Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, C

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

Alternatives: 4

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x \cdot 2 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* x 2.0) y))

C

double code(double x, double y) {
	return (x * 2.0) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 2.0d0) - y
end function

Java

public static double code(double x, double y) {
	return (x * 2.0) - y;
}

Python

def code(x, y):
	return (x * 2.0) - y

Julia

function code(x, y)
	return Float64(Float64(x * 2.0) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 2.0) - y;
end

Wolfram

code[x_, y_] := N[(N[(x * 2.0), $MachinePrecision] - y), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot 2 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* x 2.0) y))

C

double code(double x, double y) {
	return (x * 2.0) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * 2.0d0) - y
end function

Java

public static double code(double x, double y) {
	return (x * 2.0) - y;
}

Python

def code(x, y):
	return (x * 2.0) - y

Julia

function code(x, y)
	return Float64(Float64(x * 2.0) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (x * 2.0) - y;
end

Wolfram

code[x_, y_] := N[(N[(x * 2.0), $MachinePrecision] - y), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot x - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* 2.0 x) y))

C

double code(double x, double y) {
	return (2.0 * x) - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (2.0d0 * x) - y
end function

Java

public static double code(double x, double y) {
	return (2.0 * x) - y;
}

Python

def code(x, y):
	return (2.0 * x) - y

Julia

function code(x, y)
	return Float64(Float64(2.0 * x) - y)
end

MATLAB

function tmp = code(x, y)
	tmp = (2.0 * x) - y;
end

Wolfram

code[x_, y_] := N[(N[(2.0 * x), $MachinePrecision] - y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot 2 - y \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto 2 \cdot x - y \]
4. Add Preprocessing

Alternative 2: 75.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -2 \cdot 10^{-20}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x \leq 2 \cdot 10^{+55}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* 2.0 x) -2e-20)
   (* 2.0 x)
   (if (<= (* 2.0 x) 2e+55) (- y) (* 2.0 x))))

C

double code(double x, double y) {
	double tmp;
	if ((2.0 * x) <= -2e-20) {
		tmp = 2.0 * x;
	} else if ((2.0 * x) <= 2e+55) {
		tmp = -y;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((2.0d0 * x) <= (-2d-20)) then
        tmp = 2.0d0 * x
    else if ((2.0d0 * x) <= 2d+55) then
        tmp = -y
    else
        tmp = 2.0d0 * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((2.0 * x) <= -2e-20) {
		tmp = 2.0 * x;
	} else if ((2.0 * x) <= 2e+55) {
		tmp = -y;
	} else {
		tmp = 2.0 * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (2.0 * x) <= -2e-20:
		tmp = 2.0 * x
	elif (2.0 * x) <= 2e+55:
		tmp = -y
	else:
		tmp = 2.0 * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(2.0 * x) <= -2e-20)
		tmp = Float64(2.0 * x);
	elseif (Float64(2.0 * x) <= 2e+55)
		tmp = Float64(-y);
	else
		tmp = Float64(2.0 * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((2.0 * x) <= -2e-20)
		tmp = 2.0 * x;
	elseif ((2.0 * x) <= 2e+55)
		tmp = -y;
	else
		tmp = 2.0 * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(2.0 * x), $MachinePrecision], -2e-20], N[(2.0 * x), $MachinePrecision], If[LessEqual[N[(2.0 * x), $MachinePrecision], 2e+55], (-y), N[(2.0 * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < -1.99999999999999989e-20 or 2.00000000000000002e55 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 100.0%

      \[x \cdot 2 - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot x} \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \color{blue}{x \cdot 2} \]

      2. *-rgt-identity N/A

         \[\leadsto \color{blue}{\left(x \cdot 1\right)} \cdot 2 \]

      3. *-inverses N/A

         \[\leadsto \left(x \cdot \color{blue}{\frac{y}{y}}\right) \cdot 2 \]

      4. associate-/l* N/A

         \[\leadsto \color{blue}{\frac{x \cdot y}{y}} \cdot 2 \]

      5. *-commutative N/A

         \[\leadsto \frac{\color{blue}{y \cdot x}}{y} \cdot 2 \]

      6. associate-*l/ N/A

         \[\leadsto \color{blue}{\frac{\left(y \cdot x\right) \cdot 2}{y}} \]

      7. associate-*r/ N/A

         \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{2}{y}} \]

      8. associate-*r* N/A

         \[\leadsto \color{blue}{y \cdot \left(x \cdot \frac{2}{y}\right)} \]

      9. *-commutative N/A

         \[\leadsto y \cdot \color{blue}{\left(\frac{2}{y} \cdot x\right)} \]

      10. associate-*r* N/A

          \[\leadsto \color{blue}{\left(y \cdot \frac{2}{y}\right) \cdot x} \]

      11. *-commutative N/A

          \[\leadsto \color{blue}{\left(\frac{2}{y} \cdot y\right)} \cdot x \]

      12. lower-*.f64 N/A

          \[\leadsto \color{blue}{\left(\frac{2}{y} \cdot y\right) \cdot x} \]

      13. *-commutative N/A

          \[\leadsto \color{blue}{\left(y \cdot \frac{2}{y}\right)} \cdot x \]

      14. associate-*r/ N/A

          \[\leadsto \color{blue}{\frac{y \cdot 2}{y}} \cdot x \]

      15. metadata-eval N/A

          \[\leadsto \frac{y \cdot \color{blue}{\left(\mathsf{neg}\left(-2\right)\right)}}{y} \cdot x \]

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

          \[\leadsto \frac{\color{blue}{\mathsf{neg}\left(y \cdot -2\right)}}{y} \cdot x \]

      17. distribute-frac-neg N/A

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(\frac{y \cdot -2}{y}\right)\right)} \cdot x \]

      18. *-commutative N/A

          \[\leadsto \left(\mathsf{neg}\left(\frac{\color{blue}{-2 \cdot y}}{y}\right)\right) \cdot x \]

      19. associate-/l* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{-2 \cdot \frac{y}{y}}\right)\right) \cdot x \]

      20. *-inverses N/A

          \[\leadsto \left(\mathsf{neg}\left(-2 \cdot \color{blue}{1}\right)\right) \cdot x \]

      21. metadata-eval N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{-2}\right)\right) \cdot x \]

      22. metadata-eval 79.2

          \[\leadsto \color{blue}{2} \cdot x \]

   5. Applied rewrites 79.2%

      \[\leadsto \color{blue}{2 \cdot x} \]

   if -1.99999999999999989e-20 < (*.f64 x #s(literal 2 binary64)) < 2.00000000000000002e55

   1. Initial program 100.0%

      \[x \cdot 2 - y \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-1 \cdot y} \]
   4. Step-by-step derivation

      1. mul-1-neg N/A

         \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

      2. lower-neg.f64 76.0

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

   5. Applied rewrites 76.0%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;2 \cdot x \leq -2 \cdot 10^{-20}:\\ \;\;\;\;2 \cdot x\\ \mathbf{elif}\;2 \cdot x \leq 2 \cdot 10^{+55}:\\ \;\;\;\;-y\\ \mathbf{else}:\\ \;\;\;\;2 \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.3% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ -y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -y

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := (-y)

Derivation

1. Initial program 100.0%

   \[x \cdot 2 - y \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 51.9

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

5. Applied rewrites 51.9%

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

Alternative 4: 2.2% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[x \cdot 2 - y \]
2. Add Preprocessing

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{-1 \cdot y} \]
4. Step-by-step derivation

   1. mul-1-neg N/A

      \[\leadsto \color{blue}{\mathsf{neg}\left(y\right)} \]

   2. lower-neg.f64 51.9

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

5. Applied rewrites 51.9%

   \[\leadsto \color{blue}{-y} \]
6. Step-by-step derivation

7. Applied rewrites 2.2%

   \[\leadsto \color{blue}{y} \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024243 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, C"
  :precision binary64
  (- (* x 2.0) y))