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

Percentage Accurate: 100.0% → 100.0%

Time: 1.8s

Alternatives: 3

Speedup: 1.0×

• could not determine a ground truth

  1. x = -2.604405073637594e-10
  2. y = 2.0391697104977115e+84

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, 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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto 500 \cdot \left(x - y\right) \]
4. Add Preprocessing

Alternative 2: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-80} \lor \neg \left(x \leq 1.35 \cdot 10^{-13}\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -7.2e-80) (not (<= x 1.35e-13))) (* 500.0 x) (* y -500.0)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -7.2e-80) || !(x <= 1.35e-13)) {
		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 ((x <= (-7.2d-80)) .or. (.not. (x <= 1.35d-13))) 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 ((x <= -7.2e-80) || !(x <= 1.35e-13)) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -7.2e-80) or not (x <= 1.35e-13):
		tmp = 500.0 * x
	else:
		tmp = y * -500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -7.2e-80) || !(x <= 1.35e-13))
		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 ((x <= -7.2e-80) || ~((x <= 1.35e-13)))
		tmp = 500.0 * x;
	else
		tmp = y * -500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -7.2e-80], N[Not[LessEqual[x, 1.35e-13]], $MachinePrecision]], N[(500.0 * x), $MachinePrecision], N[(y * -500.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.2e-80 or 1.35000000000000005e-13 < x

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 74.9%

      \[\leadsto \color{blue}{500 \cdot x} \]

   if -7.2e-80 < x < 1.35000000000000005e-13

   1. Initial program 100.0%

      \[500 \cdot \left(x - y\right) \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 83.6%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.2 \cdot 10^{-80} \lor \neg \left(x \leq 1.35 \cdot 10^{-13}\right):\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.7% 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. Add Preprocessing

3. Taylor expanded in x around 0 49.9%

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

4. Final simplification 49.9%

   \[\leadsto y \cdot -500 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024062 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))