Data.Colour.CIE:cieLABView from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 5

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(-200, y, 200 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma -200.0 y (* 200.0 x)))

C

double code(double x, double y) {
	return fma(-200.0, y, (200.0 * x));
}

Julia

function code(x, y)
	return fma(-200.0, y, Float64(200.0 * x))
end

Wolfram

code[x_, y_] := N[(-200.0 * y + N[(200.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 99.9%

   \[\leadsto \color{blue}{-200 \cdot y + 200 \cdot x} \]
4. Step-by-step derivation

   1. fma-define 100.0%

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

5. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(-200, y, 200 \cdot x\right)} \]
6. Add Preprocessing

Alternative 2: 74.2% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+80} \lor \neg \left(y \leq -7.2 \cdot 10^{-53}\right) \land \left(y \leq -2.8 \cdot 10^{-77} \lor \neg \left(y \leq -1 \cdot 10^{-125}\right) \land \left(y \leq -4.1 \cdot 10^{-144} \lor \neg \left(y \leq 85000000\right)\right)\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.3e+80)
         (and (not (<= y -7.2e-53))
              (or (<= y -2.8e-77)
                  (and (not (<= y -1e-125))
                       (or (<= y -4.1e-144) (not (<= y 85000000.0)))))))
   (* -200.0 y)
   (* 200.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.3e+80) || (!(y <= -7.2e-53) && ((y <= -2.8e-77) || (!(y <= -1e-125) && ((y <= -4.1e-144) || !(y <= 85000000.0)))))) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * 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 <= (-3.3d+80)) .or. (.not. (y <= (-7.2d-53))) .and. (y <= (-2.8d-77)) .or. (.not. (y <= (-1d-125))) .and. (y <= (-4.1d-144)) .or. (.not. (y <= 85000000.0d0))) then
        tmp = (-200.0d0) * y
    else
        tmp = 200.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.3e+80) || (!(y <= -7.2e-53) && ((y <= -2.8e-77) || (!(y <= -1e-125) && ((y <= -4.1e-144) || !(y <= 85000000.0)))))) {
		tmp = -200.0 * y;
	} else {
		tmp = 200.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.3e+80) or (not (y <= -7.2e-53) and ((y <= -2.8e-77) or (not (y <= -1e-125) and ((y <= -4.1e-144) or not (y <= 85000000.0))))):
		tmp = -200.0 * y
	else:
		tmp = 200.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.3e+80) || (!(y <= -7.2e-53) && ((y <= -2.8e-77) || (!(y <= -1e-125) && ((y <= -4.1e-144) || !(y <= 85000000.0))))))
		tmp = Float64(-200.0 * y);
	else
		tmp = Float64(200.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.3e+80) || (~((y <= -7.2e-53)) && ((y <= -2.8e-77) || (~((y <= -1e-125)) && ((y <= -4.1e-144) || ~((y <= 85000000.0)))))))
		tmp = -200.0 * y;
	else
		tmp = 200.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.3e+80], And[N[Not[LessEqual[y, -7.2e-53]], $MachinePrecision], Or[LessEqual[y, -2.8e-77], And[N[Not[LessEqual[y, -1e-125]], $MachinePrecision], Or[LessEqual[y, -4.1e-144], N[Not[LessEqual[y, 85000000.0]], $MachinePrecision]]]]]], N[(-200.0 * y), $MachinePrecision], N[(200.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.29999999999999991e80 or -7.1999999999999998e-53 < y < -2.7999999999999999e-77 or -1.00000000000000001e-125 < y < -4.1e-144 or 8.5e7 < y

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.1%

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

   if -3.29999999999999991e80 < y < -7.1999999999999998e-53 or -2.7999999999999999e-77 < y < -1.00000000000000001e-125 or -4.1e-144 < y < 8.5e7

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 81.9%

      \[\leadsto \color{blue}{200 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+80} \lor \neg \left(y \leq -7.2 \cdot 10^{-53}\right) \land \left(y \leq -2.8 \cdot 10^{-77} \lor \neg \left(y \leq -1 \cdot 10^{-125}\right) \land \left(y \leq -4.1 \cdot 10^{-144} \lor \neg \left(y \leq 85000000\right)\right)\right):\\ \;\;\;\;-200 \cdot y\\ \mathbf{else}:\\ \;\;\;\;200 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ 200 \cdot x + -200 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (* 200.0 x) (* -200.0 y)))

C

double code(double x, double y) {
	return (200.0 * x) + (-200.0 * y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (200.0d0 * x) + ((-200.0d0) * y)
end function

Java

public static double code(double x, double y) {
	return (200.0 * x) + (-200.0 * y);
}

Python

def code(x, y):
	return (200.0 * x) + (-200.0 * y)

Julia

function code(x, y)
	return Float64(Float64(200.0 * x) + Float64(-200.0 * y))
end

MATLAB

function tmp = code(x, y)
	tmp = (200.0 * x) + (-200.0 * y);
end

Wolfram

code[x_, y_] := N[(N[(200.0 * x), $MachinePrecision] + N[(-200.0 * y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 99.9%

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

4. Final simplification 99.9%

   \[\leadsto 200 \cdot x + -200 \cdot y \]
5. Add Preprocessing

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 200 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 200.0 (- x y)))

C

double code(double x, double y) {
	return 200.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 200.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 200.0 * (x - y);
}

Python

def code(x, y):
	return 200.0 * (x - y)

Julia

function code(x, y)
	return Float64(200.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 200.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(200.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 5: 51.8% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ -200 \cdot y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -200.0 y))

C

double code(double x, double y) {
	return -200.0 * y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-200.0d0) * y
end function

Java

public static double code(double x, double y) {
	return -200.0 * y;
}

Python

def code(x, y):
	return -200.0 * y

Julia

function code(x, y)
	return Float64(-200.0 * y)
end

MATLAB

function tmp = code(x, y)
	tmp = -200.0 * y;
end

Wolfram

code[x_, y_] := N[(-200.0 * y), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[200 \cdot \left(x - y\right) \]
2. Add Preprocessing

3. Taylor expanded in x around 0 53.3%

   \[\leadsto \color{blue}{-200 \cdot y} \]
4. Add Preprocessing

Reproduce

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