Data.Colour.CIE:cieLABView from colour-2.3.3, B

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(500, x, -500 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma 500.0 x (* -500.0 y)))

C

double code(double x, double y) {
	return fma(500.0, x, (-500.0 * y));
}

Julia

function code(x, y)
	return fma(500.0, x, Float64(-500.0 * y))
end

Wolfram

code[x_, y_] := N[(500.0 * x + N[(-500.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{-500 \cdot y + 500 \cdot x} \]
3. Step-by-step derivation

   1. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-500, y, 500 \cdot x\right)} \]

4. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-500, y, 500 \cdot x\right)} \]

5. Taylor expanded in y around 0 100.0%

   \[\leadsto \color{blue}{-500 \cdot y + 500 \cdot x} \]
6. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{500 \cdot x + -500 \cdot y} \]

   2. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, -500 \cdot y\right)} \]

7. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(500, x, -500 \cdot y\right)} \]

8. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(500, x, -500 \cdot y\right) \]

Alternative 2: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-500, y, 500 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma -500.0 y (* 500.0 x)))

C

double code(double x, double y) {
	return fma(-500.0, y, (500.0 * x));
}

Julia

function code(x, y)
	return fma(-500.0, y, Float64(500.0 * x))
end

Wolfram

code[x_, y_] := N[(-500.0 * y + N[(500.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{-500 \cdot y + 500 \cdot x} \]
3. Step-by-step derivation

   1. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-500, y, 500 \cdot x\right)} \]

4. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-500, y, 500 \cdot x\right)} \]

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(-500, y, 500 \cdot x\right) \]

Alternative 3: 72.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-112}:\\ \;\;\;\;500 \cdot x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+61}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.15e-112)
   (* 500.0 x)
   (if (<= x 5.4e+61) (* -500.0 y) (* 500.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.15e-112) {
		tmp = 500.0 * x;
	} else if (x <= 5.4e+61) {
		tmp = -500.0 * y;
	} else {
		tmp = 500.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-2.15d-112)) then
        tmp = 500.0d0 * x
    else if (x <= 5.4d+61) then
        tmp = (-500.0d0) * y
    else
        tmp = 500.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.15e-112) {
		tmp = 500.0 * x;
	} else if (x <= 5.4e+61) {
		tmp = -500.0 * y;
	} else {
		tmp = 500.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.15e-112:
		tmp = 500.0 * x
	elif x <= 5.4e+61:
		tmp = -500.0 * y
	else:
		tmp = 500.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.15e-112)
		tmp = Float64(500.0 * x);
	elseif (x <= 5.4e+61)
		tmp = Float64(-500.0 * y);
	else
		tmp = Float64(500.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.15e-112)
		tmp = 500.0 * x;
	elseif (x <= 5.4e+61)
		tmp = -500.0 * y;
	else
		tmp = 500.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.15e-112], N[(500.0 * x), $MachinePrecision], If[LessEqual[x, 5.4e+61], N[(-500.0 * y), $MachinePrecision], N[(500.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -2.1499999999999999e-112 or 5.4000000000000004e61 < x

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around inf 77.5%

      \[\leadsto \color{blue}{500 \cdot x} \]

   if -2.1499999999999999e-112 < x < 5.4000000000000004e61

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around 0 80.5%

      \[\leadsto \color{blue}{-500 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.15 \cdot 10^{-112}:\\ \;\;\;\;500 \cdot x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+61}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Final simplification 100.0%

   \[\leadsto 500 \cdot \left(x - y\right) \]

Alternative 5: 50.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ -500 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -500.0 y))

C

double code(double x, double y) {
	return -500.0 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-500.0d0) * y
end function

Java

public static double code(double x, double y) {
	return -500.0 * y;
}

Python

def code(x, y):
	return -500.0 * y

Julia

function code(x, y)
	return Float64(-500.0 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -500.0 * y;
end

Wolfram

code[x_, y_] := N[(-500.0 * y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 49.8%

   \[\leadsto \color{blue}{-500 \cdot y} \]

3. Final simplification 49.8%

   \[\leadsto -500 \cdot y \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))