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. Final simplification 100.0%

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

Alternative 2: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -68000000000 \lor \neg \left(x \leq -1.75 \cdot 10^{-30}\right) \land x \leq 7 \cdot 10^{-29}:\\ \;\;\;\;\frac{-y}{200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.5e+51)
   x
   (if (or (<= x -68000000000.0) (and (not (<= x -1.75e-30)) (<= x 7e-29)))
     (/ (- y) 200.0)
     x)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.5e+51) {
		tmp = x;
	} else if ((x <= -68000000000.0) || (!(x <= -1.75e-30) && (x <= 7e-29))) {
		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 <= (-5.5d+51)) then
        tmp = x
    else if ((x <= (-68000000000.0d0)) .or. (.not. (x <= (-1.75d-30))) .and. (x <= 7d-29)) 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 <= -5.5e+51) {
		tmp = x;
	} else if ((x <= -68000000000.0) || (!(x <= -1.75e-30) && (x <= 7e-29))) {
		tmp = -y / 200.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.5e+51:
		tmp = x
	elif (x <= -68000000000.0) or (not (x <= -1.75e-30) and (x <= 7e-29)):
		tmp = -y / 200.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.5e+51)
		tmp = x;
	elseif ((x <= -68000000000.0) || (!(x <= -1.75e-30) && (x <= 7e-29)))
		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 <= -5.5e+51)
		tmp = x;
	elseif ((x <= -68000000000.0) || (~((x <= -1.75e-30)) && (x <= 7e-29)))
		tmp = -y / 200.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.5e+51], x, If[Or[LessEqual[x, -68000000000.0], And[N[Not[LessEqual[x, -1.75e-30]], $MachinePrecision], LessEqual[x, 7e-29]]], N[((-y) / 200.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if x < -5.5e51 or -6.8e10 < x < -1.7500000000000001e-30 or 6.9999999999999995e-29 < 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* 99.9%

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

      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 82.8%

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

   if -5.5e51 < x < -6.8e10 or -1.7500000000000001e-30 < x < 6.9999999999999995e-29

   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/ 99.9%

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

      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 0 83.7%

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

      1. *-commutative 83.7%

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

      2. metadata-eval 83.7%

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

      3. metadata-eval 83.7%

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

      4. distribute-rgt-neg-in 83.7%

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

      5. div-inv 83.8%

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

      6. distribute-neg-frac 83.8%

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

   6. Applied egg-rr 83.8%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.5 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -68000000000 \lor \neg \left(x \leq -1.75 \cdot 10^{-30}\right) \land x \leq 7 \cdot 10^{-29}:\\ \;\;\;\;\frac{-y}{200}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -31000000000:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.8e+48)
   x
   (if (<= x -31000000000.0)
     (* y -0.005)
     (if (<= x -1e-31) x (if (<= x 8.8e-30) (* y -0.005) x)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.8e+48) {
		tmp = x;
	} else if (x <= -31000000000.0) {
		tmp = y * -0.005;
	} else if (x <= -1e-31) {
		tmp = x;
	} else if (x <= 8.8e-30) {
		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 <= (-1.8d+48)) then
        tmp = x
    else if (x <= (-31000000000.0d0)) then
        tmp = y * (-0.005d0)
    else if (x <= (-1d-31)) then
        tmp = x
    else if (x <= 8.8d-30) 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 <= -1.8e+48) {
		tmp = x;
	} else if (x <= -31000000000.0) {
		tmp = y * -0.005;
	} else if (x <= -1e-31) {
		tmp = x;
	} else if (x <= 8.8e-30) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.8e+48:
		tmp = x
	elif x <= -31000000000.0:
		tmp = y * -0.005
	elif x <= -1e-31:
		tmp = x
	elif x <= 8.8e-30:
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.8e+48)
		tmp = x;
	elseif (x <= -31000000000.0)
		tmp = Float64(y * -0.005);
	elseif (x <= -1e-31)
		tmp = x;
	elseif (x <= 8.8e-30)
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.8e+48)
		tmp = x;
	elseif (x <= -31000000000.0)
		tmp = y * -0.005;
	elseif (x <= -1e-31)
		tmp = x;
	elseif (x <= 8.8e-30)
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.8e+48], x, If[LessEqual[x, -31000000000.0], N[(y * -0.005), $MachinePrecision], If[LessEqual[x, -1e-31], x, If[LessEqual[x, 8.8e-30], N[(y * -0.005), $MachinePrecision], x]]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.79999999999999992e48 or -3.1e10 < x < -1e-31 or 8.79999999999999933e-30 < 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* 99.9%

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

      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 82.8%

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

   if -1.79999999999999992e48 < x < -3.1e10 or -1e-31 < x < 8.79999999999999933e-30

   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/ 99.9%

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

      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 0 83.7%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -31000000000:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{elif}\;x \leq -1 \cdot 10^{-31}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{-30}:\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

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/ 99.9%

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

   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: 50.8% 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 53.8%

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

5. Final simplification 53.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))