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

Percentage Accurate: 100.0% → 100.0%

Time: 7.4s

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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.1 \cdot 10^{-122}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -8.1e-122) (- x (* x y)) (if (<= x 1.0) y (* x (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -8.1e-122) {
		tmp = x - (x * y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-8.1d-122)) then
        tmp = x - (x * y)
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -8.1e-122) {
		tmp = x - (x * y);
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -8.1e-122:
		tmp = x - (x * y)
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -8.1e-122)
		tmp = Float64(x - Float64(x * y));
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -8.1e-122)
		tmp = x - (x * y);
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -8.1e-122], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.0999999999999997e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.3%

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

   if -8.0999999999999997e-122 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 90.5%

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

   4. Taylor expanded in x around 0 89.8%

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

   if 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.3%

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

   4. Taylor expanded in y around inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-rgt-neg-out 40.2%

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

   6. Simplified 40.2%

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

Alternative 3: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.8e-105) x (if (<= x 1.0) y (* x (- y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-105) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.8d-105)) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = y
    else
        tmp = x * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-105) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = y;
	} else {
		tmp = x * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.8e-105:
		tmp = x
	elif x <= 1.0:
		tmp = y
	else:
		tmp = x * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.8e-105)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = Float64(x * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.8e-105)
		tmp = x;
	elseif (x <= 1.0)
		tmp = y;
	else
		tmp = x * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.8e-105], x, If[LessEqual[x, 1.0], y, N[(x * (-y)), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999984e-105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.1%

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

   4. Taylor expanded in y around 0 61.5%

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

   if -6.79999999999999984e-105 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 89.7%

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

   4. Taylor expanded in x around 0 89.0%

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

   if 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.3%

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

   4. Taylor expanded in y around inf 40.2%

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

      1. mul-1-neg 40.2%

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

      2. distribute-rgt-neg-out 40.2%

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

   6. Simplified 40.2%

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

Alternative 4: 73.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{-122}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e-122) (- x (* x y)) (- y (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e-122) {
		tmp = x - (x * y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.5d-122)) then
        tmp = x - (x * y)
    else
        tmp = y - (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.5e-122) {
		tmp = x - (x * y);
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e-122:
		tmp = x - (x * y)
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e-122)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = Float64(y - Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.5e-122)
		tmp = x - (x * y);
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e-122], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.49999999999999965e-122

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 90.3%

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

   if -6.49999999999999965e-122 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 70.1%

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

Alternative 5: 49.4% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -6.8e-105) x y))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-105) {
		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 (x <= (-6.8d-105)) then
        tmp = x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.8e-105) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.8e-105:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.8e-105)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.8e-105)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.8e-105], x, y]

Derivation

1. Split input into 2 regimes

2. if x < -6.79999999999999984e-105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 91.1%

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

   4. Taylor expanded in y around 0 61.5%

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

   if -6.79999999999999984e-105 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 69.8%

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

   4. Taylor expanded in x around 0 53.4%

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

Alternative 6: 38.4% 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 64.5%

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

4. Taylor expanded in y around 0 43.5%

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

Alternative 7: 2.7% 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 x around inf 64.5%

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

4. Taylor expanded in y around inf 22.6%

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

   1. mul-1-neg 22.6%

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

   2. distribute-rgt-neg-out 22.6%

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

6. Simplified 22.6%

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

   1. add-log-exp 14.5%

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

   2. add-sqr-sqrt 14.5%

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

   3. sqrt-unprod 14.5%

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

   4. exp-prod 14.5%

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

   5. add-sqr-sqrt 7.8%

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

   6. sqrt-unprod 8.3%

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

   7. sqr-neg 8.3%

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

   8. sqrt-unprod 1.5%

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

   9. add-sqr-sqrt 1.8%

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

   10. pow-flip 1.8%

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

   11. exp-prod 1.6%

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

   12. rgt-mult-inverse 2.5%

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

   13. metadata-eval 2.5%

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

   14. metadata-eval 2.5%

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

8. Applied egg-rr 2.5%

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

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))