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

Percentage Accurate: 100.0% → 100.0%

Time: 2.4s

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: 75.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+20}:\\ \;\;\;\;\frac{-y}{200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3e-15) x (if (<= x 3e+20) (/ (- y) 200.0) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3e-15) {
		tmp = x;
	} else if (x <= 3e+20) {
		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 <= (-3d-15)) then
        tmp = x
    else if (x <= 3d+20) 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 <= -3e-15) {
		tmp = x;
	} else if (x <= 3e+20) {
		tmp = -y / 200.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3e-15:
		tmp = x
	elif x <= 3e+20:
		tmp = -y / 200.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3e-15)
		tmp = x;
	elseif (x <= 3e+20)
		tmp = Float64(Float64(-y) / 200.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3e-15)
		tmp = x;
	elseif (x <= 3e+20)
		tmp = -y / 200.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3e-15], x, If[LessEqual[x, 3e+20], N[((-y) / 200.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -3e-15 or 3e20 < 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-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 77.1%

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

   if -3e-15 < x < 3e20

   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 81.6%

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

      1. *-commutative 81.6%

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

      2. metadata-eval 81.6%

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

      3. metadata-eval 81.6%

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

      4. distribute-rgt-neg-in 81.6%

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

      5. div-inv 81.8%

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

      6. distribute-neg-frac 81.8%

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

   6. Applied egg-rr 81.8%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-15}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+20}:\\ \;\;\;\;\frac{-y}{200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 75.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.9e-17) x (if (<= x 9.2e+19) (* y -0.005) x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.9e-17) {
		tmp = x;
	} else if (x <= 9.2e+19) {
		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 <= (-1.9d-17)) then
        tmp = x
    else if (x <= 9.2d+19) 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 <= -1.9e-17) {
		tmp = x;
	} else if (x <= 9.2e+19) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.9e-17:
		tmp = x
	elif x <= 9.2e+19:
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.9e-17)
		tmp = x;
	elseif (x <= 9.2e+19)
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.9e-17)
		tmp = x;
	elseif (x <= 9.2e+19)
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.9e-17], x, If[LessEqual[x, 9.2e+19], N[(y * -0.005), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9000000000000001e-17 or 9.2e19 < 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-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 77.1%

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

   if -1.9000000000000001e-17 < x < 9.2e19

   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 81.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+19}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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/ 99.8%

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

   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. Final simplification 99.8%

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

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/ 99.8%

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

   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 inf 46.9%

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

5. Final simplification 46.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))