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

Percentage Accurate: 99.7% → 99.7%

Time: 8.7s

Alternatives: 6

Speedup: 1.0×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ x + \mathsf{fma}\left(6, y, x \cdot -6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (fma 6.0 y (* x -6.0)) z)))

C

double code(double x, double y, double z) {
	return x + (fma(6.0, y, (x * -6.0)) * z);
}

Julia

function code(x, y, z)
	return Float64(x + Float64(fma(6.0, y, Float64(x * -6.0)) * z))
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(6.0 * y + N[(x * -6.0), $MachinePrecision]), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in y around 0 99.9%

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

   1. fma-define 99.9%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-6, x, 6 \cdot y\right)} \cdot z \]

5. Simplified 99.9%

   \[\leadsto x + \color{blue}{\mathsf{fma}\left(-6, x, 6 \cdot y\right)} \cdot z \]

6. Taylor expanded in x around 0 99.9%

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

   1. +-commutative 99.9%

      \[\leadsto x + \color{blue}{\left(6 \cdot y + -6 \cdot x\right)} \cdot z \]

   2. fma-define 99.9%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(6, y, -6 \cdot x\right)} \cdot z \]

8. Simplified 99.9%

   \[\leadsto x + \color{blue}{\mathsf{fma}\left(6, y, -6 \cdot x\right)} \cdot z \]

9. Final simplification 99.9%

   \[\leadsto x + \mathsf{fma}\left(6, y, x \cdot -6\right) \cdot z \]
10. Add Preprocessing

Alternative 2: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-39} \lor \neg \left(x \leq 2 \cdot 10^{+120}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-39) (not (<= x 2e+120)))
   (+ x (* -6.0 (* x z)))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-39) || !(x <= 2e+120)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.2d-39)) .or. (.not. (x <= 2d+120))) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-39) || !(x <= 2e+120)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e-39) or not (x <= 2e+120):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-39) || !(x <= 2e+120))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.2e-39) || ~((x <= 2e+120)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.2e-39], N[Not[LessEqual[x, 2e+120]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000001e-39 or 2e120 < x

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.6%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   if -2.20000000000000001e-39 < x < 2e120

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 92.4%

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

      1. *-commutative 92.4%

         \[\leadsto x + 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   5. Simplified 92.4%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-39} \lor \neg \left(x \leq 2 \cdot 10^{+120}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-43} \lor \neg \left(x \leq 2 \cdot 10^{+120}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.65e-43) (not (<= x 2e+120)))
   (+ x (* -6.0 (* x z)))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.65e-43) || !(x <= 2e+120)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.65d-43)) .or. (.not. (x <= 2d+120))) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.65e-43) || !(x <= 2e+120)) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.65e-43) or not (x <= 2e+120):
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.65e-43) || !(x <= 2e+120))
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.65e-43) || ~((x <= 2e+120)))
		tmp = x + (-6.0 * (x * z));
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.65e-43], N[Not[LessEqual[x, 2e+120]], $MachinePrecision]], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.6500000000000002e-43 or 2e120 < x

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.6%

      \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

   if -2.6500000000000002e-43 < x < 2e120

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.8%

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

      1. fma-define 99.8%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(-6, x, 6 \cdot y\right)} \cdot z \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-6, x, 6 \cdot y\right)} \cdot z \]

   6. Taylor expanded in x around 0 92.4%

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

      1. associate-*r* 92.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot z} \]

      2. *-commutative 92.5%

         \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]

      3. associate-*l* 92.5%

         \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]

   8. Simplified 92.5%

      \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.65 \cdot 10^{-43} \lor \neg \left(x \leq 2 \cdot 10^{+120}\right):\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-39} \lor \neg \left(x \leq 6.2 \cdot 10^{+120}\right):\\ \;\;\;\;x + \left(x \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.65e-39) (not (<= x 6.2e+120)))
   (+ x (* (* x -6.0) z))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-39) || !(x <= 6.2e+120)) {
		tmp = x + ((x * -6.0) * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.65d-39)) .or. (.not. (x <= 6.2d+120))) then
        tmp = x + ((x * (-6.0d0)) * z)
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.65e-39) || !(x <= 6.2e+120)) {
		tmp = x + ((x * -6.0) * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.65e-39) or not (x <= 6.2e+120):
		tmp = x + ((x * -6.0) * z)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.65e-39) || !(x <= 6.2e+120))
		tmp = Float64(x + Float64(Float64(x * -6.0) * z));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.65e-39) || ~((x <= 6.2e+120)))
		tmp = x + ((x * -6.0) * z);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.65e-39], N[Not[LessEqual[x, 6.2e+120]], $MachinePrecision]], N[(x + N[(N[(x * -6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.64999999999999992e-39 or 6.19999999999999947e120 < x

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 92.6%

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

      1. associate-*r* 92.6%

         \[\leadsto x + \color{blue}{\left(-6 \cdot x\right) \cdot z} \]

   5. Simplified 92.6%

      \[\leadsto x + \color{blue}{\left(-6 \cdot x\right) \cdot z} \]

   if -1.64999999999999992e-39 < x < 6.19999999999999947e120

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 99.8%

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

      1. fma-define 99.8%

         \[\leadsto x + \color{blue}{\mathsf{fma}\left(-6, x, 6 \cdot y\right)} \cdot z \]

   5. Simplified 99.8%

      \[\leadsto x + \color{blue}{\mathsf{fma}\left(-6, x, 6 \cdot y\right)} \cdot z \]

   6. Taylor expanded in x around 0 92.4%

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

      1. associate-*r* 92.5%

         \[\leadsto x + \color{blue}{\left(6 \cdot y\right) \cdot z} \]

      2. *-commutative 92.5%

         \[\leadsto x + \color{blue}{\left(y \cdot 6\right)} \cdot z \]

      3. associate-*l* 92.5%

         \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]

   8. Simplified 92.5%

      \[\leadsto x + \color{blue}{y \cdot \left(6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 92.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.65 \cdot 10^{-39} \lor \neg \left(x \leq 6.2 \cdot 10^{+120}\right):\\ \;\;\;\;x + \left(x \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - z \cdot \left(6 \cdot \left(x - y\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* z (* 6.0 (- x y)))))

C

double code(double x, double y, double z) {
	return x - (z * (6.0 * (x - y)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - (z * (6.0d0 * (x - y)))
end function

Java

public static double code(double x, double y, double z) {
	return x - (z * (6.0 * (x - y)));
}

Python

def code(x, y, z):
	return x - (z * (6.0 * (x - y)))

Julia

function code(x, y, z)
	return Float64(x - Float64(z * Float64(6.0 * Float64(x - y))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - (z * (6.0 * (x - y)));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Final simplification 99.9%

   \[\leadsto x - z \cdot \left(6 \cdot \left(x - y\right)\right) \]
4. Add Preprocessing

Alternative 6: 62.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ x + -6 \cdot \left(x \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* -6.0 (* x z))))

C

double code(double x, double y, double z) {
	return x + (-6.0 * (x * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((-6.0d0) * (x * z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (-6.0 * (x * z));
}

Python

def code(x, y, z):
	return x + (-6.0 * (x * z))

Julia

function code(x, y, z)
	return Float64(x + Float64(-6.0 * Float64(x * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (-6.0 * (x * z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Add Preprocessing

3. Taylor expanded in y around 0 62.9%

   \[\leadsto x + \color{blue}{-6 \cdot \left(x \cdot z\right)} \]

4. Final simplification 62.9%

   \[\leadsto x + -6 \cdot \left(x \cdot z\right) \]
5. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024034 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))