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

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

Alternatives: 5

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, 0.8× 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. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto 500 \cdot \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   2. distribute-rgt-in N/A

      \[\leadsto \color{blue}{x \cdot 500 + \left(\mathsf{neg}\left(y\right)\right) \cdot 500} \]

   3. +-commutative N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y\right)\right) \cdot 500 + x \cdot 500} \]

   4. distribute-lft-neg-out N/A

      \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot 500\right)\right)} + x \cdot 500 \]

   5. distribute-rgt-neg-in N/A

      \[\leadsto \color{blue}{y \cdot \left(\mathsf{neg}\left(500\right)\right)} + x \cdot 500 \]

   6. metadata-eval N/A

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

   7. metadata-eval N/A

      \[\leadsto y \cdot \color{blue}{\left(500 \cdot -1\right)} + x \cdot 500 \]

   8. lower-fma.f64 N/A

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, 500 \cdot -1, x \cdot 500\right)} \]

   9. metadata-eval N/A

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

   10. *-commutative N/A

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

   11. lower-*.f64 100.0

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

4. Applied rewrites 100.0%

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

Alternative 2: 74.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+60}:\\ \;\;\;\;y \cdot -500\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+29}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.1e+60)
   (* y -500.0)
   (if (<= y 2.15e+29) (* 500.0 x) (* y -500.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+60) {
		tmp = y * -500.0;
	} else if (y <= 2.15e+29) {
		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 <= (-2.1d+60)) then
        tmp = y * (-500.0d0)
    else if (y <= 2.15d+29) 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 <= -2.1e+60) {
		tmp = y * -500.0;
	} else if (y <= 2.15e+29) {
		tmp = 500.0 * x;
	} else {
		tmp = y * -500.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.1e+60:
		tmp = y * -500.0
	elif y <= 2.15e+29:
		tmp = 500.0 * x
	else:
		tmp = y * -500.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.1e+60)
		tmp = Float64(y * -500.0);
	elseif (y <= 2.15e+29)
		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 <= -2.1e+60)
		tmp = y * -500.0;
	elseif (y <= 2.15e+29)
		tmp = 500.0 * x;
	else
		tmp = y * -500.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.1e+60], N[(y * -500.0), $MachinePrecision], If[LessEqual[y, 2.15e+29], N[(500.0 * x), $MachinePrecision], N[(y * -500.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.1000000000000001e60 or 2.1500000000000001e29 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-*.f64 76.7

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

   5. Applied rewrites 76.7%

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

   if -2.1000000000000001e60 < y < 2.1500000000000001e29

   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 76.4

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

   5. Applied rewrites 76.4%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+60}:\\ \;\;\;\;y \cdot -500\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{+29}:\\ \;\;\;\;500 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot -500\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 100.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[500 \cdot \left(x - y\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. sub-neg N/A

      \[\leadsto 500 \cdot \color{blue}{\left(x + \left(\mathsf{neg}\left(y\right)\right)\right)} \]

   2. distribute-rgt-in N/A

      \[\leadsto \color{blue}{x \cdot 500 + \left(\mathsf{neg}\left(y\right)\right) \cdot 500} \]

   3. *-commutative N/A

      \[\leadsto x \cdot 500 + \color{blue}{500 \cdot \left(\mathsf{neg}\left(y\right)\right)} \]

   4. lower-fma.f64 N/A

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

   5. *-commutative N/A

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

   6. distribute-lft-neg-out N/A

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

   7. distribute-rgt-neg-in N/A

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

   8. metadata-eval N/A

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

   9. metadata-eval N/A

      \[\leadsto \mathsf{fma}\left(x, 500, y \cdot \color{blue}{\left(500 \cdot -1\right)}\right) \]

   10. lower-*.f64 N/A

       \[\leadsto \mathsf{fma}\left(x, 500, \color{blue}{y \cdot \left(500 \cdot -1\right)}\right) \]

   11. metadata-eval 100.0

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

4. Applied rewrites 100.0%

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

Alternative 4: 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. Add Preprocessing

Alternative 5: 51.3% accurate, 1.5× 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

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

   1. lower-*.f64 46.0

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

5. Applied rewrites 46.0%

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

6. Final simplification 46.0%

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

Reproduce

herbie shell --seed 2024216 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))