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

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

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: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3600:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3600.0) (- 1.0 x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3600.0) {
		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 <= 3600.0d0) 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 <= 3600.0) {
		tmp = 1.0 - x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3600.0:
		tmp = 1.0 - x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3600.0)
		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 <= 3600.0)
		tmp = 1.0 - x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3600.0], N[(1.0 - x), $MachinePrecision], (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3600

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.8%

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

   if 3600 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. neg-mul-1 75.7%

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

   4. Simplified 75.7%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3600:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 3: 74.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{-13}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.25e-13) (- 1.0 x) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.25e-13) {
		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 <= 2.25d-13) 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 <= 2.25e-13) {
		tmp = 1.0 - x;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.25e-13:
		tmp = 1.0 - x
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.25e-13)
		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 <= 2.25e-13)
		tmp = 1.0 - x;
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.25e-13], N[(1.0 - x), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.25e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.6%

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

   if 2.25e-13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.6%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.25 \cdot 10^{-13}:\\ \;\;\;\;1 - x\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 4: 51.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3600:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3600.0) (- x) (- y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3600.0) {
		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 <= 3600.0d0) 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 <= 3600.0) {
		tmp = -x;
	} else {
		tmp = -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3600.0:
		tmp = -x
	else:
		tmp = -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3600.0)
		tmp = Float64(-x);
	else
		tmp = Float64(-y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3600.0)
		tmp = -x;
	else
		tmp = -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3600.0], (-x), (-y)]

Derivation

1. Split input into 2 regimes

2. if y < 3600

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 49.1%

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

      1. neg-mul-1 49.1%

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

   4. Simplified 49.1%

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

   if 3600 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 75.7%

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

      1. neg-mul-1 75.7%

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

   4. Simplified 75.7%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3600:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;-y\\ \end{array} \]

Alternative 5: 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 42.4%

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

   1. neg-mul-1 42.4%

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

4. Simplified 42.4%

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

5. Final simplification 42.4%

   \[\leadsto -x \]

Alternative 6: 2.3% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

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

   1. associate--l- 100.0%

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

   2. flip-- 59.3%

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

   3. metadata-eval 59.3%

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

3. Applied egg-rr 59.3%

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

   1. sub-neg 59.3%

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

   2. +-commutative 59.3%

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

   3. distribute-rgt-neg-in 59.3%

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

   4. fma-def 59.3%

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

   5. +-commutative 59.3%

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

   6. distribute-neg-in 59.3%

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

   7. +-commutative 59.3%

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

   8. sub-neg 59.3%

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

   9. +-commutative 59.3%

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

5. Simplified 59.3%

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

   1. fma-udef 59.3%

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

   2. +-commutative 59.3%

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

   3. add-sqr-sqrt 29.6%

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

   4. sqrt-unprod 50.7%

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

   5. sqr-neg 50.7%

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

   6. sqrt-unprod 21.2%

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

   7. add-sqr-sqrt 43.9%

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

   8. difference-of-squares 43.6%

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

7. Applied egg-rr 43.6%

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

   1. +-commutative 43.6%

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

   2. difference-of-squares 43.9%

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

   3. fma-def 43.9%

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

   4. +-commutative 43.9%

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

9. Simplified 43.9%

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

10. Taylor expanded in y around inf 2.1%

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

11. Final simplification 2.1%

    \[\leadsto y \]

Reproduce

herbie shell --seed 2023213 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))