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

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 5

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. Final simplification 100.0%

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

Alternative 2: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7800:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.25e-125) x (if (<= x 7800.0) (* y -0.005) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.25e-125) {
		tmp = x;
	} else if (x <= 7800.0) {
		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 <= (-2.25d-125)) then
        tmp = x
    else if (x <= 7800.0d0) 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 <= -2.25e-125) {
		tmp = x;
	} else if (x <= 7800.0) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.25e-125:
		tmp = x
	elif x <= 7800.0:
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.25e-125)
		tmp = x;
	elseif (x <= 7800.0)
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.25e-125)
		tmp = x;
	elseif (x <= 7800.0)
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.25e-125], x, If[LessEqual[x, 7800.0], N[(y * -0.005), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25000000000000006e-125 or 7800 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/l* 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + y \cdot -0.005} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.0%

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

   if -2.25000000000000006e-125 < x < 7800

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/l* 99.8%

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

      6. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot -0.005} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - 0.005\right)} \]

   6. Taylor expanded in x around 0 83.1%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 7800:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.15:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.25e-125) x (if (<= x 0.15) (/ y -200.0) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.25e-125) {
		tmp = x;
	} else if (x <= 0.15) {
		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 <= (-2.25d-125)) then
        tmp = x
    else if (x <= 0.15d0) 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 <= -2.25e-125) {
		tmp = x;
	} else if (x <= 0.15) {
		tmp = y / -200.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.25e-125:
		tmp = x
	elif x <= 0.15:
		tmp = y / -200.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.25e-125)
		tmp = x;
	elseif (x <= 0.15)
		tmp = Float64(y / -200.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.25e-125)
		tmp = x;
	elseif (x <= 0.15)
		tmp = y / -200.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.25e-125], x, If[LessEqual[x, 0.15], N[(y / -200.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -2.25000000000000006e-125 or 0.149999999999999994 < x

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/l* 99.9%

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

      6. metadata-eval 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + y \cdot -0.005} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 71.0%

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

   if -2.25000000000000006e-125 < x < 0.149999999999999994

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-frac-neg 100.0%

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

      3. neg-mul-1 100.0%

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

      4. *-commutative 100.0%

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

      5. associate-/l* 99.8%

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

      6. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + y \cdot -0.005} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

      \[\leadsto \color{blue}{y \cdot \left(\frac{x}{y} - 0.005\right)} \]

   6. Taylor expanded in x around 0 83.1%

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

      1. metadata-eval 83.1%

         \[\leadsto y \cdot \color{blue}{\left(-0.005\right)} \]

      2. metadata-eval 83.1%

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

      3. distribute-rgt-neg-in 83.1%

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

      4. div-inv 83.3%

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

      5. distribute-neg-frac2 83.3%

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

      6. metadata-eval 83.3%

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

   8. Applied egg-rr 83.3%

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

4. Final simplification 75.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.25 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 0.15:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot -0.005 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* y -0.005)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * (-0.005d0))
end function

Java

public static double code(double x, double y) {
	return x + (y * -0.005);
}

Python

def code(x, y):
	return x + (y * -0.005)

Julia

function code(x, y)
	return Float64(x + Float64(y * -0.005))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y * -0.005);
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. distribute-frac-neg 100.0%

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

   3. neg-mul-1 100.0%

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

   4. *-commutative 100.0%

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

   5. associate-/l* 99.9%

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

   6. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot -0.005} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto x + y \cdot -0.005 \]
6. Add Preprocessing

Alternative 5: 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. Step-by-step derivation

   1. sub-neg 100.0%

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

   2. distribute-frac-neg 100.0%

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

   3. neg-mul-1 100.0%

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

   4. *-commutative 100.0%

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

   5. associate-/l* 99.9%

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

   6. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + y \cdot -0.005} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 51.5%

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

6. Final simplification 51.5%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024071 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))