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

Percentage Accurate: 99.9% → 100.0%

Time: 5.3s

Alternatives: 4

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

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

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 100.0%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto 200 \cdot \left(x + \color{blue}{\left(\mathsf{neg}\left(y\right)\right)}\right) \]

   2. +-commutative N/A

      \[\leadsto 200 \cdot \left(\left(\mathsf{neg}\left(y\right)\right) + \color{blue}{x}\right) \]

   3. distribute-lft-in N/A

      \[\leadsto 200 \cdot \left(\mathsf{neg}\left(y\right)\right) + \color{blue}{200 \cdot x} \]

   4. neg-mul-1 N/A

      \[\leadsto 200 \cdot \left(-1 \cdot y\right) + 200 \cdot x \]

   5. associate-*r* N/A

      \[\leadsto \left(200 \cdot -1\right) \cdot y + \color{blue}{200} \cdot x \]

   6. *-commutative N/A

      \[\leadsto \left(200 \cdot -1\right) \cdot y + x \cdot \color{blue}{200} \]

   7. fma-define N/A

      \[\leadsto \mathsf{fma}\left(200 \cdot -1, \color{blue}{y}, x \cdot 200\right) \]

   8. fma-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(\left(200 \cdot -1\right), \color{blue}{y}, \left(x \cdot 200\right)\right) \]

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma.f64}\left(-200, y, \left(x \cdot 200\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{fma.f64}\left(-200, y, \left(200 \cdot x\right)\right) \]

   11. *-lowering-*.f64 100.0%

       \[\leadsto \mathsf{fma.f64}\left(-200, y, \mathsf{*.f64}\left(200, x\right)\right) \]

4. Applied egg-rr 100.0%

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

Alternative 2: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-63}:\\ \;\;\;\;200 \cdot x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+19}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.2e-63) (* 200.0 x) (if (<= x 1.3e+19) (* -200.0 y) (* 200.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.2e-63) {
		tmp = 200.0 * x;
	} else if (x <= 1.3e+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 (x <= (-4.2d-63)) then
        tmp = 200.0d0 * x
    else if (x <= 1.3d+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 (x <= -4.2e-63) {
		tmp = 200.0 * x;
	} else if (x <= 1.3e+19) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.2e-63:
		tmp = 200.0 * x
	elif x <= 1.3e+19:
		tmp = -200.0 * y
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.2e-63)
		tmp = Float64(200.0 * x);
	elseif (x <= 1.3e+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 (x <= -4.2e-63)
		tmp = 200.0 * x;
	elseif (x <= 1.3e+19)
		tmp = -200.0 * y;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.2e-63], N[(200.0 * x), $MachinePrecision], If[LessEqual[x, 1.3e+19], N[(-200.0 * y), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -4.2e-63 or 1.3e19 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 80.2%

         \[\leadsto \mathsf{*.f64}\left(200, \color{blue}{x}\right) \]

   5. Simplified 80.2%

      \[\leadsto \color{blue}{200 \cdot x} \]

   if -4.2e-63 < x < 1.3e19

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 78.2%

         \[\leadsto \mathsf{*.f64}\left(-200, \color{blue}{y}\right) \]

   5. Simplified 78.2%

      \[\leadsto \color{blue}{-200 \cdot y} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 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 100.0%

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

Alternative 4: 51.2% 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 100.0%

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

3. Taylor expanded in x around 0

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

   1. *-lowering-*.f64 46.6%

      \[\leadsto \mathsf{*.f64}\left(-200, \color{blue}{y}\right) \]

5. Simplified 46.6%

   \[\leadsto \color{blue}{-200 \cdot y} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024161 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))