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

Percentage Accurate: 100.0% → 100.0%

Time: 3.5s

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

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

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]

Derivation

1. Initial program 100.0%

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

Alternative 2: 74.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -500000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 \leq 10^{+64}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= (* x 2.0) -500000000.0)
   (* x 2.0)
   (if (<= (* x 2.0) 1e+64) (- 0.0 y) (* x 2.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x * 2.0) <= -500000000.0) {
		tmp = x * 2.0;
	} else if ((x * 2.0) <= 1e+64) {
		tmp = 0.0 - y;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x * 2.0d0) <= (-500000000.0d0)) then
        tmp = x * 2.0d0
    else if ((x * 2.0d0) <= 1d+64) then
        tmp = 0.0d0 - y
    else
        tmp = x * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x * 2.0) <= -500000000.0) {
		tmp = x * 2.0;
	} else if ((x * 2.0) <= 1e+64) {
		tmp = 0.0 - y;
	} else {
		tmp = x * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x * 2.0) <= -500000000.0:
		tmp = x * 2.0
	elif (x * 2.0) <= 1e+64:
		tmp = 0.0 - y
	else:
		tmp = x * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (Float64(x * 2.0) <= -500000000.0)
		tmp = Float64(x * 2.0);
	elseif (Float64(x * 2.0) <= 1e+64)
		tmp = Float64(0.0 - y);
	else
		tmp = Float64(x * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x * 2.0) <= -500000000.0)
		tmp = x * 2.0;
	elseif ((x * 2.0) <= 1e+64)
		tmp = 0.0 - y;
	else
		tmp = x * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[N[(x * 2.0), $MachinePrecision], -500000000.0], N[(x * 2.0), $MachinePrecision], If[LessEqual[N[(x * 2.0), $MachinePrecision], 1e+64], N[(0.0 - y), $MachinePrecision], N[(x * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x #s(literal 2 binary64)) < -5e8 or 1.00000000000000002e64 < (*.f64 x #s(literal 2 binary64))

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. metadata-eval N/A

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

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

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

      3. *-lft-identity N/A

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

      4. *-inverses N/A

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

      5. associate-*l/ N/A

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

      6. associate-*r/ N/A

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

      7. associate-*r/ N/A

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

      8. +-rgt-identity N/A

         \[\leadsto \color{blue}{\left(\mathsf{neg}\left(y \cdot \left(-2 \cdot \frac{x}{y}\right)\right)\right) + 0} \]

      9. *-commutative N/A

         \[\leadsto \left(\mathsf{neg}\left(\color{blue}{\left(-2 \cdot \frac{x}{y}\right) \cdot y}\right)\right) + 0 \]

      10. associate-*l* N/A

          \[\leadsto \left(\mathsf{neg}\left(\color{blue}{-2 \cdot \left(\frac{x}{y} \cdot y\right)}\right)\right) + 0 \]

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

          \[\leadsto \color{blue}{\left(\mathsf{neg}\left(-2\right)\right) \cdot \left(\frac{x}{y} \cdot y\right)} + 0 \]

      12. metadata-eval N/A

          \[\leadsto \color{blue}{2} \cdot \left(\frac{x}{y} \cdot y\right) + 0 \]

      13. associate-*l* N/A

          \[\leadsto \color{blue}{\left(2 \cdot \frac{x}{y}\right) \cdot y} + 0 \]

      14. associate-*r/ N/A

          \[\leadsto \color{blue}{\frac{2 \cdot x}{y}} \cdot y + 0 \]

      15. *-commutative N/A

          \[\leadsto \frac{\color{blue}{x \cdot 2}}{y} \cdot y + 0 \]

      16. associate-/l* N/A

          \[\leadsto \color{blue}{\left(x \cdot \frac{2}{y}\right)} \cdot y + 0 \]

      17. associate-*l* N/A

          \[\leadsto \color{blue}{x \cdot \left(\frac{2}{y} \cdot y\right)} + 0 \]

      18. accelerator-lowering-fma.f64 N/A

          \[\leadsto \color{blue}{\mathsf{fma}\left(x, \frac{2}{y} \cdot y, 0\right)} \]

      19. associate-*l/ N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{\frac{2 \cdot y}{y}}, 0\right) \]

      20. associate-/l* N/A

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{2 \cdot \frac{y}{y}}, 0\right) \]

      21. *-inverses N/A

          \[\leadsto \mathsf{fma}\left(x, 2 \cdot \color{blue}{1}, 0\right) \]

      22. metadata-eval 84.7

          \[\leadsto \mathsf{fma}\left(x, \color{blue}{2}, 0\right) \]

   5. Simplified 84.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, 2, 0\right)} \]
   6. Step-by-step derivation

      1. +-rgt-identity N/A

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

      2. *-lowering-*.f64 84.7

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

   7. Applied egg-rr 84.7%

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

   if -5e8 < (*.f64 x #s(literal 2 binary64)) < 1.00000000000000002e64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

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

      1. mul-1-neg N/A

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

      2. neg-sub0 N/A

         \[\leadsto \color{blue}{0 - y} \]

      3. --lowering--.f64 74.2

         \[\leadsto \color{blue}{0 - y} \]

   5. Simplified 74.2%

      \[\leadsto \color{blue}{0 - y} \]
   6. Step-by-step derivation

      1. sub0-neg N/A

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

      2. neg-lowering-neg.f64 74.2

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

   7. Applied egg-rr 74.2%

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

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot 2 \leq -500000000:\\ \;\;\;\;x \cdot 2\\ \mathbf{elif}\;x \cdot 2 \leq 10^{+64}:\\ \;\;\;\;0 - y\\ \mathbf{else}:\\ \;\;\;\;x \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.8% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ 0 - y \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 0.0 y))

C

double code(double x, double y) {
	return 0.0 - y;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0 - y
end function

Java

public static double code(double x, double y) {
	return 0.0 - y;
}

Python

def code(x, y):
	return 0.0 - y

Julia

function code(x, y)
	return Float64(0.0 - y)
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0 - y;
end

Wolfram

code[x_, y_] := N[(0.0 - y), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - y} \]

   3. --lowering--.f64 50.7

      \[\leadsto \color{blue}{0 - y} \]

5. Simplified 50.7%

   \[\leadsto \color{blue}{0 - y} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. neg-lowering-neg.f64 50.7

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

7. Applied egg-rr 50.7%

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

8. Final simplification 50.7%

   \[\leadsto 0 - y \]
9. Add Preprocessing

Alternative 4: 2.3% 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 x around 0

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

   1. mul-1-neg N/A

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

   2. neg-sub0 N/A

      \[\leadsto \color{blue}{0 - y} \]

   3. --lowering--.f64 50.7

      \[\leadsto \color{blue}{0 - y} \]

5. Simplified 50.7%

   \[\leadsto \color{blue}{0 - y} \]
6. Step-by-step derivation

   1. sub0-neg N/A

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

   2. +-lft-identity N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\left(0 + y\right)}\right) \]

   3. flip3-+ N/A

      \[\leadsto \mathsf{neg}\left(\color{blue}{\frac{{0}^{3} + {y}^{3}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)}}\right) \]

   4. distribute-neg-frac N/A

      \[\leadsto \color{blue}{\frac{\mathsf{neg}\left(\left({0}^{3} + {y}^{3}\right)\right)}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)}} \]

   5. metadata-eval N/A

      \[\leadsto \frac{\mathsf{neg}\left(\left(\color{blue}{0} + {y}^{3}\right)\right)}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   6. +-lft-identity N/A

      \[\leadsto \frac{\mathsf{neg}\left(\color{blue}{{y}^{3}}\right)}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   7. cube-neg N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{3}}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   8. sqr-pow N/A

      \[\leadsto \frac{\color{blue}{{\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(y\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   9. pow-prod-down N/A

      \[\leadsto \frac{\color{blue}{{\left(\left(\mathsf{neg}\left(y\right)\right) \cdot \left(\mathsf{neg}\left(y\right)\right)\right)}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   10. sqr-neg N/A

       \[\leadsto \frac{{\color{blue}{\left(y \cdot y\right)}}^{\left(\frac{3}{2}\right)}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   11. pow-prod-down N/A

       \[\leadsto \frac{\color{blue}{{y}^{\left(\frac{3}{2}\right)} \cdot {y}^{\left(\frac{3}{2}\right)}}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   12. sqr-pow N/A

       \[\leadsto \frac{\color{blue}{{y}^{3}}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   13. +-lft-identity N/A

       \[\leadsto \frac{\color{blue}{0 + {y}^{3}}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   14. metadata-eval N/A

       \[\leadsto \frac{\color{blue}{{0}^{3}} + {y}^{3}}{0 \cdot 0 + \left(y \cdot y - 0 \cdot y\right)} \]

   15. flip3-+ N/A

       \[\leadsto \color{blue}{0 + y} \]

   16. +-lft-identity 2.8

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

7. Applied egg-rr 2.8%

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

Reproduce

herbie shell --seed 2024196 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, C"
  :precision binary64
  (- (* x 2.0) y))