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

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

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: 99.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq -10000 \lor \neg \left(1 - x \leq 2\right):\\ \;\;\;\;\left(-x\right) - y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (- 1.0 x) -10000.0) (not (<= (- 1.0 x) 2.0)))
   (- (- x) y)
   (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) <= -10000.0) || !((1.0 - x) <= 2.0)) {
		tmp = -x - y;
	} 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 (((1.0d0 - x) <= (-10000.0d0)) .or. (.not. ((1.0d0 - x) <= 2.0d0))) then
        tmp = -x - y
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (((1.0 - x) <= -10000.0) || !((1.0 - x) <= 2.0)) {
		tmp = -x - y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) <= -10000.0) or not ((1.0 - x) <= 2.0):
		tmp = -x - y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(1.0 - x) <= -10000.0) || !(Float64(1.0 - x) <= 2.0))
		tmp = Float64(Float64(-x) - y);
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (((1.0 - x) <= -10000.0) || ~(((1.0 - x) <= 2.0)))
		tmp = -x - y;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[N[(1.0 - x), $MachinePrecision], -10000.0], N[Not[LessEqual[N[(1.0 - x), $MachinePrecision], 2.0]], $MachinePrecision]], N[((-x) - y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 x) < -1e4 or 2 < (-.f64 1 x)

   1. Initial program 100.0%

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

      1. flip3-- 28.5%

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

      2. div-inv 28.4%

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

      3. fma-neg 28.4%

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

      4. metadata-eval 28.4%

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

      5. metadata-eval 28.4%

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

      6. +-commutative 28.4%

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

      7. distribute-rgt-out 28.4%

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

      8. +-commutative 28.4%

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

      9. fma-def 28.4%

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

   3. Applied egg-rr 28.4%

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

      1. fma-neg 28.4%

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

   5. Simplified 28.4%

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

   6. Taylor expanded in x around inf 99.1%

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

      1. neg-mul-1 99.1%

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

   8. Simplified 99.1%

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

   if -1e4 < (-.f64 1 x) < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.0%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq -10000 \lor \neg \left(1 - x \leq 2\right):\\ \;\;\;\;\left(-x\right) - y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 3: 85.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+102} \lor \neg \left(y \leq -7.8 \cdot 10^{+59}\right) \land \left(y \leq -24500 \lor \neg \left(y \leq 7.4 \cdot 10^{+36}\right)\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.2e+102)
         (and (not (<= y -7.8e+59)) (or (<= y -24500.0) (not (<= y 7.4e+36)))))
   (- y)
   (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.2e+102) || (!(y <= -7.8e+59) && ((y <= -24500.0) || !(y <= 7.4e+36)))) {
		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 <= (-7.2d+102)) .or. (.not. (y <= (-7.8d+59))) .and. (y <= (-24500.0d0)) .or. (.not. (y <= 7.4d+36))) 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 <= -7.2e+102) || (!(y <= -7.8e+59) && ((y <= -24500.0) || !(y <= 7.4e+36)))) {
		tmp = -y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.2e+102) or (not (y <= -7.8e+59) and ((y <= -24500.0) or not (y <= 7.4e+36))):
		tmp = -y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.2e+102) || (!(y <= -7.8e+59) && ((y <= -24500.0) || !(y <= 7.4e+36))))
		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 <= -7.2e+102) || (~((y <= -7.8e+59)) && ((y <= -24500.0) || ~((y <= 7.4e+36)))))
		tmp = -y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.2e+102], And[N[Not[LessEqual[y, -7.8e+59]], $MachinePrecision], Or[LessEqual[y, -24500.0], N[Not[LessEqual[y, 7.4e+36]], $MachinePrecision]]]], (-y), N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.2000000000000003e102 or -7.80000000000000043e59 < y < -24500 or 7.40000000000000058e36 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   4. Simplified 80.8%

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

   if -7.2000000000000003e102 < y < -7.80000000000000043e59 or -24500 < y < 7.40000000000000058e36

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 94.7%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{+102} \lor \neg \left(y \leq -7.8 \cdot 10^{+59}\right) \land \left(y \leq -24500 \lor \neg \left(y \leq 7.4 \cdot 10^{+36}\right)\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]

Alternative 4: 87.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq -10000:\\ \;\;\;\;1 - x\\ \mathbf{elif}\;1 - x \leq 5 \cdot 10^{+54}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (- 1.0 x) -10000.0)
   (- 1.0 x)
   (if (<= (- 1.0 x) 5e+54) (- 1.0 y) (- x))))

C

double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= -10000.0) {
		tmp = 1.0 - x;
	} else if ((1.0 - x) <= 5e+54) {
		tmp = 1.0 - y;
	} 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) <= (-10000.0d0)) then
        tmp = 1.0d0 - x
    else if ((1.0d0 - x) <= 5d+54) then
        tmp = 1.0d0 - y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((1.0 - x) <= -10000.0) {
		tmp = 1.0 - x;
	} else if ((1.0 - x) <= 5e+54) {
		tmp = 1.0 - y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (1.0 - x) <= -10000.0:
		tmp = 1.0 - x
	elif (1.0 - x) <= 5e+54:
		tmp = 1.0 - y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(1.0 - x) <= -10000.0)
		tmp = Float64(1.0 - x);
	elseif (Float64(1.0 - x) <= 5e+54)
		tmp = Float64(1.0 - y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((1.0 - x) <= -10000.0)
		tmp = 1.0 - x;
	elseif ((1.0 - x) <= 5e+54)
		tmp = 1.0 - y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(1.0 - x), $MachinePrecision], -10000.0], N[(1.0 - x), $MachinePrecision], If[LessEqual[N[(1.0 - x), $MachinePrecision], 5e+54], N[(1.0 - y), $MachinePrecision], (-x)]]

Derivation

1. Split input into 3 regimes

2. if (-.f64 1 x) < -1e4

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.8%

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

   if -1e4 < (-.f64 1 x) < 5.00000000000000005e54

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 96.7%

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

   if 5.00000000000000005e54 < (-.f64 1 x)

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.8%

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

      1. neg-mul-1 80.8%

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

   4. Simplified 80.8%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq -10000:\\ \;\;\;\;1 - x\\ \mathbf{elif}\;1 - x \leq 5 \cdot 10^{+54}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 63.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+56} \lor \neg \left(x \leq 2.25 \cdot 10^{+19}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.65e+56) (not (<= x 2.25e+19))) (- x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.65e+56) || !(x <= 2.25e+19)) {
		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 <= (-1.65d+56)) .or. (.not. (x <= 2.25d+19))) 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 <= -1.65e+56) || !(x <= 2.25e+19)) {
		tmp = -x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.65e+56) or not (x <= 2.25e+19):
		tmp = -x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.65e+56) || !(x <= 2.25e+19))
		tmp = Float64(-x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.65e+56) || ~((x <= 2.25e+19)))
		tmp = -x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.65e+56], N[Not[LessEqual[x, 2.25e+19]], $MachinePrecision]], (-x), (-y)]

Derivation

1. Split input into 2 regimes

2. if x < -1.65000000000000001e56 or 2.25e19 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.5%

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

      1. neg-mul-1 78.5%

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

   4. Simplified 78.5%

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

   if -1.65000000000000001e56 < x < 2.25e19

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 57.0%

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

      1. neg-mul-1 57.0%

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

   4. Simplified 57.0%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{+56} \lor \neg \left(x \leq 2.25 \cdot 10^{+19}\right):\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

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))