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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 4

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, 0.8× 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. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift--.f64 N/A

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

   3. sub-neg N/A

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

   4. +-commutative N/A

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

   5. distribute-lft-in N/A

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

   6. neg-mul-1 N/A

      \[\leadsto 500 \cdot \color{blue}{\left(-1 \cdot y\right)} + 500 \cdot x \]

   7. associate-*r* N/A

      \[\leadsto \color{blue}{\left(500 \cdot -1\right) \cdot y} + 500 \cdot x \]

   8. *-commutative N/A

      \[\leadsto \left(500 \cdot -1\right) \cdot y + \color{blue}{x \cdot 500} \]

   9. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(500 \cdot -1, y, x \cdot 500\right)} \]

   10. metadata-eval N/A

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

   11. lower-*.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -55000000000000 \lor \neg \left(x \leq 3 \cdot 10^{+19}\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -55000000000000.0) (not (<= x 3e+19)))
   (* 500.0 x)
   (* -500.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -55000000000000.0) || !(x <= 3e+19)) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-55000000000000.0d0)) .or. (.not. (x <= 3d+19))) then
        tmp = 500.0d0 * x
    else
        tmp = (-500.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -55000000000000.0) || !(x <= 3e+19)) {
		tmp = 500.0 * x;
	} else {
		tmp = -500.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -55000000000000.0) or not (x <= 3e+19):
		tmp = 500.0 * x
	else:
		tmp = -500.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -55000000000000.0) || !(x <= 3e+19))
		tmp = Float64(500.0 * x);
	else
		tmp = Float64(-500.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -55000000000000.0) || ~((x <= 3e+19)))
		tmp = 500.0 * x;
	else
		tmp = -500.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -55000000000000.0], N[Not[LessEqual[x, 3e+19]], $MachinePrecision]], N[(500.0 * x), $MachinePrecision], N[(-500.0 * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e13 or 3e19 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 83.1

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

   5. Applied rewrites 83.1%

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

   if -5.5e13 < x < 3e19

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 75.5

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

   5. Applied rewrites 75.5%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -55000000000000 \lor \neg \left(x \leq 3 \cdot 10^{+19}\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;-500 \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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 4: 51.3% accurate, 1.5× 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

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

   1. lower-*.f64 52.3

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

5. Applied rewrites 52.3%

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

Reproduce

herbie shell --seed 2024324 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))