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

Percentage Accurate: 100.0% → 100.0%

Time: 3.2s

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: 73.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.92 \cdot 10^{+37}:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-200}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.92e+37) (/ y -200.0) (if (<= y 7.8e+99) x (/ y -200.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.92e+37) {
		tmp = y / -200.0;
	} else if (y <= 7.8e+99) {
		tmp = x;
	} else {
		tmp = y / -200.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.92d+37)) then
        tmp = y / (-200.0d0)
    else if (y <= 7.8d+99) then
        tmp = x
    else
        tmp = y / (-200.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.92e+37) {
		tmp = y / -200.0;
	} else if (y <= 7.8e+99) {
		tmp = x;
	} else {
		tmp = y / -200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.92e+37:
		tmp = y / -200.0
	elif y <= 7.8e+99:
		tmp = x
	else:
		tmp = y / -200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.92e+37)
		tmp = Float64(y / -200.0);
	elseif (y <= 7.8e+99)
		tmp = x;
	else
		tmp = Float64(y / -200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.92e+37)
		tmp = y / -200.0;
	elseif (y <= 7.8e+99)
		tmp = x;
	else
		tmp = y / -200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.92e+37], N[(y / -200.0), $MachinePrecision], If[LessEqual[y, 7.8e+99], x, N[(y / -200.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.91999999999999994e37 or 7.79999999999999989e99 < y

   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. *-lowering-*.f64 85.4%

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

   5. Simplified 85.4%

      \[\leadsto \color{blue}{-0.005 \cdot y} \]
   6. Step-by-step derivation

      1. metadata-eval N/A

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

      2. metadata-eval N/A

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

      3. distribute-lft-neg-in N/A

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

      4. associate-/r/ N/A

         \[\leadsto \mathsf{neg}\left(\frac{1}{\frac{200}{y}}\right) \]

      5. clear-num N/A

         \[\leadsto \mathsf{neg}\left(\frac{y}{200}\right) \]

      6. distribute-neg-frac2 N/A

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

      7. /-lowering-/.f64 N/A

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

      8. metadata-eval 85.7%

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

   7. Applied egg-rr 85.7%

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

   if -1.91999999999999994e37 < y < 7.79999999999999989e99

   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 76.9%

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

Alternative 3: 73.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+32}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.3e+32) (* y -0.005) (if (<= y 8e+99) x (* y -0.005))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.3e+32) {
		tmp = y * -0.005;
	} else if (y <= 8e+99) {
		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 <= (-6.3d+32)) then
        tmp = y * (-0.005d0)
    else if (y <= 8d+99) 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 <= -6.3e+32) {
		tmp = y * -0.005;
	} else if (y <= 8e+99) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.3e+32:
		tmp = y * -0.005
	elif y <= 8e+99:
		tmp = x
	else:
		tmp = y * -0.005
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.3e+32)
		tmp = Float64(y * -0.005);
	elseif (y <= 8e+99)
		tmp = x;
	else
		tmp = Float64(y * -0.005);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.3e+32)
		tmp = y * -0.005;
	elseif (y <= 8e+99)
		tmp = x;
	else
		tmp = y * -0.005;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.3e+32], N[(y * -0.005), $MachinePrecision], If[LessEqual[y, 8e+99], x, N[(y * -0.005), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3000000000000002e32 or 7.9999999999999997e99 < y

   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. *-lowering-*.f64 85.4%

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

   5. Simplified 85.4%

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

   if -6.3000000000000002e32 < y < 7.9999999999999997e99

   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 76.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.3 \cdot 10^{+32}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+99}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.2% accurate, 5.0× 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 52.8%

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))