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

Percentage Accurate: 100.0% → 100.0%

Time: 2.7s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y, -500, 500 \cdot x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma y -500.0 (* 500.0 x)))

C

double code(double x, double y) {
	return fma(y, -500.0, (500.0 * x));
}

Julia

function code(x, y)
	return fma(y, -500.0, Float64(500.0 * x))
end

Wolfram

code[x_, y_] := N[(y * -500.0 + N[(500.0 * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 100.0%

   \[\leadsto \color{blue}{500 \cdot x + -500 \cdot y} \]
3. Step-by-step derivation

   1. +-commutative 100.0%

      \[\leadsto \color{blue}{-500 \cdot y + 500 \cdot x} \]

   2. *-commutative 100.0%

      \[\leadsto \color{blue}{y \cdot -500} + 500 \cdot x \]

   3. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, -500, 500 \cdot x\right)} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, -500, 500 \cdot x\right)} \]

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(y, -500, 500 \cdot x\right) \]

Alternative 2: 73.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot -500\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-41} \lor \neg \left(y \leq 8.8 \cdot 10^{-5}\right) \land y \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.2e+15)
   (* y -500.0)
   (if (or (<= y 1.95e-41) (and (not (<= y 8.8e-5)) (<= y 2.5e+69)))
     (* 500.0 x)
     (* y -500.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = y * -500.0;
	} else if ((y <= 1.95e-41) || (!(y <= 8.8e-5) && (y <= 2.5e+69))) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.2d+15)) then
        tmp = y * (-500.0d0)
    else if ((y <= 1.95d-41) .or. (.not. (y <= 8.8d-5)) .and. (y <= 2.5d+69)) then
        tmp = 500.0d0 * x
    else
        tmp = y * (-500.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.2e+15) {
		tmp = y * -500.0;
	} else if ((y <= 1.95e-41) || (!(y <= 8.8e-5) && (y <= 2.5e+69))) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.2e+15:
		tmp = y * -500.0
	elif (y <= 1.95e-41) or (not (y <= 8.8e-5) and (y <= 2.5e+69)):
		tmp = 500.0 * x
	else:
		tmp = y * -500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.2e+15)
		tmp = Float64(y * -500.0);
	elseif ((y <= 1.95e-41) || (!(y <= 8.8e-5) && (y <= 2.5e+69)))
		tmp = Float64(500.0 * x);
	else
		tmp = Float64(y * -500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.2e+15)
		tmp = y * -500.0;
	elseif ((y <= 1.95e-41) || (~((y <= 8.8e-5)) && (y <= 2.5e+69)))
		tmp = 500.0 * x;
	else
		tmp = y * -500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.2e+15], N[(y * -500.0), $MachinePrecision], If[Or[LessEqual[y, 1.95e-41], And[N[Not[LessEqual[y, 8.8e-5]], $MachinePrecision], LessEqual[y, 2.5e+69]]], N[(500.0 * x), $MachinePrecision], N[(y * -500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.2e15 or 1.94999999999999995e-41 < y < 8.7999999999999998e-5 or 2.50000000000000018e69 < y

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around 0 80.5%

      \[\leadsto \color{blue}{-500 \cdot y} \]

   if -4.2e15 < y < 1.94999999999999995e-41 or 8.7999999999999998e-5 < y < 2.50000000000000018e69

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]

   2. Taylor expanded in x around inf 77.3%

      \[\leadsto \color{blue}{500 \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot -500\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-41} \lor \neg \left(y \leq 8.8 \cdot 10^{-5}\right) \land y \leq 2.5 \cdot 10^{+69}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \]

Alternative 3: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 500 \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* 500.0 (- x y)))

C

double code(double x, double y) {
	return 500.0 * (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 500.0d0 * (x - y)
end function

Java

public static double code(double x, double y) {
	return 500.0 * (x - y);
}

Python

def code(x, y):
	return 500.0 * (x - y)

Julia

function code(x, y)
	return Float64(500.0 * Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = 500.0 * (x - y);
end

Wolfram

code[x_, y_] := N[(500.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Final simplification 100.0%

   \[\leadsto 500 \cdot \left(x - y\right) \]

Alternative 4: 52.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ y \cdot -500 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* y -500.0))

C

double code(double x, double y) {
	return y * -500.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y * (-500.0d0)
end function

Java

public static double code(double x, double y) {
	return y * -500.0;
}

Python

def code(x, y):
	return y * -500.0

Julia

function code(x, y)
	return Float64(y * -500.0)
end

MATLAB

function tmp = code(x, y)
	tmp = y * -500.0;
end

Wolfram

code[x_, y_] := N[(y * -500.0), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]

2. Taylor expanded in x around 0 51.7%

   \[\leadsto \color{blue}{-500 \cdot y} \]

3. Final simplification 51.7%

   \[\leadsto y \cdot -500 \]

Reproduce

herbie shell --seed 2023181 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))