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

Percentage Accurate: 100.0% → 100.0%

Time: 2.5s

Alternatives: 6

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-rgt-in 100.0%

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

   3. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 100.0% accurate, 0.0× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 100.0%

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

   1. fma-def 100.0%

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

5. Simplified 100.0%

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

6. Final simplification 100.0%

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

Alternative 3: 74.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+59} \lor \neg \left(y \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3e+59) (not (<= y 2e-9))) (* y -500.0) (* x 500.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3e+59) || !(y <= 2e-9)) {
		tmp = y * -500.0;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-3d+59)) .or. (.not. (y <= 2d-9))) then
        tmp = y * (-500.0d0)
    else
        tmp = x * 500.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3e+59) || !(y <= 2e-9)) {
		tmp = y * -500.0;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3e+59) or not (y <= 2e-9):
		tmp = y * -500.0
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3e+59) || !(y <= 2e-9))
		tmp = Float64(y * -500.0);
	else
		tmp = Float64(x * 500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3e+59) || ~((y <= 2e-9)))
		tmp = y * -500.0;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3e+59], N[Not[LessEqual[y, 2e-9]], $MachinePrecision]], N[(y * -500.0), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e59 or 2.00000000000000012e-9 < y

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.6%

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

   if -3e59 < y < 2.00000000000000012e-9

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.8%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+59} \lor \neg \left(y \leq 2 \cdot 10^{-9}\right):\\ \;\;\;\;y \cdot -500\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto x \cdot 500 + y \cdot -500 \]
5. Add Preprocessing

Alternative 5: 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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto 500 \cdot \left(x - y\right) \]
4. Add Preprocessing

Alternative 6: 51.0% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 51.7%

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

4. Final simplification 51.7%

   \[\leadsto y \cdot -500 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))