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

Percentage Accurate: 100.0% → 100.0%

Time: 2.6s

Alternatives: 3

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, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4e-33) (* x 500.0) (if (<= x 4.1e+55) (* -500.0 y) (* x 500.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4e-33) {
		tmp = x * 500.0;
	} else if (x <= 4.1e+55) {
		tmp = -500.0 * y;
	} else {
		tmp = x * 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 <= (-1.4d-33)) then
        tmp = x * 500.0d0
    else if (x <= 4.1d+55) then
        tmp = (-500.0d0) * y
    else
        tmp = x * 500.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.4e-33) {
		tmp = x * 500.0;
	} else if (x <= 4.1e+55) {
		tmp = -500.0 * y;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4e-33:
		tmp = x * 500.0
	elif x <= 4.1e+55:
		tmp = -500.0 * y
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4e-33)
		tmp = Float64(x * 500.0);
	elseif (x <= 4.1e+55)
		tmp = Float64(-500.0 * y);
	else
		tmp = Float64(x * 500.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.4e-33)
		tmp = x * 500.0;
	elseif (x <= 4.1e+55)
		tmp = -500.0 * y;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4e-33], N[(x * 500.0), $MachinePrecision], If[LessEqual[x, 4.1e+55], N[(-500.0 * y), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.4e-33 or 4.09999999999999981e55 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 79.2

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

   5. Applied rewrites 79.2%

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

   if -1.4e-33 < x < 4.09999999999999981e55

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 76.1

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

   5. Applied rewrites 76.1%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-33}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+55}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ x \cdot 500 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 49.5

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

5. Applied rewrites 49.5%

   \[\leadsto \color{blue}{x \cdot 500} \]
6. Add Preprocessing

Reproduce

herbie shell --seed 2024243 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))