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

Percentage Accurate: 100.0% → 100.0%

Time: 7.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + y\right) - x \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) - x \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + y\right) - x \cdot y \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

Alternative 2: 73.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x (- y)) (if (<= y 4.3e-116) x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 4.3e-116) {
		tmp = x;
	} else {
		tmp = y * (1.0 - 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 <= (-1.0d0)) then
        tmp = x * -y
    else if (y <= 4.3d-116) then
        tmp = x
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 4.3e-116) {
		tmp = x;
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * -y
	elif y <= 4.3e-116:
		tmp = x
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 4.3e-116)
		tmp = x;
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * -y;
	elseif (y <= 4.3e-116)
		tmp = x;
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 4.3e-116], x, N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 51.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.8%

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

      2. *-commutative 51.8%

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

      3. distribute-rgt-neg-in 51.8%

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

   6. Simplified 51.8%

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

   if -1 < y < 4.2999999999999997e-116

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.5%

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

   4. Taylor expanded in y around 0 83.5%

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

   if 4.2999999999999997e-116 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-116}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x (- y)) (if (<= y 1.9e-114) x y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 1.9e-114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x * -y
    else if (y <= 1.9d-114) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 1.9e-114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * -y
	elif y <= 1.9e-114:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * Float64(-y));
	elseif (y <= 1.9e-114)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * -y;
	elseif (y <= 1.9e-114)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * (-y)), $MachinePrecision], If[LessEqual[y, 1.9e-114], x, y]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

   4. Taylor expanded in x around inf 51.8%

      \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
   5. Step-by-step derivation

      1. mul-1-neg 51.8%

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

      2. *-commutative 51.8%

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

      3. distribute-rgt-neg-in 51.8%

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

   6. Simplified 51.8%

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

   if -1 < y < 1.8999999999999999e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 83.5%

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

   4. Taylor expanded in y around 0 83.5%

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

   if 1.8999999999999999e-114 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.0%

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

   4. Taylor expanded in x around 0 54.0%

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

4. Final simplification 65.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{-64}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e-64) (- x (* x y)) (* y (- 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e-64) {
		tmp = x - (x * y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.85d-64)) then
        tmp = x - (x * y)
    else
        tmp = y * (1.0d0 - x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e-64) {
		tmp = x - (x * y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e-64:
		tmp = x - (x * y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e-64)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e-64)
		tmp = x - (x * y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e-64], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.84999999999999999e-64

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 95.0%

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

   if -1.84999999999999999e-64 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 66.8%

      \[\leadsto \color{blue}{y \cdot \left(1 - x\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 50.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.65 \cdot 10^{-114}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.65e-114) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.65e-114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.65d-114) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.65e-114) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.65e-114:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.65e-114)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.65e-114)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.65e-114], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 1.65000000000000017e-114

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 72.9%

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

   4. Taylor expanded in y around 0 57.3%

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

   if 1.65000000000000017e-114 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.0%

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

   4. Taylor expanded in x around 0 54.0%

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

Alternative 6: 38.8% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in x around inf 63.6%

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

4. Taylor expanded in y around 0 42.4%

   \[\leadsto \color{blue}{x} \]
5. Add Preprocessing

Alternative 7: 2.6% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 0.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

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

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 59.4%

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

4. Taylor expanded in x around inf 23.9%

   \[\leadsto \color{blue}{-1 \cdot \left(x \cdot y\right)} \]
5. Step-by-step derivation

   1. mul-1-neg 23.9%

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

   2. *-commutative 23.9%

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

   3. distribute-rgt-neg-in 23.9%

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

6. Simplified 23.9%

   \[\leadsto \color{blue}{y \cdot \left(-x\right)} \]
7. Step-by-step derivation

   1. add-log-exp 15.7%

      \[\leadsto \color{blue}{\log \left(e^{y \cdot \left(-x\right)}\right)} \]

   2. add-sqr-sqrt 15.7%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{y \cdot \left(-x\right)}} \cdot \sqrt{e^{y \cdot \left(-x\right)}}\right)} \]

   3. sqrt-unprod 15.7%

      \[\leadsto \log \color{blue}{\left(\sqrt{e^{y \cdot \left(-x\right)} \cdot e^{y \cdot \left(-x\right)}}\right)} \]

   4. exp-prod 15.7%

      \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot \color{blue}{{\left(e^{y}\right)}^{\left(-x\right)}}}\right) \]

   5. add-sqr-sqrt 7.8%

      \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\sqrt{x} \cdot \sqrt{x}}\right)}}\right) \]

   6. sqrt-unprod 8.1%

      \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\sqrt{x \cdot x}}\right)}}\right) \]

   7. sqr-neg 8.1%

      \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\sqrt{\color{blue}{\left(-x\right) \cdot \left(-x\right)}}\right)}}\right) \]

   8. sqrt-unprod 2.0%

      \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\sqrt{-x} \cdot \sqrt{-x}}\right)}}\right) \]

   9. add-sqr-sqrt 2.3%

      \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot {\left(e^{y}\right)}^{\left(-\color{blue}{\left(-x\right)}\right)}}\right) \]

   10. pow-flip 2.3%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot \color{blue}{\frac{1}{{\left(e^{y}\right)}^{\left(-x\right)}}}}\right) \]

   11. exp-prod 1.7%

       \[\leadsto \log \left(\sqrt{e^{y \cdot \left(-x\right)} \cdot \frac{1}{\color{blue}{e^{y \cdot \left(-x\right)}}}}\right) \]

   12. rgt-mult-inverse 2.6%

       \[\leadsto \log \left(\sqrt{\color{blue}{1}}\right) \]

   13. metadata-eval 2.6%

       \[\leadsto \log \color{blue}{1} \]

   14. metadata-eval 2.6%

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

8. Applied egg-rr 2.6%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024185 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))