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

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

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

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

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: 63.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+36}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-210}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-171}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+36)
   (- y)
   (if (<= y 2.1e-210)
     (- x)
     (if (<= y 1.45e-171) 1.0 (if (<= y 2.6e+14) (- x) (- y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+36) {
		tmp = -y;
	} else if (y <= 2.1e-210) {
		tmp = -x;
	} else if (y <= 1.45e-171) {
		tmp = 1.0;
	} else if (y <= 2.6e+14) {
		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 <= (-4.2d+36)) then
        tmp = -y
    else if (y <= 2.1d-210) then
        tmp = -x
    else if (y <= 1.45d-171) then
        tmp = 1.0d0
    else if (y <= 2.6d+14) 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 <= -4.2e+36) {
		tmp = -y;
	} else if (y <= 2.1e-210) {
		tmp = -x;
	} else if (y <= 1.45e-171) {
		tmp = 1.0;
	} else if (y <= 2.6e+14) {
		tmp = -x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+36:
		tmp = -y
	elif y <= 2.1e-210:
		tmp = -x
	elif y <= 1.45e-171:
		tmp = 1.0
	elif y <= 2.6e+14:
		tmp = -x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+36)
		tmp = Float64(-y);
	elseif (y <= 2.1e-210)
		tmp = Float64(-x);
	elseif (y <= 1.45e-171)
		tmp = 1.0;
	elseif (y <= 2.6e+14)
		tmp = Float64(-x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+36)
		tmp = -y;
	elseif (y <= 2.1e-210)
		tmp = -x;
	elseif (y <= 1.45e-171)
		tmp = 1.0;
	elseif (y <= 2.6e+14)
		tmp = -x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+36], (-y), If[LessEqual[y, 2.1e-210], (-x), If[LessEqual[y, 1.45e-171], 1.0, If[LessEqual[y, 2.6e+14], (-x), (-y)]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.20000000000000009e36 or 2.6e14 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.0%

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

      1. mul-1-neg 84.0%

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

   4. Simplified 84.0%

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

   if -4.20000000000000009e36 < y < 2.10000000000000016e-210 or 1.4499999999999999e-171 < y < 2.6e14

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 62.4%

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

      1. mul-1-neg 62.4%

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

   4. Simplified 62.4%

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

   if 2.10000000000000016e-210 < y < 1.4499999999999999e-171

   1. Initial program 100.0%

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

      1. flip-- 100.0%

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

      2. clear-num 100.0%

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

      3. clear-num 100.0%

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

      4. flip-- 100.0%

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

      5. associate--l- 100.0%

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

   3. Applied egg-rr 100.0%

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

   4. Taylor expanded in y around 0 100.0%

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

   5. Taylor expanded in x around 0 80.8%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+36}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{-210}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.45 \cdot 10^{-171}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+14}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+38} \lor \neg \left(y \leq 4.3 \cdot 10^{+23}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5e+38) (not (<= y 4.3e+23))) (- y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5e+38) || !(y <= 4.3e+23)) {
		tmp = -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 ((y <= (-5d+38)) .or. (.not. (y <= 4.3d+23))) then
        tmp = -y
    else
        tmp = 1.0d0 - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5e+38) || !(y <= 4.3e+23)) {
		tmp = -y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5e+38) or not (y <= 4.3e+23):
		tmp = -y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5e+38) || !(y <= 4.3e+23))
		tmp = Float64(-y);
	else
		tmp = Float64(1.0 - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5e+38) || ~((y <= 4.3e+23)))
		tmp = -y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5e+38], N[Not[LessEqual[y, 4.3e+23]], $MachinePrecision]], (-y), N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.9999999999999997e38 or 4.2999999999999999e23 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 84.0%

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

      1. mul-1-neg 84.0%

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

   4. Simplified 84.0%

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

   if -4.9999999999999997e38 < y < 4.2999999999999999e23

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+38} \lor \neg \left(y \leq 4.3 \cdot 10^{+23}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 4: 87.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+23}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e+35) (- y) (if (<= y 6e+23) (- 1.0 x) (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e+35) {
		tmp = -y;
	} else if (y <= 6e+23) {
		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 <= (-2.6d+35)) then
        tmp = -y
    else if (y <= 6d+23) 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 <= -2.6e+35) {
		tmp = -y;
	} else if (y <= 6e+23) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e+35:
		tmp = -y
	elif y <= 6e+23:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e+35)
		tmp = Float64(-y);
	elseif (y <= 6e+23)
		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 <= -2.6e+35)
		tmp = -y;
	elseif (y <= 6e+23)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e+35], (-y), If[LessEqual[y, 6e+23], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.60000000000000007e35

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.7%

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

      1. mul-1-neg 83.7%

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

   4. Simplified 83.7%

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

   if -2.60000000000000007e35 < y < 6.0000000000000002e23

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 96.9%

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

   if 6.0000000000000002e23 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 84.3%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+35}:\\ \;\;\;\;-y\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+23}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 5: 61.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.0))) (- x) 1.0))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(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)) .or. (.not. (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) || !(x <= 1.0)) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = -x
	else:
		tmp = 1.0
	return tmp

Julia

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

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], (-x), 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 69.3%

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

      1. mul-1-neg 69.3%

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

   4. Simplified 69.3%

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

   if -1 < x < 1

   1. Initial program 100.0%

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

      1. flip-- 71.6%

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

      2. clear-num 71.5%

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

      3. clear-num 71.5%

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

      4. flip-- 99.8%

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

      5. associate--l- 99.8%

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

   3. Applied egg-rr 99.8%

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

   4. Taylor expanded in y around 0 43.6%

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

   5. Taylor expanded in x around 0 41.9%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 25.6% 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. flip-- 54.3%

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

   2. clear-num 54.2%

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

   3. clear-num 54.2%

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

   4. flip-- 99.8%

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

   5. associate--l- 99.8%

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

3. Applied egg-rr 99.8%

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

4. Taylor expanded in y around 0 57.7%

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

5. Taylor expanded in x around 0 20.9%

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

6. Final simplification 20.9%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023326 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))