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

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

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

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

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 * 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-define 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. Taylor expanded in x around 0 100.0%

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

   1. metadata-eval 100.0%

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

   2. distribute-lft-neg-in 100.0%

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

   3. *-commutative 100.0%

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

   4. +-commutative 100.0%

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

   5. fma-define 100.0%

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

   6. distribute-lft-neg-in 100.0%

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

   7. metadata-eval 100.0%

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

7. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, 500, -500 \cdot y\right)} \]
8. 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-define 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: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-98} \lor \neg \left(y \leq 4.2 \cdot 10^{-62}\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.5e-98) (not (<= y 4.2e-62))) (* -500.0 y) (* x 500.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e-98) || !(y <= 4.2e-62)) {
		tmp = -500.0 * y;
	} 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 <= (-5.5d-98)) .or. (.not. (y <= 4.2d-62))) then
        tmp = (-500.0d0) * y
    else
        tmp = x * 500.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e-98) || !(y <= 4.2e-62)) {
		tmp = -500.0 * y;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.5e-98) or not (y <= 4.2e-62):
		tmp = -500.0 * y
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.5e-98) || !(y <= 4.2e-62))
		tmp = Float64(-500.0 * y);
	else
		tmp = Float64(x * 500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.5e-98) || ~((y <= 4.2e-62)))
		tmp = -500.0 * y;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.5e-98], N[Not[LessEqual[y, 4.2e-62]], $MachinePrecision]], N[(-500.0 * y), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.4999999999999997e-98 or 4.1999999999999998e-62 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 80.0%

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

   if -5.4999999999999997e-98 < y < 4.1999999999999998e-62

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.3%

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

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{-98} \lor \neg \left(y \leq 4.2 \cdot 10^{-62}\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[(-500.0 * y), $MachinePrecision] + 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. Final simplification 100.0%

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

Alternative 6: 50.8% 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. Add Preprocessing

3. Taylor expanded in x around 0 52.2%

   \[\leadsto \color{blue}{-500 \cdot y} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024191 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))