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

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 7

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: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-286}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 65000:\\ \;\;\;\;1 + y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.2e-286) (- x) (if (<= y 65000.0) (+ 1.0 y) (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.2e-286) {
		tmp = -x;
	} else if (y <= 65000.0) {
		tmp = 1.0 + y;
	} 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 <= (-6.2d-286)) then
        tmp = -x
    else if (y <= 65000.0d0) then
        tmp = 1.0d0 + y
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.2e-286) {
		tmp = -x;
	} else if (y <= 65000.0) {
		tmp = 1.0 + y;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.2e-286:
		tmp = -x
	elif y <= 65000.0:
		tmp = 1.0 + y
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.2e-286)
		tmp = Float64(-x);
	elseif (y <= 65000.0)
		tmp = Float64(1.0 + y);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.2e-286)
		tmp = -x;
	elseif (y <= 65000.0)
		tmp = 1.0 + y;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.2e-286], (-x), If[LessEqual[y, 65000.0], N[(1.0 + y), $MachinePrecision], (-y)]]

Derivation

1. Split input into 3 regimes

2. if y < -6.19999999999999964e-286

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 40.7%

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

      1. neg-mul-1 40.7%

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

   5. Simplified 40.7%

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

   if -6.19999999999999964e-286 < y < 65000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 58.2%

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

      1. sub-neg 58.2%

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

      2. add-sqr-sqrt 8.2%

         \[\leadsto 1 + \color{blue}{\sqrt{-y} \cdot \sqrt{-y}} \]

      3. sqrt-unprod 57.1%

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

      4. sqr-neg 57.1%

         \[\leadsto 1 + \sqrt{\color{blue}{y \cdot y}} \]

      5. sqrt-unprod 49.0%

         \[\leadsto 1 + \color{blue}{\sqrt{y} \cdot \sqrt{y}} \]

      6. add-sqr-sqrt 57.1%

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

      7. +-commutative 57.1%

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

   5. Applied egg-rr 57.1%

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

   if 65000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. neg-mul-1 72.8%

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

   5. Simplified 72.8%

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

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{-286}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 65000:\\ \;\;\;\;1 + y\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.56 \cdot 10^{-285}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 65000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.56e-285) (- x) (if (<= y 65000.0) 1.0 (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.56e-285) {
		tmp = -x;
	} else if (y <= 65000.0) {
		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 <= (-1.56d-285)) then
        tmp = -x
    else if (y <= 65000.0d0) 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 <= -1.56e-285) {
		tmp = -x;
	} else if (y <= 65000.0) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.56e-285:
		tmp = -x
	elif y <= 65000.0:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.56e-285)
		tmp = Float64(-x);
	elseif (y <= 65000.0)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.56e-285)
		tmp = -x;
	elseif (y <= 65000.0)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.56e-285], (-x), If[LessEqual[y, 65000.0], 1.0, (-y)]]

Derivation

1. Split input into 3 regimes

2. if y < -1.55999999999999998e-285

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 40.7%

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

      1. neg-mul-1 40.7%

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

   5. Simplified 40.7%

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

   if -1.55999999999999998e-285 < y < 65000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 58.2%

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

   4. Taylor expanded in y around 0 57.1%

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

   if 65000 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.8%

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

      1. neg-mul-1 72.8%

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

   5. Simplified 72.8%

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

Alternative 4: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 4.9 \cdot 10^{+27}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 4.9e+27) (- 1.0 x) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 4.9e+27) {
		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 <= 4.9d+27) 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 <= 4.9e+27) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 4.9e+27:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 4.9e+27)
		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 <= 4.9e+27)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 4.9e+27], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.90000000000000015e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.5%

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

   if 4.90000000000000015e27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 81.5%

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

Alternative 5: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.5 \cdot 10^{+27}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 8.5e+27) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.5e+27) {
		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 <= 8.5d+27) 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 <= 8.5e+27) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.5e+27:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.5e+27)
		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 <= 8.5e+27)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.5e+27], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 8.5e27

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.5%

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

   if 8.5e27 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.5%

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

      1. neg-mul-1 81.5%

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

   5. Simplified 81.5%

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

Alternative 6: 42.5% 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 74.6%

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

      1. neg-mul-1 74.6%

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

   5. Simplified 74.6%

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

   if -1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 75.6%

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

   4. Taylor expanded in y around 0 38.9%

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

Alternative 7: 25.7% 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 0 62.7%

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

4. Taylor expanded in y around 0 30.0%

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

Reproduce

herbie shell --seed 2024146 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))