%

      \[\leadsto \color{blue}{\frac{1 - {x}^{2}}{1 + x}} \]
   7. Step-by-step derivation

      1. unpow2 57.0%

         \[\leadsto \frac{1 - \color{blue}{x \cdot x}}{1 + x} \]

   8. Simplified 57.0%

      \[\leadsto \color{blue}{\frac{1 - x \cdot x}{1 + x}} \]

   9. Taylor expanded in x around 0 57.0%

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

4. Final simplification 58.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.4 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-44}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-277}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-261}:\\ \;\;\;\;-y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-188}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 75.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - x) <= 1.0)
		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) <= 1.0)
		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], 1.0], N[(1.0 - y), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.1%

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

   if 1 < (-.f64 1 x)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 84.2%

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

4. Final simplification 76.8%

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

Alternative 4: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 920000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 920000.0) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 920000.0) {
		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 <= 920000.0d0) 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 <= 920000.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 920000.0:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 920000.0)
		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 <= 920000.0)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 920000.0], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 9.2e5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.3%

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

   if 9.2e5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 77.3%

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

      1. neg-mul-1 77.3%

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

   4. Simplified 77.3%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 920000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5: 43.7% accurate, 1.2× 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. Taylor expanded in x around inf 82.1%

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

      1. neg-mul-1 82.1%

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

   4. Simplified 82.1%

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

   if -1 < x

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. flip-- 63.0%

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

      3. metadata-eval 63.0%

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

   3. Applied egg-rr 63.0%

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

      1. +-commutative 63.0%

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

      2. +-commutative 63.0%

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

      3. associate-+r+ 63.0%

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

   5. Simplified 63.0%

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

   6. Taylor expanded in y around 0 42.6%

      \[\leadsto \color{blue}{\frac{1 - {x}^{2}}{1 + x}} \]
   7. Step-by-step derivation

      1. unpow2 42.6%

         \[\leadsto \frac{1 - \color{blue}{x \cdot x}}{1 + x} \]

   8. Simplified 42.6%

      \[\leadsto \color{blue}{\frac{1 - x \cdot x}{1 + x}} \]

   9. Taylor expanded in x around 0 30.7%

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

4. Final simplification 43.8%

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

Alternative 6: 26.3% 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%

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

   2. flip-- 57.8%

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

   3. metadata-eval 57.8%

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

3. Applied egg-rr 57.8%

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

   1. +-commutative 57.8%

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

   2. +-commutative 57.8%

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

   3. associate-+r+ 57.8%

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

5. Simplified 57.8%

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

6. Taylor expanded in y around 0 41.6%

   \[\leadsto \color{blue}{\frac{1 - {x}^{2}}{1 + x}} \]
7. Step-by-step derivation

   1. unpow2 41.6%

      \[\leadsto \frac{1 - \color{blue}{x \cdot x}}{1 + x} \]

8. Simplified 41.6%

   \[\leadsto \color{blue}{\frac{1 - x \cdot x}{1 + x}} \]

9. Taylor expanded in x around 0 24.2%

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

10. Final simplification 24.2%

    \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023256 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))