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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

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: 61.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(1 - x\right) - y\\ \mathbf{if}\;t\_0 \leq -2000:\\ \;\;\;\;-y\\ \mathbf{elif}\;t\_0 \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (- 1.0 x) y)))
   (if (<= t_0 -2000.0) (- y) (if (<= t_0 2.0) 1.0 (- x)))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) - y;
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = -y;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 - x) - y
    if (t_0 <= (-2000.0d0)) then
        tmp = -y
    else if (t_0 <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 - x) - y;
	double tmp;
	if (t_0 <= -2000.0) {
		tmp = -y;
	} else if (t_0 <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 - x) - y
	tmp = 0
	if t_0 <= -2000.0:
		tmp = -y
	elif t_0 <= 2.0:
		tmp = 1.0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) - y)
	tmp = 0.0
	if (t_0 <= -2000.0)
		tmp = Float64(-y);
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 - x) - y;
	tmp = 0.0;
	if (t_0 <= -2000.0)
		tmp = -y;
	elseif (t_0 <= 2.0)
		tmp = 1.0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision]}, If[LessEqual[t$95$0, -2000.0], (-y), If[LessEqual[t$95$0, 2.0], 1.0, (-x)]]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 (-.f64 #s(literal 1 binary64) x) y) < -2e3

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. lower-neg.f64 52.1

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

   5. Applied rewrites 52.1%

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

   if -2e3 < (-.f64 (-.f64 #s(literal 1 binary64) x) y) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 98.9

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

   5. Applied rewrites 98.9%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 97.2%

      \[\leadsto 1 \]

   if 2 < (-.f64 (-.f64 #s(literal 1 binary64) x) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

      2. lower-neg.f64 45.6

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

   5. Applied rewrites 45.6%

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

Alternative 3: 81.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - x\right) - y \leq -2000:\\ \;\;\;\;\left(-x\right) - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (- 1.0 x) y) -2000.0) (- (- x) y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) - y) <= -2000.0) {
		tmp = -x - 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) - y) <= (-2000.0d0)) then
        tmp = -x - 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) - y) <= -2000.0) {
		tmp = -x - y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) - y) <= -2000.0:
		tmp = -x - y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) - y) <= -2000.0)
		tmp = Float64(Float64(-x) - 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) - y) <= -2000.0)
		tmp = -x - y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision], -2000.0], N[((-x) - y), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 #s(literal 1 binary64) x) y) < -2e3

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(x\right)\right)} - y \]

      2. lower-neg.f64 98.9

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

   5. Applied rewrites 98.9%

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

   if -2e3 < (-.f64 (-.f64 #s(literal 1 binary64) x) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 74.3

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

   5. Applied rewrites 74.3%

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

Alternative 4: 63.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - x\right) - y \leq 0.9999999999999999:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (- 1.0 x) y) 0.9999999999999999) (- 1.0 y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) - y) <= 0.9999999999999999) {
		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) - y) <= 0.9999999999999999d0) 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) - y) <= 0.9999999999999999) {
		tmp = 1.0 - y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) - y) <= 0.9999999999999999:
		tmp = 1.0 - y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) - y) <= 0.9999999999999999)
		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) - y) <= 0.9999999999999999)
		tmp = 1.0 - y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision], 0.9999999999999999], N[(1.0 - y), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 #s(literal 1 binary64) x) y) < 0.999999999999999889

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

   5. Applied rewrites 53.3%

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

   if 0.999999999999999889 < (-.f64 (-.f64 #s(literal 1 binary64) x) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 73.9

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

   5. Applied rewrites 73.9%

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

Alternative 5: 63.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - x\right) - y \leq -2000:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- (- 1.0 x) y) -2000.0) (- y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) - y) <= -2000.0) {
		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 (((1.0d0 - x) - y) <= (-2000.0d0)) 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 (((1.0 - x) - y) <= -2000.0) {
		tmp = -y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) - y) <= -2000.0:
		tmp = -y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) - y) <= -2000.0)
		tmp = Float64(-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) - y) <= -2000.0)
		tmp = -y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision], -2000.0], (-y), N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 #s(literal 1 binary64) x) y) < -2e3

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. lower-neg.f64 52.1

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

   5. Applied rewrites 52.1%

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

   if -2e3 < (-.f64 (-.f64 #s(literal 1 binary64) x) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 74.3

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

   5. Applied rewrites 74.3%

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

Alternative 6: 43.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\left(1 - x\right) - y \leq 2:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= (- (- 1.0 x) y) 2.0) 1.0 (- x)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) - y) <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -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) - y) <= 2.0d0) then
        tmp = 1.0d0
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) - y) <= 2.0) {
		tmp = 1.0;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) - y) <= 2.0:
		tmp = 1.0
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(Float64(1.0 - x) - y) <= 2.0)
		tmp = 1.0;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) - y) <= 2.0)
		tmp = 1.0;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(N[(1.0 - x), $MachinePrecision] - y), $MachinePrecision], 2.0], 1.0, (-x)]

Derivation

1. Split input into 2 regimes

2. if (-.f64 (-.f64 #s(literal 1 binary64) x) y) < 2

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. lower--.f64 73.0

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

   5. Applied rewrites 73.0%

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

   6. Taylor expanded in x around 0

      \[\leadsto 1 \]
   7. Step-by-step derivation

   8. Applied rewrites 49.6%

      \[\leadsto 1 \]

   if 2 < (-.f64 (-.f64 #s(literal 1 binary64) x) y)

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(x\right)} \]

      2. lower-neg.f64 45.6

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

   5. Applied rewrites 45.6%

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

Alternative 7: 25.7% accurate, 7.0× 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 0

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

   1. lower--.f64 64.8

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

5. Applied rewrites 64.8%

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

6. Taylor expanded in x around 0

   \[\leadsto 1 \]
7. Step-by-step derivation

8. Applied rewrites 35.6%

   \[\leadsto 1 \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024240 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))