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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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: 74.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+31}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-93}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.6e+31) (* x 500.0) (if (<= x 2.3e-93) (* -500.0 y) (* x 500.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.6e+31) {
		tmp = x * 500.0;
	} else if (x <= 2.3e-93) {
		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 <= (-6.6d+31)) then
        tmp = x * 500.0d0
    else if (x <= 2.3d-93) 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 <= -6.6e+31) {
		tmp = x * 500.0;
	} else if (x <= 2.3e-93) {
		tmp = -500.0 * y;
	} else {
		tmp = x * 500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.6e+31:
		tmp = x * 500.0
	elif x <= 2.3e-93:
		tmp = -500.0 * y
	else:
		tmp = x * 500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.6e+31)
		tmp = Float64(x * 500.0);
	elseif (x <= 2.3e-93)
		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 <= -6.6e+31)
		tmp = x * 500.0;
	elseif (x <= 2.3e-93)
		tmp = -500.0 * y;
	else
		tmp = x * 500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.6e+31], N[(x * 500.0), $MachinePrecision], If[LessEqual[x, 2.3e-93], N[(-500.0 * y), $MachinePrecision], N[(x * 500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -6.59999999999999985e31 or 2.2999999999999998e-93 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. lower-*.f64 76.0

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

   5. Applied rewrites 76.0%

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

   if -6.59999999999999985e31 < x < 2.2999999999999998e-93

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+31}:\\ \;\;\;\;x \cdot 500\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-93}:\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 500\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.4% accurate, 1.5× 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. Add Preprocessing

3. Taylor expanded in x around 0

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

   1. lower-*.f64 52.0

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

5. Applied rewrites 52.0%

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

Reproduce

herbie shell --seed 2024332 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))