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

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

Alternatives: 4

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: 75.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+22}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 8e+22) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8e+22) {
		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 <= 8d+22) 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 <= 8e+22) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8e+22:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8e+22)
		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 <= 8e+22)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8e+22], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 8e22

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.0%

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

   if 8e22 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.2%

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

      1. neg-mul-1 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{+22}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 50.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+23}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.12e+23) (- x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.12e+23) {
		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 <= 1.12d+23) 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 <= 1.12e+23) {
		tmp = -x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.12e+23:
		tmp = -x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.12e+23)
		tmp = Float64(-x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.12e+23)
		tmp = -x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.12e+23], (-x), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 1.12e23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 48.1%

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

      1. neg-mul-1 48.1%

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

   4. Simplified 48.1%

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

   if 1.12e23 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.2%

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

      1. neg-mul-1 80.2%

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

   4. Simplified 80.2%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{+23}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 4: 38.7% accurate, 2.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x))

C

double code(double x, double y) {
	return -x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -x
end function

Java

public static double code(double x, double y) {
	return -x;
}

Python

def code(x, y):
	return -x

Julia

function code(x, y)
	return Float64(-x)
end

MATLAB

function tmp = code(x, y)
	tmp = -x;
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around inf 43.1%

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

   1. neg-mul-1 43.1%

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

4. Simplified 43.1%

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

5. Final simplification 43.1%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023208 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))