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

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_] := N[(500.0 * x + N[(-500.0 * y), $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. fma-def 100.0%

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

4. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+19} \lor \neg \left(y \leq -7.1 \cdot 10^{-47}\right) \land \left(y \leq -2.8 \cdot 10^{-141} \lor \neg \left(y \leq 5.2 \cdot 10^{-111}\right) \land \left(y \leq 4.8 \cdot 10^{-36} \lor \neg \left(y \leq 9.4 \cdot 10^{+58}\right)\right)\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.8e+19)
         (and (not (<= y -7.1e-47))
              (or (<= y -2.8e-141)
                  (and (not (<= y 5.2e-111))
                       (or (<= y 4.8e-36) (not (<= y 9.4e+58)))))))
   (* -500.0 y)
   (* 500.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.8e+19) || (!(y <= -7.1e-47) && ((y <= -2.8e-141) || (!(y <= 5.2e-111) && ((y <= 4.8e-36) || !(y <= 9.4e+58)))))) {
		tmp = -500.0 * y;
	} else {
		tmp = 500.0 * 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 <= (-5.8d+19)) .or. (.not. (y <= (-7.1d-47))) .and. (y <= (-2.8d-141)) .or. (.not. (y <= 5.2d-111)) .and. (y <= 4.8d-36) .or. (.not. (y <= 9.4d+58))) then
        tmp = (-500.0d0) * y
    else
        tmp = 500.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.8e+19) || (!(y <= -7.1e-47) && ((y <= -2.8e-141) || (!(y <= 5.2e-111) && ((y <= 4.8e-36) || !(y <= 9.4e+58)))))) {
		tmp = -500.0 * y;
	} else {
		tmp = 500.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.8e+19) or (not (y <= -7.1e-47) and ((y <= -2.8e-141) or (not (y <= 5.2e-111) and ((y <= 4.8e-36) or not (y <= 9.4e+58))))):
		tmp = -500.0 * y
	else:
		tmp = 500.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.8e+19) || (!(y <= -7.1e-47) && ((y <= -2.8e-141) || (!(y <= 5.2e-111) && ((y <= 4.8e-36) || !(y <= 9.4e+58))))))
		tmp = Float64(-500.0 * y);
	else
		tmp = Float64(500.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.8e+19) || (~((y <= -7.1e-47)) && ((y <= -2.8e-141) || (~((y <= 5.2e-111)) && ((y <= 4.8e-36) || ~((y <= 9.4e+58)))))))
		tmp = -500.0 * y;
	else
		tmp = 500.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.8e+19], And[N[Not[LessEqual[y, -7.1e-47]], $MachinePrecision], Or[LessEqual[y, -2.8e-141], And[N[Not[LessEqual[y, 5.2e-111]], $MachinePrecision], Or[LessEqual[y, 4.8e-36], N[Not[LessEqual[y, 9.4e+58]], $MachinePrecision]]]]]], N[(-500.0 * y), $MachinePrecision], N[(500.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.8e19 or -7.1000000000000002e-47 < y < -2.80000000000000012e-141 or 5.19999999999999965e-111 < y < 4.8e-36 or 9.39999999999999944e58 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.9%

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

   if -5.8e19 < y < -7.1000000000000002e-47 or -2.80000000000000012e-141 < y < 5.19999999999999965e-111 or 4.8e-36 < y < 9.39999999999999944e58

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 86.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+19} \lor \neg \left(y \leq -7.1 \cdot 10^{-47}\right) \land \left(y \leq -2.8 \cdot 10^{-141} \lor \neg \left(y \leq 5.2 \cdot 10^{-111}\right) \land \left(y \leq 4.8 \cdot 10^{-36} \lor \neg \left(y \leq 9.4 \cdot 10^{+58}\right)\right)\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \]

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: 50.2% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 49.6%

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

3. Final simplification 49.6%

   \[\leadsto -500 \cdot y \]

Reproduce

herbie shell --seed 2023173 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))