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

Percentage Accurate: 99.9% → 100.0%

Time: 3.4s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(200, x, -200 \cdot y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma 200.0 x (* -200.0 y)))

C

double code(double x, double y) {
	return fma(200.0, x, (-200.0 * y));
}

Julia

function code(x, y)
	return fma(200.0, x, Float64(-200.0 * y))
end

Wolfram

code[x_, y_] := N[(200.0 * x + N[(-200.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in y around inf 87.0%

   \[\leadsto \color{blue}{y \cdot \left(200 \cdot \frac{x}{y} - 200\right)} \]

4. Taylor expanded in y around 0 100.0%

   \[\leadsto \color{blue}{-200 \cdot y + 200 \cdot x} \]
5. Step-by-step derivation

   1. *-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot -200} + 200 \cdot x \]

   2. +-commutative 100.0%

      \[\leadsto \color{blue}{200 \cdot x + y \cdot -200} \]

   3. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(200, x, y \cdot -200\right)} \]

   4. *-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(200, x, \color{blue}{-200 \cdot y}\right) \]

6. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(200, x, -200 \cdot y\right)} \]

7. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(200, x, -200 \cdot y\right) \]
8. Add Preprocessing

Alternative 2: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-200, y, 200 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma -200.0 y (* 200.0 x)))

C

double code(double x, double y) {
	return fma(-200.0, y, (200.0 * x));
}

Julia

function code(x, y)
	return fma(-200.0, y, Float64(200.0 * x))
end

Wolfram

code[x_, y_] := N[(-200.0 * y + N[(200.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{-200 \cdot y + 200 \cdot x} \]
4. Step-by-step derivation

   1. fma-define 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]

6. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(-200, y, 200 \cdot x\right) \]
7. Add Preprocessing

Alternative 3: 75.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+38} \lor \neg \left(y \leq 3.4 \cdot 10^{+19}\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.35e+38) (not (<= y 3.4e+19))) (* -200.0 y) (* 200.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.35e+38) || !(y <= 3.4e+19)) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * 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 <= (-1.35d+38)) .or. (.not. (y <= 3.4d+19))) then
        tmp = (-200.0d0) * y
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.35e+38) || !(y <= 3.4e+19)) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.35e+38) or not (y <= 3.4e+19):
		tmp = -200.0 * y
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.35e+38) || !(y <= 3.4e+19))
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.35e+38) || ~((y <= 3.4e+19)))
		tmp = -200.0 * y;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.35e+38], N[Not[LessEqual[y, 3.4e+19]], $MachinePrecision]], N[(-200.0 * y), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.34999999999999998e38 or 3.4e19 < y

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 89.6%

      \[\leadsto \color{blue}{-200 \cdot y} \]

   if -1.34999999999999998e38 < y < 3.4e19

   1. Initial program 100.0%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 82.7%

      \[\leadsto \color{blue}{200 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 85.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+38} \lor \neg \left(y \leq 3.4 \cdot 10^{+19}\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y + 200 \cdot x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (* -200.0 y) (* 200.0 x)))

C

double code(double x, double y) {
	return (-200.0 * y) + (200.0 * x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((-200.0d0) * y) + (200.0d0 * x)
end function

Java

public static double code(double x, double y) {
	return (-200.0 * y) + (200.0 * x);
}

Python

def code(x, y):
	return (-200.0 * y) + (200.0 * x)

Julia

function code(x, y)
	return Float64(Float64(-200.0 * y) + Float64(200.0 * x))
end

MATLAB

function tmp = code(x, y)
	tmp = (-200.0 * y) + (200.0 * x);
end

Wolfram

code[x_, y_] := N[(N[(-200.0 * y), $MachinePrecision] + N[(200.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{-200 \cdot y + 200 \cdot x} \]

4. Final simplification 100.0%

   \[\leadsto -200 \cdot y + 200 \cdot x \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto 200 \cdot \left(x - y\right) \]
4. Add Preprocessing

Alternative 6: 51.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -200.0 y))

C

double code(double x, double y) {
	return -200.0 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-200.0d0) * y
end function

Java

public static double code(double x, double y) {
	return -200.0 * y;
}

Python

def code(x, y):
	return -200.0 * y

Julia

function code(x, y)
	return Float64(-200.0 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -200.0 * y;
end

Wolfram

code[x_, y_] := N[(-200.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 50.3%

   \[\leadsto \color{blue}{-200 \cdot y} \]

4. Final simplification 50.3%

   \[\leadsto -200 \cdot y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))