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

Percentage Accurate: 100.0% → 100.0%

Time: 3.9s

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: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.7 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+82}:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.7e+55) x (if (<= x 1.25e+82) (/ y -200.0) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.7e+55) {
		tmp = x;
	} else if (x <= 1.25e+82) {
		tmp = y / -200.0;
	} else {
		tmp = 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 <= (-4.7d+55)) then
        tmp = x
    else if (x <= 1.25d+82) then
        tmp = y / (-200.0d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.7e+55) {
		tmp = x;
	} else if (x <= 1.25e+82) {
		tmp = y / -200.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.7e+55:
		tmp = x
	elif x <= 1.25e+82:
		tmp = y / -200.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.7e+55)
		tmp = x;
	elseif (x <= 1.25e+82)
		tmp = Float64(y / -200.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.7e+55)
		tmp = x;
	elseif (x <= 1.25e+82)
		tmp = y / -200.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.7e+55], x, If[LessEqual[x, 1.25e+82], N[(y / -200.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.7000000000000001e55 or 1.25000000000000004e82 < x

   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 83.2%

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

   if -4.7000000000000001e55 < x < 1.25000000000000004e82

   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 75.9%

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

   5. Simplified 75.9%

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

      1. *-commutative N/A

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

      2. metadata-eval N/A

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

      3. div-inv N/A

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

      4. /-lowering-/.f64 76.1%

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

   7. Applied egg-rr 76.1%

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

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.6e+55) x (if (<= x 1.8e+74) (* y -0.005) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+55) {
		tmp = x;
	} else if (x <= 1.8e+74) {
		tmp = y * -0.005;
	} else {
		tmp = 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 <= (-1.6d+55)) then
        tmp = x
    else if (x <= 1.8d+74) then
        tmp = y * (-0.005d0)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.6e+55) {
		tmp = x;
	} else if (x <= 1.8e+74) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.6e+55:
		tmp = x
	elif x <= 1.8e+74:
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.6e+55)
		tmp = x;
	elseif (x <= 1.8e+74)
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.6e+55)
		tmp = x;
	elseif (x <= 1.8e+74)
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.6e+55], x, If[LessEqual[x, 1.8e+74], N[(y * -0.005), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6000000000000001e55 or 1.79999999999999994e74 < x

   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 83.2%

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

   if -1.6000000000000001e55 < x < 1.79999999999999994e74

   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 75.9%

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

   5. Simplified 75.9%

      \[\leadsto \color{blue}{-0.005 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.6 \cdot 10^{+55}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.2% 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 47.8%

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

Reproduce

herbie shell --seed 2024158 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))