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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

Alternatives: 6

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, 0.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \mathsf{fma}\left(x, 1 - y, y\right) \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))

C

assert(x < y);
double code(double x, double y) {
	return fma(x, (1.0 - y), y);
}

Julia

x, y = sort([x, y])
function code(x, y)
	return fma(x, Float64(1.0 - y), y)
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x * N[(1.0 - y), $MachinePrecision] + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. +-commutative 100.0%

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

   2. associate--l+ 100.0%

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

   3. +-commutative 100.0%

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

   4. *-rgt-identity 100.0%

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

   5. distribute-lft-out-- 100.0%

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

   6. unsub-neg 100.0%

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

   7. +-commutative 100.0%

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

   8. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, \left(-y\right) + 1, y\right)} \]

   9. +-commutative 100.0%

      \[\leadsto \mathsf{fma}\left(x, \color{blue}{1 + \left(-y\right)}, y\right) \]

   10. unsub-neg 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, 1 - y, y\right) \]

Alternative 2: 80.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -440000 \lor \neg \left(y \leq 1.8 \cdot 10^{+144} \lor \neg \left(y \leq 8 \cdot 10^{+159}\right) \land y \leq 2.1 \cdot 10^{+298}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (or (<= y -440000.0)
         (not (or (<= y 1.8e+144) (and (not (<= y 8e+159)) (<= y 2.1e+298)))))
   (* x (- y))
   (+ x y)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if ((y <= -440000.0) || !((y <= 1.8e+144) || (!(y <= 8e+159) && (y <= 2.1e+298)))) {
		tmp = x * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-440000.0d0)) .or. (.not. (y <= 1.8d+144) .or. (.not. (y <= 8d+159)) .and. (y <= 2.1d+298))) then
        tmp = x * -y
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if ((y <= -440000.0) || !((y <= 1.8e+144) || (!(y <= 8e+159) && (y <= 2.1e+298)))) {
		tmp = x * -y;
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if (y <= -440000.0) or not ((y <= 1.8e+144) or (not (y <= 8e+159) and (y <= 2.1e+298))):
		tmp = x * -y
	else:
		tmp = x + y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if ((y <= -440000.0) || !((y <= 1.8e+144) || (!(y <= 8e+159) && (y <= 2.1e+298))))
		tmp = Float64(x * Float64(-y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -440000.0) || ~(((y <= 1.8e+144) || (~((y <= 8e+159)) && (y <= 2.1e+298)))))
		tmp = x * -y;
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[Or[LessEqual[y, -440000.0], N[Not[Or[LessEqual[y, 1.8e+144], And[N[Not[LessEqual[y, 8e+159]], $MachinePrecision], LessEqual[y, 2.1e+298]]]], $MachinePrecision]], N[(x * (-y)), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.4e5 or 1.7999999999999999e144 < y < 7.9999999999999994e159 or 2.0999999999999998e298 < y

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 54.9%

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

   5. Taylor expanded in y around inf 54.9%

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

      1. mul-1-neg 54.9%

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

      2. *-commutative 54.9%

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

      3. distribute-rgt-neg-in 54.9%

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

   7. Simplified 54.9%

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

   if -4.4e5 < y < 1.7999999999999999e144 or 7.9999999999999994e159 < y < 2.0999999999999998e298

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 86.3%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -440000 \lor \neg \left(y \leq 1.8 \cdot 10^{+144} \lor \neg \left(y \leq 8 \cdot 10^{+159}\right) \land y \leq 2.1 \cdot 10^{+298}\right):\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 98.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -32 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (or (<= x -32.0) (not (<= x 1.0))) (* x (- 1.0 y)) (+ x y)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if ((x <= -32.0) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-32.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if ((x <= -32.0) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if (x <= -32.0) or not (x <= 1.0):
		tmp = x * (1.0 - y)
	else:
		tmp = x + y
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if ((x <= -32.0) || !(x <= 1.0))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -32.0) || ~((x <= 1.0)))
		tmp = x * (1.0 - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[Or[LessEqual[x, -32.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -32 or 1 < x

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.1%

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

   if -32 < x < 1

   1. Initial program 100.0%

      \[\left(x + y\right) - x \cdot y \]
   2. Step-by-step derivation

      1. associate--l+ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -32 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (+ x (- y (* x y))))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + (y - (x * y))
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return x + (y - (x * y))

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(x + Float64(y - Float64(x * y)))
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x + (y - (x * y));
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x + N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto x + \left(y - x \cdot y\right) \]

Alternative 5: 75.3% accurate, 2.3× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x + y \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (+ x y))

C

assert(x < y);
double code(double x, double y) {
	return x + y;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x + y
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return x + y

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(x + y)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x + y;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(x + y), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in x around 0 75.2%

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

5. Final simplification 75.2%

   \[\leadsto x + y \]

Alternative 6: 37.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ x \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 x)

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return x

Julia

x, y = sort([x, y])
function code(x, y)
	return x
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = x;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[\left(x + y\right) - x \cdot y \]
2. Step-by-step derivation

   1. associate--l+ 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around 0 40.3%

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

5. Final simplification 40.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023230 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))