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

Percentage Accurate: 100.0% → 100.0%

Time: 4.5s

Alternatives: 5

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. Final simplification 100.0%

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

Alternative 2: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;1 - x \leq -50000000 \lor \neg \left(1 - x \leq 1\right):\\ \;\;\;\;\left(-x\right) - y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= (- 1.0 x) -50000000.0) (not (<= (- 1.0 x) 1.0)))
   (- (- x) y)
   (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if (((1.0 - x) <= -50000000.0) || !((1.0 - x) <= 1.0)) {
		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) <= (-50000000.0d0)) .or. (.not. ((1.0d0 - x) <= 1.0d0))) 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) <= -50000000.0) || !((1.0 - x) <= 1.0)) {
		tmp = -x - y;
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if ((1.0 - x) <= -50000000.0) or not ((1.0 - x) <= 1.0):
		tmp = -x - y
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((Float64(1.0 - x) <= -50000000.0) || !(Float64(1.0 - x) <= 1.0))
		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) <= -50000000.0) || ~(((1.0 - x) <= 1.0)))
		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], -50000000.0], N[Not[LessEqual[N[(1.0 - x), $MachinePrecision], 1.0]], $MachinePrecision]], N[((-x) - y), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (-.f64 1 x) < -5e7 or 1 < (-.f64 1 x)

   1. Initial program 100.0%

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

      1. flip-- 51.8%

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

      2. div-inv 51.7%

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

      3. fma-neg 51.7%

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

      4. metadata-eval 51.7%

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

      5. pow2 51.7%

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

   4. Applied egg-rr 51.7%

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

   5. Taylor expanded in x around inf 51.1%

      \[\leadsto \mathsf{fma}\left(1 - {x}^{2}, \color{blue}{\frac{1}{x}}, -y\right) \]

   6. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. unsub-neg 99.5%

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

      3. mul-1-neg 99.5%

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

   8. Simplified 99.5%

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

   if -5e7 < (-.f64 1 x) < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.5%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;1 - x \leq -50000000 \lor \neg \left(1 - x \leq 1\right):\\ \;\;\;\;\left(-x\right) - y\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+25} \lor \neg \left(y \leq 6 \cdot 10^{+31}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.4e+25) (not (<= y 6e+31))) (- y) (- 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e+25) || !(y <= 6e+31)) {
		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 <= (-4.4d+25)) .or. (.not. (y <= 6d+31))) 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 <= -4.4e+25) || !(y <= 6e+31)) {
		tmp = -y;
	} else {
		tmp = 1.0 - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.4e+25) or not (y <= 6e+31):
		tmp = -y
	else:
		tmp = 1.0 - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.4e+25) || !(y <= 6e+31))
		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 <= -4.4e+25) || ~((y <= 6e+31)))
		tmp = -y;
	else
		tmp = 1.0 - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.4e+25], N[Not[LessEqual[y, 6e+31]], $MachinePrecision]], (-y), N[(1.0 - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4000000000000001e25 or 5.99999999999999978e31 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. neg-mul-1 78.6%

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

   5. Simplified 78.6%

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

   if -4.4000000000000001e25 < y < 5.99999999999999978e31

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 93.7%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+25} \lor \neg \left(y \leq 6 \cdot 10^{+31}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;1 - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+24} \lor \neg \left(y \leq 1.15 \cdot 10^{+32}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.2e+24) (not (<= y 1.15e+32))) (- y) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.2e+24) || !(y <= 1.15e+32)) {
		tmp = -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 ((y <= (-6.2d+24)) .or. (.not. (y <= 1.15d+32))) then
        tmp = -y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -6.2e+24) || !(y <= 1.15e+32)) {
		tmp = -y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.2e+24) or not (y <= 1.15e+32):
		tmp = -y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.2e+24) || !(y <= 1.15e+32))
		tmp = Float64(-y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.2e+24) || ~((y <= 1.15e+32)))
		tmp = -y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.2e+24], N[Not[LessEqual[y, 1.15e+32]], $MachinePrecision]], (-y), (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -6.20000000000000022e24 or 1.15e32 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.6%

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

      1. neg-mul-1 78.6%

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

   5. Simplified 78.6%

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

   if -6.20000000000000022e24 < y < 1.15e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 59.6%

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

      1. neg-mul-1 59.6%

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

   5. Simplified 59.6%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+24} \lor \neg \left(y \leq 1.15 \cdot 10^{+32}\right):\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.8% 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. Add Preprocessing

3. Taylor expanded in x around inf 44.3%

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

   1. neg-mul-1 44.3%

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

5. Simplified 44.3%

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

6. Final simplification 44.3%

   \[\leadsto -x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(FPCore (x y)
  :name "Data.Colour.CIE.Chromaticity:chromaCoords from colour-2.3.3"
  :precision binary64
  (- (- 1.0 x) y))