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

Percentage Accurate: 100.0% → 100.0%

Time: 2.2s

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. Final simplification 100.0%

   \[\leadsto x - \frac{y}{200} \]

Alternative 2: 72.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-25} \lor \neg \left(y \leq 5 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{-y}{200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -6.7e-25) (not (<= y 5e-139))) (/ (- y) 200.0) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -6.7e-25) || !(y <= 5e-139)) {
		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 ((y <= (-6.7d-25)) .or. (.not. (y <= 5d-139))) 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 ((y <= -6.7e-25) || !(y <= 5e-139)) {
		tmp = -y / 200.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -6.7e-25) or not (y <= 5e-139):
		tmp = -y / 200.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -6.7e-25) || !(y <= 5e-139))
		tmp = Float64(Float64(-y) / 200.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -6.7e-25) || ~((y <= 5e-139)))
		tmp = -y / 200.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -6.7e-25], N[Not[LessEqual[y, 5e-139]], $MachinePrecision]], N[((-y) / 200.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -6.70000000000000032e-25 or 5.00000000000000034e-139 < 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-neg-frac 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. associate-/l* 99.7%

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

      5. associate-/r/ 99.8%

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

      6. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 74.5%

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

      1. *-commutative 74.5%

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

      2. metadata-eval 74.5%

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

      3. metadata-eval 74.5%

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

      4. distribute-rgt-neg-in 74.5%

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

      5. div-inv 74.6%

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

      6. distribute-neg-frac 74.6%

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

   6. Applied egg-rr 74.6%

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

   if -6.70000000000000032e-25 < y < 5.00000000000000034e-139

   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-neg-frac 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. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 86.3%

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

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-25} \lor \neg \left(y \leq 5 \cdot 10^{-139}\right):\\ \;\;\;\;\frac{-y}{200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 72.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-24}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.05e-24) (* y -0.005) (if (<= y 5.5e-138) x (* y -0.005))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.05e-24) {
		tmp = y * -0.005;
	} else if (y <= 5.5e-138) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.05d-24)) then
        tmp = y * (-0.005d0)
    else if (y <= 5.5d-138) then
        tmp = x
    else
        tmp = y * (-0.005d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.05e-24) {
		tmp = y * -0.005;
	} else if (y <= 5.5e-138) {
		tmp = x;
	} else {
		tmp = y * -0.005;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.05e-24:
		tmp = y * -0.005
	elif y <= 5.5e-138:
		tmp = x
	else:
		tmp = y * -0.005
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.05e-24)
		tmp = Float64(y * -0.005);
	elseif (y <= 5.5e-138)
		tmp = x;
	else
		tmp = Float64(y * -0.005);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.05e-24)
		tmp = y * -0.005;
	elseif (y <= 5.5e-138)
		tmp = x;
	else
		tmp = y * -0.005;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.05e-24], N[(y * -0.005), $MachinePrecision], If[LessEqual[y, 5.5e-138], x, N[(y * -0.005), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.05000000000000007e-24 or 5.5000000000000003e-138 < 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-neg-frac 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. associate-/l* 99.7%

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

      5. associate-/r/ 99.8%

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

      6. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around 0 74.5%

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

   if -2.05000000000000007e-24 < y < 5.5000000000000003e-138

   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-neg-frac 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. associate-/l* 100.0%

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

      5. associate-/r/ 100.0%

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

      6. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 86.3%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.05 \cdot 10^{-24}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -0.005\\ \end{array} \]

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-neg-frac 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. associate-/l* 99.8%

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

   5. associate-/r/ 99.9%

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

   6. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto x + y \cdot -0.005 \]

Alternative 5: 51.1% 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-neg-frac 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. associate-/l* 99.8%

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

   5. associate-/r/ 99.9%

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

   6. metadata-eval 99.9%

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

3. Simplified 99.9%

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

4. Taylor expanded in x around inf 48.1%

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

5. Final simplification 48.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023202 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))