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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 49.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00033:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-258}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.00033) (- x) (if (<= x -3.2e-258) 1.0 (- y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.00033) {
		tmp = -x;
	} else if (x <= -3.2e-258) {
		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 (x <= (-0.00033d0)) then
        tmp = -x
    else if (x <= (-3.2d-258)) 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 (x <= -0.00033) {
		tmp = -x;
	} else if (x <= -3.2e-258) {
		tmp = 1.0;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.00033:
		tmp = -x
	elif x <= -3.2e-258:
		tmp = 1.0
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.00033)
		tmp = Float64(-x);
	elseif (x <= -3.2e-258)
		tmp = 1.0;
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.00033)
		tmp = -x;
	elseif (x <= -3.2e-258)
		tmp = 1.0;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.00033], (-x), If[LessEqual[x, -3.2e-258], 1.0, (-y)]]

Derivation

1. Split input into 3 regimes

2. if x < -3.3e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   if -3.3e-4 < x < -3.2000000000000002e-258

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. flip3-- 76.6%

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

      3. metadata-eval 76.6%

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

      4. metadata-eval 76.6%

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

      5. *-un-lft-identity 76.6%

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

      6. fma-define 76.6%

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

   4. Applied egg-rr 76.6%

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

      1. +-commutative 76.6%

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

      2. fma-undefine 76.6%

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

      3. distribute-lft1-in 76.6%

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

      4. +-commutative 76.6%

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

      5. *-commutative 76.6%

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

      6. +-commutative 76.6%

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

      7. associate-+r+ 76.6%

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

      8. +-commutative 76.6%

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

      9. associate-+l+ 76.6%

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

   6. Simplified 76.6%

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

   7. Taylor expanded in x around 0 72.6%

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

   8. Taylor expanded in y around 0 51.9%

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

   if -3.2000000000000002e-258 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 46.0%

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

      1. neg-mul-1 46.0%

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

   5. Simplified 46.0%

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

Alternative 3: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 12500:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 12500.0) (- 1.0 x) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 12500.0) {
		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 <= 12500.0d0) 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 <= 12500.0) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 12500.0:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 12500.0)
		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 <= 12500.0)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 12500.0], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 12500

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.9%

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

   if 12500 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.8%

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

Alternative 4: 75.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.1 \cdot 10^{+31}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 7.1e+31) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.1e+31) {
		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 <= 7.1d+31) 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 <= 7.1e+31) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.1e+31:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.1e+31)
		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 <= 7.1e+31)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.1e+31], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 7.09999999999999961e31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.1%

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

   if 7.09999999999999961e31 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 82.2%

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

      1. neg-mul-1 82.2%

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

   5. Simplified 82.2%

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

Alternative 5: 44.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.00033:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -0.00033) (- x) 1.0))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.00033) {
		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 <= (-0.00033d0)) 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 <= -0.00033) {
		tmp = -x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.00033:
		tmp = -x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.00033)
		tmp = Float64(-x);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.00033)
		tmp = -x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.00033], (-x), 1.0]

Derivation

1. Split input into 2 regimes

2. if x < -3.3e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.7%

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

      1. neg-mul-1 75.7%

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

   5. Simplified 75.7%

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

   if -3.3e-4 < x

   1. Initial program 100.0%

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

      1. associate--l- 100.0%

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

      2. flip3-- 52.4%

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

      3. metadata-eval 52.4%

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

      4. metadata-eval 52.4%

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

      5. *-un-lft-identity 52.4%

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

      6. fma-define 52.4%

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

   4. Applied egg-rr 52.4%

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

      1. +-commutative 52.4%

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

      2. fma-undefine 52.4%

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

      3. distribute-lft1-in 52.4%

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

      4. +-commutative 52.4%

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

      5. *-commutative 52.4%

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

      6. +-commutative 52.4%

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

      7. associate-+r+ 52.4%

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

      8. +-commutative 52.4%

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

      9. associate-+l+ 52.4%

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

   6. Simplified 52.4%

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

   7. Taylor expanded in x around 0 46.6%

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

   8. Taylor expanded in y around 0 32.0%

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

Alternative 6: 26.9% 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. Step-by-step derivation

   1. associate--l- 100.0%

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

   2. flip3-- 44.4%

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

   3. metadata-eval 44.4%

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

   4. metadata-eval 44.4%

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

   5. *-un-lft-identity 44.4%

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

   6. fma-define 44.4%

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

4. Applied egg-rr 44.4%

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

   1. +-commutative 44.4%

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

   2. fma-undefine 44.4%

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

   3. distribute-lft1-in 44.4%

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

   4. +-commutative 44.4%

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

   5. *-commutative 44.4%

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

   6. +-commutative 44.4%

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

   7. associate-+r+ 44.4%

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

   8. +-commutative 44.4%

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

   9. associate-+l+ 44.4%

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

6. Simplified 44.4%

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

7. Taylor expanded in x around 0 35.5%

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

8. Taylor expanded in y around 0 24.4%

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

Reproduce

herbie shell --seed 2024101 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))