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

Percentage Accurate: 100.0% → 100.0%

Time: 1.5s

Alternatives: 4

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[200 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 100.0%

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

   1. +-commutative 100.0%

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

   2. *-commutative 100.0%

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

   3. fma-def 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+56}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-24} \lor \neg \left(y \leq 4100000000\right) \land y \leq 4.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9.2e+56)
   (* -200.0 y)
   (if (or (<= y 1.3e-24) (and (not (<= y 4100000000.0)) (<= y 4.5e+30)))
     (* x 200.0)
     (* -200.0 y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9.2e+56) {
		tmp = -200.0 * y;
	} else if ((y <= 1.3e-24) || (!(y <= 4100000000.0) && (y <= 4.5e+30))) {
		tmp = x * 200.0;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-9.2d+56)) then
        tmp = (-200.0d0) * y
    else if ((y <= 1.3d-24) .or. (.not. (y <= 4100000000.0d0)) .and. (y <= 4.5d+30)) then
        tmp = x * 200.0d0
    else
        tmp = (-200.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -9.2e+56) {
		tmp = -200.0 * y;
	} else if ((y <= 1.3e-24) || (!(y <= 4100000000.0) && (y <= 4.5e+30))) {
		tmp = x * 200.0;
	} else {
		tmp = -200.0 * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9.2e+56:
		tmp = -200.0 * y
	elif (y <= 1.3e-24) or (not (y <= 4100000000.0) and (y <= 4.5e+30)):
		tmp = x * 200.0
	else:
		tmp = -200.0 * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9.2e+56)
		tmp = Float64(-200.0 * y);
	elseif ((y <= 1.3e-24) || (!(y <= 4100000000.0) && (y <= 4.5e+30)))
		tmp = Float64(x * 200.0);
	else
		tmp = Float64(-200.0 * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9.2e+56)
		tmp = -200.0 * y;
	elseif ((y <= 1.3e-24) || (~((y <= 4100000000.0)) && (y <= 4.5e+30)))
		tmp = x * 200.0;
	else
		tmp = -200.0 * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9.2e+56], N[(-200.0 * y), $MachinePrecision], If[Or[LessEqual[y, 1.3e-24], And[N[Not[LessEqual[y, 4100000000.0]], $MachinePrecision], LessEqual[y, 4.5e+30]]], N[(x * 200.0), $MachinePrecision], N[(-200.0 * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -9.20000000000000058e56 or 1.3e-24 < y < 4.1e9 or 4.49999999999999995e30 < y

   1. Initial program 100.0%

      \[200 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around 0 86.6%

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

   if -9.20000000000000058e56 < y < 1.3e-24 or 4.1e9 < y < 4.49999999999999995e30

   1. Initial program 99.9%

      \[200 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around inf 77.8%

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

4. Final simplification 82.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.2 \cdot 10^{+56}:\\ \;\;\;\;-200 \cdot y\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-24} \lor \neg \left(y \leq 4100000000\right) \land y \leq 4.5 \cdot 10^{+30}:\\ \;\;\;\;x \cdot 200\\ \mathbf{else}:\\ \;\;\;\;-200 \cdot y\\ \end{array} \]

Alternative 3: 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 100.0%

   \[200 \cdot \left(x - y\right) \]

2. Final simplification 100.0%

   \[\leadsto 200 \cdot \left(x - y\right) \]

Alternative 4: 49.6% 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 100.0%

   \[200 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 53.9%

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

3. Final simplification 53.9%

   \[\leadsto -200 \cdot y \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, C"
  :precision binary64
  (* 200.0 (- x y)))