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

Percentage Accurate: 100.0% → 100.0%

Time: 4.7s

Alternatives: 3

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: 73.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+76} \lor \neg \left(y \leq -1 \cdot 10^{+45} \lor \neg \left(y \leq -1.09 \cdot 10^{-103}\right) \land y \leq 1.3 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.7e+76)
         (not (or (<= y -1e+45) (and (not (<= y -1.09e-103)) (<= y 1.3e-19)))))
   (* y -0.005)
   x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.7e+76) || !((y <= -1e+45) || (!(y <= -1.09e-103) && (y <= 1.3e-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 ((y <= (-4.7d+76)) .or. (.not. (y <= (-1d+45)) .or. (.not. (y <= (-1.09d-103))) .and. (y <= 1.3d-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 ((y <= -4.7e+76) || !((y <= -1e+45) || (!(y <= -1.09e-103) && (y <= 1.3e-19)))) {
		tmp = y * -0.005;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.7e+76) or not ((y <= -1e+45) or (not (y <= -1.09e-103) and (y <= 1.3e-19))):
		tmp = y * -0.005
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.7e+76) || !((y <= -1e+45) || (!(y <= -1.09e-103) && (y <= 1.3e-19))))
		tmp = Float64(y * -0.005);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -4.7e+76) || ~(((y <= -1e+45) || (~((y <= -1.09e-103)) && (y <= 1.3e-19)))))
		tmp = y * -0.005;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.7e+76], N[Not[Or[LessEqual[y, -1e+45], And[N[Not[LessEqual[y, -1.09e-103]], $MachinePrecision], LessEqual[y, 1.3e-19]]]], $MachinePrecision]], N[(y * -0.005), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -4.7000000000000003e76 or -9.9999999999999993e44 < y < -1.09e-103 or 1.30000000000000006e-19 < 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. +-commutative 100.0%

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

      4. neg-mul-1 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-/l* 99.8%

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

      7. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-1}{200}, x\right)} \]

      8. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{-0.005}, x\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.005, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 79.0%

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

   if -4.7000000000000003e76 < y < -9.9999999999999993e44 or -1.09e-103 < y < 1.30000000000000006e-19

   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. +-commutative 100.0%

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

      4. neg-mul-1 100.0%

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

      5. *-commutative 100.0%

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

      6. associate-/l* 100.0%

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

      7. fma-define 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-1}{200}, x\right)} \]

      8. metadata-eval 100.0%

         \[\leadsto \mathsf{fma}\left(y, \color{blue}{-0.005}, x\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.005, x\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0 86.8%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.7 \cdot 10^{+76} \lor \neg \left(y \leq -1 \cdot 10^{+45} \lor \neg \left(y \leq -1.09 \cdot 10^{-103}\right) \land y \leq 1.3 \cdot 10^{-19}\right):\\ \;\;\;\;y \cdot -0.005\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 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-frac-neg 100.0%

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

   3. +-commutative 100.0%

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

   4. neg-mul-1 100.0%

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

   5. *-commutative 100.0%

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

   6. associate-/l* 99.9%

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

   7. fma-define 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{-1}{200}, x\right)} \]

   8. metadata-eval 99.9%

      \[\leadsto \mathsf{fma}\left(y, \color{blue}{-0.005}, x\right) \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, -0.005, x\right)} \]
4. Add Preprocessing

5. Taylor expanded in y around 0 49.2%

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

Reproduce

herbie shell --seed 2024111 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLAB from colour-2.3.3, D"
  :precision binary64
  (- x (/ y 200.0)))