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

Percentage Accurate: 100.0% → 100.0%

Time: 2.1s

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, 0.1× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (fma x (- 1.0 y) y))

C

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

Julia

function code(x, y)
	return fma(x, Float64(1.0 - y), y)
end

Wolfram

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: 98.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.4) (not (<= x 1.0))) (* x (- 1.0 y)) (+ x y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.0)) {
		tmp = x * (1.0 - 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 <= (-1.4d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = x * (1.0d0 - y)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.4) || !(x <= 1.0)) {
		tmp = x * (1.0 - y);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.4) or not (x <= 1.0):
		tmp = x * (1.0 - y)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.4) || !(x <= 1.0))
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.4) || ~((x <= 1.0)))
		tmp = x * (1.0 - y);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.4], 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 < -1.3999999999999999 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 99.7%

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

   if -1.3999999999999999 < 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 y around 0 100.0%

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

   5. Taylor expanded in x around 0 98.4%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]

Alternative 3: 80.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-277}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.4) (* x (- 1.0 y)) (if (<= x -4.5e-277) (+ x y) (- y (* x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.4) {
		tmp = x * (1.0 - y);
	} else if (x <= -4.5e-277) {
		tmp = 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 <= (-1.4d0)) then
        tmp = x * (1.0d0 - y)
    else if (x <= (-4.5d-277)) then
        tmp = 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 <= -1.4) {
		tmp = x * (1.0 - y);
	} else if (x <= -4.5e-277) {
		tmp = x + y;
	} else {
		tmp = y - (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.4:
		tmp = x * (1.0 - y)
	elif x <= -4.5e-277:
		tmp = x + y
	else:
		tmp = y - (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.4)
		tmp = Float64(x * Float64(1.0 - y));
	elseif (x <= -4.5e-277)
		tmp = 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 <= -1.4)
		tmp = x * (1.0 - y);
	elseif (x <= -4.5e-277)
		tmp = x + y;
	else
		tmp = y - (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.4], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -4.5e-277], N[(x + y), $MachinePrecision], N[(y - N[(x * y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.3999999999999999

   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 99.5%

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

   if -1.3999999999999999 < x < -4.49999999999999992e-277

   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 0 100.0%

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

   5. Taylor expanded in x around 0 99.1%

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

   if -4.49999999999999992e-277 < 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 y around inf 61.7%

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

      1. sub-neg 61.7%

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

      2. distribute-rgt-in 61.7%

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

      3. *-lft-identity 61.7%

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

      4. cancel-sign-sub-inv 61.7%

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

      5. *-commutative 61.7%

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

   6. Simplified 61.7%

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

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{-277}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;y - x \cdot y\\ \end{array} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

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

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(x + Float64(y - Float64(x * y)))
end

MATLAB

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

Wolfram

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: 50.1% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.2e-105) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.2e-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 (y <= 3.2d-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 (y <= 3.2e-105) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.2e-105:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.2e-105)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3.2e-105)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.2e-105], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 3.19999999999999981e-105

   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 52.5%

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

   if 3.19999999999999981e-105 < 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 0 61.2%

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

4. Final simplification 55.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.2 \cdot 10^{-105}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 6: 75.6% accurate, 2.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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 y around 0 100.0%

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

5. Taylor expanded in x around 0 77.8%

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

6. Final simplification 77.8%

   \[\leadsto x + y \]

Alternative 7: 39.2% 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. 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 39.1%

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

5. Final simplification 39.1%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023207 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))