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

Percentage Accurate: 100.0% → 100.0%

Time: 2.8s

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: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+80} \lor \neg \left(y \leq -6.2 \cdot 10^{-54} \lor \neg \left(y \leq -2.8 \cdot 10^{-77}\right) \land \left(y \leq -1 \cdot 10^{-125} \lor \neg \left(y \leq -5.2 \cdot 10^{-143}\right) \land y \leq 185000000\right)\right):\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.15e+80)
         (not
          (or (<= y -6.2e-54)
              (and (not (<= y -2.8e-77))
                   (or (<= y -1e-125)
                       (and (not (<= y -5.2e-143)) (<= y 185000000.0)))))))
   (* y -0.005)
   x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.15e+80) || !((y <= -6.2e-54) || (!(y <= -2.8e-77) && ((y <= -1e-125) || (!(y <= -5.2e-143) && (y <= 185000000.0)))))) {
		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 ((y <= (-3.15d+80)) .or. (.not. (y <= (-6.2d-54)) .or. (.not. (y <= (-2.8d-77))) .and. (y <= (-1d-125)) .or. (.not. (y <= (-5.2d-143))) .and. (y <= 185000000.0d0))) 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 ((y <= -3.15e+80) || !((y <= -6.2e-54) || (!(y <= -2.8e-77) && ((y <= -1e-125) || (!(y <= -5.2e-143) && (y <= 185000000.0)))))) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.15e+80) or not ((y <= -6.2e-54) or (not (y <= -2.8e-77) and ((y <= -1e-125) or (not (y <= -5.2e-143) and (y <= 185000000.0))))):
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.15e+80) || !((y <= -6.2e-54) || (!(y <= -2.8e-77) && ((y <= -1e-125) || (!(y <= -5.2e-143) && (y <= 185000000.0))))))
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.15e+80) || ~(((y <= -6.2e-54) || (~((y <= -2.8e-77)) && ((y <= -1e-125) || (~((y <= -5.2e-143)) && (y <= 185000000.0)))))))
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.15e+80], N[Not[Or[LessEqual[y, -6.2e-54], And[N[Not[LessEqual[y, -2.8e-77]], $MachinePrecision], Or[LessEqual[y, -1e-125], And[N[Not[LessEqual[y, -5.2e-143]], $MachinePrecision], LessEqual[y, 185000000.0]]]]]], $MachinePrecision]], N[(y * -0.005), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -3.14999999999999989e80 or -6.20000000000000008e-54 < y < -2.7999999999999999e-77 or -1.00000000000000001e-125 < y < -5.19999999999999974e-143 or 1.85e8 < y

   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 y around inf 99.8%

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

   6. Taylor expanded in x around 0 82.5%

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

   if -3.14999999999999989e80 < y < -6.20000000000000008e-54 or -2.7999999999999999e-77 < y < -1.00000000000000001e-125 or -5.19999999999999974e-143 < y < 1.85e8

   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 82.5%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+80} \lor \neg \left(y \leq -6.2 \cdot 10^{-54} \lor \neg \left(y \leq -2.8 \cdot 10^{-77}\right) \land \left(y \leq -1 \cdot 10^{-125} \lor \neg \left(y \leq -5.2 \cdot 10^{-143}\right) \land y \leq 185000000\right)\right):\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+80}:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-53}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -2.8 \cdot 10^{-77}:\\ \;\;\;\;\frac{y}{-200}\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-125}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -4.1 \cdot 10^{-144}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 85000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{-200}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.15e+80)
   (/ y -200.0)
   (if (<= y -7.2e-53)
     x
     (if (<= y -2.8e-77)
       (/ y -200.0)
       (if (<= y -1e-125)
         x
         (if (<= y -4.1e-144)
           (* y -0.005)
           (if (<= y 85000000.0) x (/ y -200.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.15e+80) {
		tmp = y / -200.0;
	} else if (y <= -7.2e-53) {
		tmp = x;
	} else if (y <= -2.8e-77) {
		tmp = y / -200.0;
	} else if (y <= -1e-125) {
		tmp = x;
	} else if (y <= -4.1e-144) {
		tmp = y * -0.005;
	} else if (y <= 85000000.0) {
		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 <= (-3.15d+80)) then
        tmp = y / (-200.0d0)
    else if (y <= (-7.2d-53)) then
        tmp = x
    else if (y <= (-2.8d-77)) then
        tmp = y / (-200.0d0)
    else if (y <= (-1d-125)) then
        tmp = x
    else if (y <= (-4.1d-144)) then
        tmp = y * (-0.005d0)
    else if (y <= 85000000.0d0) 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 <= -3.15e+80) {
		tmp = y / -200.0;
	} else if (y <= -7.2e-53) {
		tmp = x;
	} else if (y <= -2.8e-77) {
		tmp = y / -200.0;
	} else if (y <= -1e-125) {
		tmp = x;
	} else if (y <= -4.1e-144) {
		tmp = y * -0.005;
	} else if (y <= 85000000.0) {
		tmp = x;
	} else {
		tmp = y / -200.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.15e+80:
		tmp = y / -200.0
	elif y <= -7.2e-53:
		tmp = x
	elif y <= -2.8e-77:
		tmp = y / -200.0
	elif y <= -1e-125:
		tmp = x
	elif y <= -4.1e-144:
		tmp = y * -0.005
	elif y <= 85000000.0:
		tmp = x
	else:
		tmp = y / -200.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.15e+80)
		tmp = Float64(y / -200.0);
	elseif (y <= -7.2e-53)
		tmp = x;
	elseif (y <= -2.8e-77)
		tmp = Float64(y / -200.0);
	elseif (y <= -1e-125)
		tmp = x;
	elseif (y <= -4.1e-144)
		tmp = Float64(y * -0.005);
	elseif (y <= 85000000.0)
		tmp = x;
	else
		tmp = Float64(y / -200.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.15e+80)
		tmp = y / -200.0;
	elseif (y <= -7.2e-53)
		tmp = x;
	elseif (y <= -2.8e-77)
		tmp = y / -200.0;
	elseif (y <= -1e-125)
		tmp = x;
	elseif (y <= -4.1e-144)
		tmp = y * -0.005;
	elseif (y <= 85000000.0)
		tmp = x;
	else
		tmp = y / -200.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.15e+80], N[(y / -200.0), $MachinePrecision], If[LessEqual[y, -7.2e-53], x, If[LessEqual[y, -2.8e-77], N[(y / -200.0), $MachinePrecision], If[LessEqual[y, -1e-125], x, If[LessEqual[y, -4.1e-144], N[(y * -0.005), $MachinePrecision], If[LessEqual[y, 85000000.0], x, N[(y / -200.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.14999999999999989e80 or -7.1999999999999998e-53 < y < -2.7999999999999999e-77 or 8.5e7 < y

   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 82.0%

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

      1. metadata-eval 82.0%

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

      2. metadata-eval 82.0%

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

      3. distribute-rgt-neg-in 82.0%

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

      4. div-inv 82.1%

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

      5. distribute-neg-frac2 82.1%

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

      6. metadata-eval 82.1%

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

   8. Applied egg-rr 82.1%

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

   if -3.14999999999999989e80 < y < -7.1999999999999998e-53 or -2.7999999999999999e-77 < y < -1.00000000000000001e-125 or -4.1e-144 < y < 8.5e7

   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 82.5%

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

   if -1.00000000000000001e-125 < y < -4.1e-144

   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* 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   6. Taylor expanded in x around 0 89.6%

      \[\leadsto y \cdot \color{blue}{-0.005} \]
3. Recombined 3 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: 49.9% 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 48.3%

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

Reproduce

herbie shell --seed 2024091 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))