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

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

Alternatives: 7

Speedup: 1.0×

• Unsound rule application detected in e-graph. Results may not be sound.

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: 61.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-y\right)\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* x (- y))))
   (if (<= y -1.0) t_0 (if (<= y 7e-44) x (if (<= y 1.75e+139) y t_0)))))

C

double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 7e-44) {
		tmp = x;
	} else if (y <= 1.75e+139) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x * -y
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= 7d-44) then
        tmp = x
    else if (y <= 1.75d+139) then
        tmp = y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x * -y;
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 7e-44) {
		tmp = x;
	} else if (y <= 1.75e+139) {
		tmp = y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x * -y
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= 7e-44:
		tmp = x
	elif y <= 1.75e+139:
		tmp = y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x * Float64(-y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 7e-44)
		tmp = x;
	elseif (y <= 1.75e+139)
		tmp = y;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x * -y;
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 7e-44)
		tmp = x;
	elseif (y <= 1.75e+139)
		tmp = y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x * (-y)), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 7e-44], x, If[LessEqual[y, 1.75e+139], y, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.74999999999999989e139 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.1%

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

   3. Taylor expanded in x around inf 60.0%

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

      1. mul-1-neg 60.0%

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

      2. distribute-rgt-neg-out 60.0%

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

   5. Simplified 60.0%

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

   if -1 < y < 6.9999999999999995e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.4%

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

   if 6.9999999999999995e-44 < y < 1.74999999999999989e139

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 60.1%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.75 \cdot 10^{+139}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x (- y)) (if (<= y 9.5e-44) x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * -y;
	} else if (y <= 9.5e-44) {
		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 <= 9.5d-44) 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 <= 9.5e-44) {
		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 <= 9.5e-44:
		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 <= 9.5e-44)
		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 <= 9.5e-44)
		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, 9.5e-44], 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. Taylor expanded in y around inf 98.6%

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

   3. Taylor expanded in x around inf 56.3%

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

      1. mul-1-neg 56.3%

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

      2. distribute-rgt-neg-out 56.3%

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

   5. Simplified 56.3%

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

   if -1 < y < 9.49999999999999924e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.4%

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

   if 9.49999999999999924e-44 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 94.4%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot \left(-y\right)\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 4: 74.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8.2e-44) (* x (- 1.0 y)) (* y (- 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8.2e-44) {
		tmp = x * (1.0 - 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 (y <= 8.2d-44) then
        tmp = x * (1.0d0 - 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 (y <= 8.2e-44) {
		tmp = x * (1.0 - y);
	} else {
		tmp = y * (1.0 - x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8.2e-44:
		tmp = x * (1.0 - y)
	else:
		tmp = y * (1.0 - x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8.2e-44)
		tmp = Float64(x * Float64(1.0 - y));
	else
		tmp = Float64(y * Float64(1.0 - x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8.2e-44)
		tmp = x * (1.0 - y);
	else
		tmp = y * (1.0 - x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8.2e-44], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.19999999999999984e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.0%

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

   if 8.19999999999999984e-44 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 94.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{-44}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 5: 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. Final simplification 100.0%

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

Alternative 6: 51.6% accurate, 2.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 7e-44) x y))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7e-44) {
		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 <= 7d-44) 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 <= 7e-44) {
		tmp = x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7e-44:
		tmp = x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7e-44)
		tmp = x;
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7e-44)
		tmp = x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7e-44], x, y]

Derivation

1. Split input into 2 regimes

2. if y < 6.9999999999999995e-44

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 51.9%

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

   if 6.9999999999999995e-44 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 48.3%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 7: 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. Taylor expanded in y around 0 38.3%

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

3. Final simplification 38.3%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023174 
(FPCore (x y)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, A"
  :precision binary64
  (- (+ x y) (* x y)))