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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

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. Add Preprocessing

Alternative 2: 72.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-128} \lor \neg \left(x \leq 1.45 \cdot 10^{-5}\right) \land x \leq 165000000000:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.9e-9)
   x
   (if (or (<= x 2.6e-128) (and (not (<= x 1.45e-5)) (<= x 165000000000.0)))
     (/ y -200.0)
     x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.9e-9) {
		tmp = x;
	} else if ((x <= 2.6e-128) || (!(x <= 1.45e-5) && (x <= 165000000000.0))) {
		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 <= (-3.9d-9)) then
        tmp = x
    else if ((x <= 2.6d-128) .or. (.not. (x <= 1.45d-5)) .and. (x <= 165000000000.0d0)) 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 <= -3.9e-9) {
		tmp = x;
	} else if ((x <= 2.6e-128) || (!(x <= 1.45e-5) && (x <= 165000000000.0))) {
		tmp = y / -200.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.9e-9:
		tmp = x
	elif (x <= 2.6e-128) or (not (x <= 1.45e-5) and (x <= 165000000000.0)):
		tmp = y / -200.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.9e-9)
		tmp = x;
	elseif ((x <= 2.6e-128) || (!(x <= 1.45e-5) && (x <= 165000000000.0)))
		tmp = Float64(y / -200.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.9e-9)
		tmp = x;
	elseif ((x <= 2.6e-128) || (~((x <= 1.45e-5)) && (x <= 165000000000.0)))
		tmp = y / -200.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.9e-9], x, If[Or[LessEqual[x, 2.6e-128], And[N[Not[LessEqual[x, 1.45e-5]], $MachinePrecision], LessEqual[x, 165000000000.0]]], N[(y / -200.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9000000000000002e-9 or 2.59999999999999981e-128 < x < 1.45e-5 or 1.65e11 < 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 78.7%

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

   if -3.9000000000000002e-9 < x < 2.59999999999999981e-128 or 1.45e-5 < x < 1.65e11

   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 99.8%

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

   6. Taylor expanded in x around 0 84.5%

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

      1. metadata-eval 84.5%

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

      2. metadata-eval 84.5%

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

      3. distribute-rgt-neg-in 84.5%

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

      4. div-inv 84.6%

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

      5. distribute-neg-frac2 84.6%

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

      6. metadata-eval 84.6%

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

   8. Applied egg-rr 84.6%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.9 \cdot 10^{-9}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-128} \lor \neg \left(x \leq 1.45 \cdot 10^{-5}\right) \land x \leq 165000000000:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-5}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-128}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3e-5) x (if (<= x 2.6e-128) (* y -0.005) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3e-5) {
		tmp = x;
	} else if (x <= 2.6e-128) {
		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 <= (-3d-5)) then
        tmp = x
    else if (x <= 2.6d-128) 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 <= -3e-5) {
		tmp = x;
	} else if (x <= 2.6e-128) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3e-5:
		tmp = x
	elif x <= 2.6e-128:
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3e-5)
		tmp = x;
	elseif (x <= 2.6e-128)
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3e-5)
		tmp = x;
	elseif (x <= 2.6e-128)
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3e-5], x, If[LessEqual[x, 2.6e-128], N[(y * -0.005), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3.00000000000000008e-5 or 2.59999999999999981e-128 < 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 75.3%

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

   if -3.00000000000000008e-5 < x < 2.59999999999999981e-128

   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 99.8%

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

   6. Taylor expanded in x around 0 84.2%

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

Alternative 5: 50.7% 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 52.1%

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

Reproduce

herbie shell --seed 2024086 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))