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

Percentage Accurate: 100.0% → 100.0%

Time: 2.2s

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

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

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 99.9%

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

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

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+18} \lor \neg \left(y \leq 2.8 \cdot 10^{-13}\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.6e+18) (not (<= y 2.8e-13))) (* -500.0 y) (* 500.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.6e+18) || !(y <= 2.8e-13)) {
		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 ((y <= (-8.6d+18)) .or. (.not. (y <= 2.8d-13))) 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 ((y <= -8.6e+18) || !(y <= 2.8e-13)) {
		tmp = -500.0 * y;
	} else {
		tmp = 500.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.6e+18) or not (y <= 2.8e-13):
		tmp = -500.0 * y
	else:
		tmp = 500.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.6e+18) || !(y <= 2.8e-13))
		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 ((y <= -8.6e+18) || ~((y <= 2.8e-13)))
		tmp = -500.0 * y;
	else
		tmp = 500.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.6e+18], N[Not[LessEqual[y, 2.8e-13]], $MachinePrecision]], N[(-500.0 * y), $MachinePrecision], N[(500.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6e18 or 2.8000000000000002e-13 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 81.7%

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

   if -8.6e18 < y < 2.8000000000000002e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.7%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{+18} \lor \neg \left(y \leq 2.8 \cdot 10^{-13}\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

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

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 99.9%

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

3. Final simplification 99.9%

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

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 99.9%

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

3. Taylor expanded in x around 0 53.1%

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

4. Final simplification 53.1%

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

Reproduce

herbie shell --seed 2024029 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))