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

Percentage Accurate: 100.0% → 100.0%

Time: 1.7s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{500} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (/ y 500.0)))

C

double code(double x, double y) {
	return x + (y / 500.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y / 500.0d0)
end function

Java

public static double code(double x, double y) {
	return x + (y / 500.0);
}

Python

def code(x, y):
	return x + (y / 500.0)

Julia

function code(x, y)
	return Float64(x + Float64(y / 500.0))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y / 500.0);
end

Wolfram

code[x_, y_] := N[(x + N[(y / 500.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto x + \frac{y}{500} \]
4. Add Preprocessing

Alternative 2: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7000000 \lor \neg \left(x \leq -6 \cdot 10^{-46}\right) \land x \leq 2.9 \cdot 10^{+108}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -4.2e+28)
   x
   (if (or (<= x -7000000.0) (and (not (<= x -6e-46)) (<= x 2.9e+108)))
     (* y 0.002)
     x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -4.2e+28) {
		tmp = x;
	} else if ((x <= -7000000.0) || (!(x <= -6e-46) && (x <= 2.9e+108))) {
		tmp = y * 0.002;
	} 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 <= (-4.2d+28)) then
        tmp = x
    else if ((x <= (-7000000.0d0)) .or. (.not. (x <= (-6d-46))) .and. (x <= 2.9d+108)) then
        tmp = y * 0.002d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -4.2e+28) {
		tmp = x;
	} else if ((x <= -7000000.0) || (!(x <= -6e-46) && (x <= 2.9e+108))) {
		tmp = y * 0.002;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -4.2e+28:
		tmp = x
	elif (x <= -7000000.0) or (not (x <= -6e-46) and (x <= 2.9e+108)):
		tmp = y * 0.002
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -4.2e+28)
		tmp = x;
	elseif ((x <= -7000000.0) || (!(x <= -6e-46) && (x <= 2.9e+108)))
		tmp = Float64(y * 0.002);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -4.2e+28)
		tmp = x;
	elseif ((x <= -7000000.0) || (~((x <= -6e-46)) && (x <= 2.9e+108)))
		tmp = y * 0.002;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -4.2e+28], x, If[Or[LessEqual[x, -7000000.0], And[N[Not[LessEqual[x, -6e-46]], $MachinePrecision], LessEqual[x, 2.9e+108]]], N[(y * 0.002), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -4.19999999999999978e28 or -7e6 < x < -5.99999999999999975e-46 or 2.90000000000000007e108 < x

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

      2. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

      4. neg-mul-1 100.0%

         \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

      5. associate-/l* 99.9%

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

      6. associate-/r/ 99.9%

         \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

      7. cancel-sign-sub-inv 99.9%

         \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

      8. metadata-eval 99.9%

         \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

      9. metadata-eval 99.9%

         \[\leadsto x + \color{blue}{0.002} \cdot y \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.9%

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

   if -4.19999999999999978e28 < x < -7e6 or -5.99999999999999975e-46 < x < 2.90000000000000007e108

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

      2. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

      4. neg-mul-1 100.0%

         \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

      5. associate-/l* 99.6%

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

      6. associate-/r/ 99.8%

         \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

      7. cancel-sign-sub-inv 99.8%

         \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

      8. metadata-eval 99.8%

         \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

      9. metadata-eval 99.8%

         \[\leadsto x + \color{blue}{0.002} \cdot y \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 79.6%

      \[\leadsto \color{blue}{0.002 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -7000000 \lor \neg \left(x \leq -6 \cdot 10^{-46}\right) \land x \leq 2.9 \cdot 10^{+108}:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -95:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.5e+28)
   x
   (if (<= x -95.0)
     (* y 0.002)
     (if (<= x -1.3e-48) x (if (<= x 2.4e+107) (/ y 500.0) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.5e+28) {
		tmp = x;
	} else if (x <= -95.0) {
		tmp = y * 0.002;
	} else if (x <= -1.3e-48) {
		tmp = x;
	} else if (x <= 2.4e+107) {
		tmp = y / 500.0;
	} 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 <= (-5.5d+28)) then
        tmp = x
    else if (x <= (-95.0d0)) then
        tmp = y * 0.002d0
    else if (x <= (-1.3d-48)) then
        tmp = x
    else if (x <= 2.4d+107) then
        tmp = y / 500.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -5.5e+28) {
		tmp = x;
	} else if (x <= -95.0) {
		tmp = y * 0.002;
	} else if (x <= -1.3e-48) {
		tmp = x;
	} else if (x <= 2.4e+107) {
		tmp = y / 500.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.5e+28:
		tmp = x
	elif x <= -95.0:
		tmp = y * 0.002
	elif x <= -1.3e-48:
		tmp = x
	elif x <= 2.4e+107:
		tmp = y / 500.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.5e+28)
		tmp = x;
	elseif (x <= -95.0)
		tmp = Float64(y * 0.002);
	elseif (x <= -1.3e-48)
		tmp = x;
	elseif (x <= 2.4e+107)
		tmp = Float64(y / 500.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.5e+28)
		tmp = x;
	elseif (x <= -95.0)
		tmp = y * 0.002;
	elseif (x <= -1.3e-48)
		tmp = x;
	elseif (x <= 2.4e+107)
		tmp = y / 500.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.5e+28], x, If[LessEqual[x, -95.0], N[(y * 0.002), $MachinePrecision], If[LessEqual[x, -1.3e-48], x, If[LessEqual[x, 2.4e+107], N[(y / 500.0), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if x < -5.5000000000000003e28 or -95 < x < -1.29999999999999994e-48 or 2.4000000000000001e107 < x

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

      2. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

      4. neg-mul-1 100.0%

         \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

      5. associate-/l* 99.9%

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

      6. associate-/r/ 99.9%

         \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

      7. cancel-sign-sub-inv 99.9%

         \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

      8. metadata-eval 99.9%

         \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

      9. metadata-eval 99.9%

         \[\leadsto x + \color{blue}{0.002} \cdot y \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 84.9%

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

   if -5.5000000000000003e28 < x < -95

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

      2. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

      4. neg-mul-1 100.0%

         \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

      5. associate-/l* 99.4%

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

      6. associate-/r/ 100.0%

         \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

      7. cancel-sign-sub-inv 100.0%

         \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

      8. metadata-eval 100.0%

         \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

      9. metadata-eval 100.0%

         \[\leadsto x + \color{blue}{0.002} \cdot y \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 100.0%

      \[\leadsto \color{blue}{0.002 \cdot y} \]

   if -1.29999999999999994e-48 < x < 2.4000000000000001e107

   1. Initial program 100.0%

      \[x + \frac{y}{500} \]
   2. Step-by-step derivation

      1. remove-double-neg 100.0%

         \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

      2. distribute-frac-neg 100.0%

         \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

      3. unsub-neg 100.0%

         \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

      4. neg-mul-1 100.0%

         \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

      5. associate-/l* 99.6%

         \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

      6. associate-/r/ 99.8%

         \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

      7. cancel-sign-sub-inv 99.8%

         \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

      8. metadata-eval 99.8%

         \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

      9. metadata-eval 99.8%

         \[\leadsto x + \color{blue}{0.002} \cdot y \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 78.8%

      \[\leadsto \color{blue}{0.002 \cdot y} \]
   6. Step-by-step derivation

      1. *-commutative 78.8%

         \[\leadsto \color{blue}{y \cdot 0.002} \]

      2. metadata-eval 78.8%

         \[\leadsto y \cdot \color{blue}{\frac{1}{500}} \]

      3. div-inv 79.0%

         \[\leadsto \color{blue}{\frac{y}{500}} \]

   7. Applied egg-rr 79.0%

      \[\leadsto \color{blue}{\frac{y}{500}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -95:\\ \;\;\;\;y \cdot 0.002\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+107}:\\ \;\;\;\;\frac{y}{500}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot 0.002 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ x (* y 0.002)))

C

double code(double x, double y) {
	return x + (y * 0.002);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y * 0.002d0)
end function

Java

public static double code(double x, double y) {
	return x + (y * 0.002);
}

Python

def code(x, y):
	return x + (y * 0.002)

Julia

function code(x, y)
	return Float64(x + Float64(y * 0.002))
end

MATLAB

function tmp = code(x, y)
	tmp = x + (y * 0.002);
end

Wolfram

code[x_, y_] := N[(x + N[(y * 0.002), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x + \frac{y}{500} \]
2. Step-by-step derivation

   1. remove-double-neg 100.0%

      \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

   2. distribute-frac-neg 100.0%

      \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

   3. unsub-neg 100.0%

      \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

   4. neg-mul-1 100.0%

      \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

   5. associate-/l* 99.7%

      \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

   6. associate-/r/ 99.9%

      \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

   7. cancel-sign-sub-inv 99.9%

      \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

   8. metadata-eval 99.9%

      \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

   9. metadata-eval 99.9%

      \[\leadsto x + \color{blue}{0.002} \cdot y \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto x + y \cdot 0.002 \]
6. Add Preprocessing

Alternative 5: 50.6% 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%

   \[x + \frac{y}{500} \]
2. Step-by-step derivation

   1. remove-double-neg 100.0%

      \[\leadsto x + \color{blue}{\left(-\left(-\frac{y}{500}\right)\right)} \]

   2. distribute-frac-neg 100.0%

      \[\leadsto x + \left(-\color{blue}{\frac{-y}{500}}\right) \]

   3. unsub-neg 100.0%

      \[\leadsto \color{blue}{x - \frac{-y}{500}} \]

   4. neg-mul-1 100.0%

      \[\leadsto x - \frac{\color{blue}{-1 \cdot y}}{500} \]

   5. associate-/l* 99.7%

      \[\leadsto x - \color{blue}{\frac{-1}{\frac{500}{y}}} \]

   6. associate-/r/ 99.9%

      \[\leadsto x - \color{blue}{\frac{-1}{500} \cdot y} \]

   7. cancel-sign-sub-inv 99.9%

      \[\leadsto \color{blue}{x + \left(-\frac{-1}{500}\right) \cdot y} \]

   8. metadata-eval 99.9%

      \[\leadsto x + \left(-\color{blue}{-0.002}\right) \cdot y \]

   9. metadata-eval 99.9%

      \[\leadsto x + \color{blue}{0.002} \cdot y \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{x + 0.002 \cdot y} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 52.1%

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

6. Final simplification 52.1%

   \[\leadsto x \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024010 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, C"
  :precision binary64
  (+ x (/ y 500.0)))