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

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

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, 0.8× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

4. Applied rewrites 44.0%

   \[\leadsto 500 \cdot \color{blue}{\mathsf{fma}\left(\sqrt{-y}, \sqrt{-y}, x\right)} \]
5. Step-by-step derivation

   1. lift-*.f64 N/A

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

   2. lift-fma.f64 N/A

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

   3. lift-sqrt.f64 N/A

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

   4. lift-sqrt.f64 N/A

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

   5. rem-square-sqrt N/A

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

   6. distribute-lft-in N/A

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

   7. lift-neg.f64 N/A

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

   8. distribute-rgt-neg-out N/A

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

   9. distribute-lft-neg-in N/A

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

   10. metadata-eval N/A

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

   11. *-commutative N/A

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

   12. remove-double-neg N/A

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

   13. lift-neg.f64 N/A

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

   14. lift-*.f64 N/A

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

   15. lower-fma.f64 N/A

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

   16. lift-neg.f64 N/A

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

   17. remove-double-neg 100.0

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

   18. lift-*.f64 N/A

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

   19. *-commutative N/A

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

   20. lower-*.f64 100.0

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

6. Applied rewrites 100.0%

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

Alternative 2: 74.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-51} \lor \neg \left(y \leq 2250000\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.5e-51) (not (<= y 2250000.0))) (* -500.0 y) (* 500.0 x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -4.5e-51) || !(y <= 2250000.0)) {
		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 <= (-4.5d-51)) .or. (.not. (y <= 2250000.0d0))) 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 <= -4.5e-51) || !(y <= 2250000.0)) {
		tmp = -500.0 * y;
	} else {
		tmp = 500.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -4.5e-51) or not (y <= 2250000.0):
		tmp = -500.0 * y
	else:
		tmp = 500.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -4.5e-51) || !(y <= 2250000.0))
		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 <= -4.5e-51) || ~((y <= 2250000.0)))
		tmp = -500.0 * y;
	else
		tmp = 500.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -4.5e-51], N[Not[LessEqual[y, 2250000.0]], $MachinePrecision]], N[(-500.0 * y), $MachinePrecision], N[(500.0 * x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999974e-51 or 2.25e6 < y

   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 81.5

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

   5. Applied rewrites 81.5%

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

   if -4.49999999999999974e-51 < y < 2.25e6

   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 79.4

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

   5. Applied rewrites 79.4%

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

4. Final simplification 80.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-51} \lor \neg \left(y \leq 2250000\right):\\ \;\;\;\;-500 \cdot y\\ \mathbf{else}:\\ \;\;\;\;500 \cdot x\\ \end{array} \]
5. Add Preprocessing

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. Add Preprocessing
3. Add Preprocessing

Alternative 4: 50.5% 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 54.6

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

5. Applied rewrites 54.6%

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

Reproduce

herbie shell --seed 2024320 
(FPCore (x y)
  :name "Data.Colour.CIE:cieLABView from colour-2.3.3, B"
  :precision binary64
  (* 500.0 (- x y)))