Data.Colour.CIE:cieLAB from colour-2.3.3, D

Percentage Accurate: 100.0% → 100.0%

Time: 3.3s

Alternatives: 4

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 2: 71.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;\frac{y}{200} \leq -2 \cdot 10^{+118}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;\frac{y}{200} \leq 10^{-21}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (/ y 200.0) -2e+118)
   (* y -0.005)
   (if (<= (/ y 200.0) 1e-21) x (* y -0.005))))

C

double code(double x, double y) {
	double tmp;
	if ((y / 200.0) <= -2e+118) {
		tmp = y * -0.005;
	} else if ((y / 200.0) <= 1e-21) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y / 200.0d0) <= (-2d+118)) then
        tmp = y * (-0.005d0)
    else if ((y / 200.0d0) <= 1d-21) then
        tmp = x
    else
        tmp = y * (-0.005d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y / 200.0) <= -2e+118) {
		tmp = y * -0.005;
	} else if ((y / 200.0) <= 1e-21) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y / 200.0) <= -2e+118:
		tmp = y * -0.005
	elif (y / 200.0) <= 1e-21:
		tmp = x
	else:
		tmp = y * -0.005
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(y / 200.0) <= -2e+118)
		tmp = Float64(y * -0.005);
	elseif (Float64(y / 200.0) <= 1e-21)
		tmp = x;
	else
		tmp = Float64(y * -0.005);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y / 200.0) <= -2e+118)
		tmp = y * -0.005;
	elseif ((y / 200.0) <= 1e-21)
		tmp = x;
	else
		tmp = y * -0.005;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(y / 200.0), $MachinePrecision], -2e+118], N[(y * -0.005), $MachinePrecision], If[LessEqual[N[(y / 200.0), $MachinePrecision], 1e-21], x, N[(y * -0.005), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 y #s(literal 200 binary64)) < -1.99999999999999993e118 or 9.99999999999999908e-22 < (/.f64 y #s(literal 200 binary64))

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{-1}{200} \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{y \cdot \frac{-1}{200}} \]

      2. *-lowering-*.f64 82.5

         \[\leadsto \color{blue}{y \cdot -0.005} \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{y \cdot -0.005} \]

   if -1.99999999999999993e118 < (/.f64 y #s(literal 200 binary64)) < 9.99999999999999908e-22

   1. Initial program 100.0%

      \[x - \frac{y}{200} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf

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

   5. Simplified 78.5%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 99.9% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, -0.005, x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y -0.005 x))

C

double code(double x, double y) {
	return fma(y, -0.005, x);
}

Julia

function code(x, y)
	return fma(y, -0.005, x)
end

Wolfram

code[x_, y_] := N[(y * -0.005 + x), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

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

   2. +-commutative N/A

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

   3. distribute-neg-frac2 N/A

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

   4. div-inv N/A

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

   5. accelerator-lowering-fma.f64 N/A

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

   6. metadata-eval N/A

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

   7. metadata-eval 99.9

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{-0.005}, x\right) \]

4. Applied egg-rr 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.005, x\right)} \]
5. Add Preprocessing

Alternative 4: 50.0% accurate, 15.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[x - \frac{y}{200} \]
2. Add Preprocessing

3. Taylor expanded in x around inf

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

5. Simplified 51.7%

   \[\leadsto \color{blue}{x} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024204 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))