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

Percentage Accurate: 100.0% → 100.0%

Time: 3.7s

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: 80.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

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

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.3%

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

   if 2 < (-.f64 1 x)

   1. Initial program 100.0%

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

      1. flip3-- 20.9%

         \[\leadsto \color{blue}{\frac{{\left(1 - x\right)}^{3} - {y}^{3}}{\left(1 - x\right) \cdot \left(1 - x\right) + \left(y \cdot y + \left(1 - x\right) \cdot y\right)}} \]

      2. pow2 20.9%

         \[\leadsto \frac{{\left(1 - x\right)}^{3} - {y}^{3}}{\color{blue}{{\left(1 - x\right)}^{2}} + \left(y \cdot y + \left(1 - x\right) \cdot y\right)} \]

      3. distribute-rgt-out 20.9%

         \[\leadsto \frac{{\left(1 - x\right)}^{3} - {y}^{3}}{{\left(1 - x\right)}^{2} + \color{blue}{y \cdot \left(y + \left(1 - x\right)\right)}} \]

      4. +-commutative 20.9%

         \[\leadsto \frac{{\left(1 - x\right)}^{3} - {y}^{3}}{{\left(1 - x\right)}^{2} + y \cdot \color{blue}{\left(\left(1 - x\right) + y\right)}} \]

   3. Applied egg-rr 20.9%

      \[\leadsto \color{blue}{\frac{{\left(1 - x\right)}^{3} - {y}^{3}}{{\left(1 - x\right)}^{2} + y \cdot \left(\left(1 - x\right) + y\right)}} \]
   4. Step-by-step derivation

      1. unpow2 20.9%

         \[\leadsto \frac{{\left(1 - x\right)}^{3} - {y}^{3}}{\color{blue}{\left(1 - x\right) \cdot \left(1 - x\right)} + y \cdot \left(\left(1 - x\right) + y\right)} \]

      2. +-commutative 20.9%

         \[\leadsto \frac{{\left(1 - x\right)}^{3} - {y}^{3}}{\left(1 - x\right) \cdot \left(1 - x\right) + y \cdot \color{blue}{\left(y + \left(1 - x\right)\right)}} \]

      3. distribute-rgt-in 20.9%

         \[\leadsto \frac{{\left(1 - x\right)}^{3} - {y}^{3}}{\left(1 - x\right) \cdot \left(1 - x\right) + \color{blue}{\left(y \cdot y + \left(1 - x\right) \cdot y\right)}} \]

      4. flip3-- 100.0%

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

      5. flip3-- 28.2%

         \[\leadsto \color{blue}{\frac{{1}^{3} - {x}^{3}}{1 \cdot 1 + \left(x \cdot x + 1 \cdot x\right)}} - y \]

      6. div-inv 28.2%

         \[\leadsto \color{blue}{\left({1}^{3} - {x}^{3}\right) \cdot \frac{1}{1 \cdot 1 + \left(x \cdot x + 1 \cdot x\right)}} - y \]

      7. fma-neg 28.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left({1}^{3} - {x}^{3}, \frac{1}{1 \cdot 1 + \left(x \cdot x + 1 \cdot x\right)}, -y\right)} \]

      8. metadata-eval 28.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{1} - {x}^{3}, \frac{1}{1 \cdot 1 + \left(x \cdot x + 1 \cdot x\right)}, -y\right) \]

      9. metadata-eval 28.2%

         \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \frac{1}{\color{blue}{1} + \left(x \cdot x + 1 \cdot x\right)}, -y\right) \]

      10. *-un-lft-identity 28.2%

          \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \frac{1}{1 + \left(x \cdot x + \color{blue}{x}\right)}, -y\right) \]

      11. fma-def 28.2%

          \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \frac{1}{1 + \color{blue}{\mathsf{fma}\left(x, x, x\right)}}, -y\right) \]

   5. Applied egg-rr 28.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - {x}^{3}, \frac{1}{1 + \mathsf{fma}\left(x, x, x\right)}, -y\right)} \]

   6. Taylor expanded in x around inf 27.5%

      \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \color{blue}{\frac{1}{{x}^{2}}}, -y\right) \]
   7. Step-by-step derivation

      1. unpow2 27.5%

         \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \frac{1}{\color{blue}{x \cdot x}}, -y\right) \]

      2. associate-/r* 27.7%

         \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \color{blue}{\frac{\frac{1}{x}}{x}}, -y\right) \]

   8. Simplified 27.7%

      \[\leadsto \mathsf{fma}\left(1 - {x}^{3}, \color{blue}{\frac{\frac{1}{x}}{x}}, -y\right) \]

   9. Taylor expanded in x around inf 99.3%

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

       1. neg-mul-1 99.3%

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

       2. +-commutative 99.3%

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

       3. sub-neg 99.3%

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

       4. mul-1-neg 99.3%

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

   11. Simplified 99.3%

       \[\leadsto \color{blue}{\left(-y\right) - x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.5%

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

Alternative 3: 74.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq 1.000000001:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- 1.0 x) 1.000000001) (- 1.0 y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= 1.000000001) {
		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) <= 1.000000001d0) 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) <= 1.000000001) {
		tmp = 1.0 - y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (1.0 - x) <= 1.000000001:
		tmp = 1.0 - y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - x) <= 1.000000001)
		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) <= 1.000000001)
		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], 1.000000001], N[(1.0 - y), $MachinePrecision], N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 x) < 1.0000000010000001

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.4%

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

   if 1.0000000010000001 < (-.f64 1 x)

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 73.4%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq 1.000000001:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 4: 75.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 14000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 14000.0) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 14000.0) {
		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 <= 14000.0d0) 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 <= 14000.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 14000.0:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 14000.0)
		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 <= 14000.0)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 14000.0], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 14000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.1%

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

   if 14000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 76.6%

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

      1. neg-mul-1 76.6%

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

   4. Simplified 76.6%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 14000:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5: 50.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.46e-9) (- x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.46e-9) {
		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 (x <= (-1.46d-9)) then
        tmp = -x
    else
        tmp = -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.46e-9) {
		tmp = -x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.46e-9:
		tmp = -x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.46e-9)
		tmp = Float64(-x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.46e-9)
		tmp = -x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.46e-9], (-x), (-y)]

Derivation

1. Split input into 2 regimes

2. if x < -1.4599999999999999e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.2%

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

      1. neg-mul-1 71.2%

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

   4. Simplified 71.2%

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

   if -1.4599999999999999e-9 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 47.5%

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

      1. neg-mul-1 47.5%

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

   4. Simplified 47.5%

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

4. Final simplification 53.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 6: 38.9% 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 35.8%

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

   1. neg-mul-1 35.8%

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

4. Simplified 35.8%

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

5. Final simplification 35.8%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023309 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))