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

Percentage Accurate: 99.7% → 99.8%

Time: 7.6s

Alternatives: 10

Speedup: 1.0×

• 20.8% 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: 99.8% accurate, 1.0× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-188} \lor \neg \left(y \leq 1.35 \cdot 10^{-151}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.9e-188) (not (<= y 1.35e-151)))
   (+ x (* 6.0 (* y z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-188) || !(y <= 1.35e-151)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * 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 ((y <= (-2.9d-188)) .or. (.not. (y <= 1.35d-151))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.9e-188) || !(y <= 1.35e-151)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.9e-188) or not (y <= 1.35e-151):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.9e-188) || !(y <= 1.35e-151))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.9e-188) || ~((y <= 1.35e-151)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.9e-188], N[Not[LessEqual[y, 1.35e-151]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9000000000000001e-188 or 1.35000000000000004e-151 < y

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   if -2.9000000000000001e-188 < y < 1.35000000000000004e-151

   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 98.1%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{-188} \lor \neg \left(y \leq 1.35 \cdot 10^{-151}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-185} \lor \neg \left(y \leq 1.35 \cdot 10^{-151}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8e-185) (not (<= y 1.35e-151)))
   (+ x (* 6.0 (* y z)))
   (+ x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e-185) || !(y <= 1.35e-151)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	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 ((y <= (-8d-185)) .or. (.not. (y <= 1.35d-151))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (z * (x * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8e-185) || !(y <= 1.35e-151)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8e-185) or not (y <= 1.35e-151):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8e-185) || !(y <= 1.35e-151))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8e-185) || ~((y <= 1.35e-151)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8e-185], N[Not[LessEqual[y, 1.35e-151]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.9999999999999999e-185 or 1.35000000000000004e-151 < y

   1. Initial program 99.4%

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

   3. Taylor expanded in y around inf 87.7%

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

      1. *-commutative 87.7%

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

   5. Simplified 87.7%

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

   if -7.9999999999999999e-185 < y < 1.35000000000000004e-151

   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 98.1%

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

      1. associate-*r* 98.2%

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

   5. Simplified 98.2%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{-185} \lor \neg \left(y \leq 1.35 \cdot 10^{-151}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-185}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-151}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -7.8e-185)
   (+ x (* z (* y 6.0)))
   (if (<= y 1.35e-151) (+ x (* z (* x -6.0))) (+ x (* 6.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -7.8e-185) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 1.35e-151) {
		tmp = x + (z * (x * -6.0));
	} 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 (y <= (-7.8d-185)) then
        tmp = x + (z * (y * 6.0d0))
    else if (y <= 1.35d-151) then
        tmp = x + (z * (x * (-6.0d0)))
    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 (y <= -7.8e-185) {
		tmp = x + (z * (y * 6.0));
	} else if (y <= 1.35e-151) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -7.8e-185:
		tmp = x + (z * (y * 6.0))
	elif y <= 1.35e-151:
		tmp = x + (z * (x * -6.0))
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -7.8e-185)
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	elseif (y <= 1.35e-151)
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	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 (y <= -7.8e-185)
		tmp = x + (z * (y * 6.0));
	elseif (y <= 1.35e-151)
		tmp = x + (z * (x * -6.0));
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -7.8e-185], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e-151], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.7999999999999999e-185

   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 90.2%

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

   if -7.7999999999999999e-185 < y < 1.35000000000000004e-151

   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 98.1%

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

      1. associate-*r* 98.2%

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

   5. Simplified 98.2%

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

   if 1.35000000000000004e-151 < y

   1. Initial program 99.0%

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

   3. Taylor expanded in y around inf 85.6%

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

      1. *-commutative 85.6%

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

   5. Simplified 85.6%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{-185}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-151}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 6.2 \cdot 10^{+20}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 6.2e+20))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 6.2e+20)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	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 ((z <= (-0.17d0)) .or. (.not. (z <= 6.2d+20))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 6.2e+20)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 6.2e+20):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 6.2e+20))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 6.2e+20)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 6.2e+20]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 6.2e20 < z

   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 48.7%

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

   4. Taylor expanded in z around inf 48.0%

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

   if -0.170000000000000012 < z < 6.2e20

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 74.9%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 6.2 \cdot 10^{+20}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17) (* x (* z -6.0)) (if (<= z 6.2e+20) x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 6.2e+20) {
		tmp = x;
	} else {
		tmp = -6.0 * (x * 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 (z <= (-0.17d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 6.2d+20) then
        tmp = x
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 6.2e+20) {
		tmp = x;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = x * (z * -6.0)
	elif z <= 6.2e+20:
		tmp = x
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 6.2e+20)
		tmp = x;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = x * (z * -6.0);
	elseif (z <= 6.2e+20)
		tmp = x;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+20], x, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 45.9%

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

   4. Taylor expanded in z around inf 44.7%

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

      1. *-commutative 44.7%

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

      2. associate-*r* 44.8%

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

   6. Simplified 44.8%

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

   if -0.170000000000000012 < z < 6.2e20

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 74.9%

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

   if 6.2e20 < z

   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 52.5%

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

   4. Taylor expanded in z around inf 52.5%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17) (* x (* z -6.0)) (if (<= z 6.2e+20) x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 6.2e+20) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	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 (z <= (-0.17d0)) then
        tmp = x * (z * (-6.0d0))
    else if (z <= 6.2d+20) then
        tmp = x
    else
        tmp = z * (x * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = x * (z * -6.0);
	} else if (z <= 6.2e+20) {
		tmp = x;
	} else {
		tmp = z * (x * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = x * (z * -6.0)
	elif z <= 6.2e+20:
		tmp = x
	else:
		tmp = z * (x * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(x * Float64(z * -6.0));
	elseif (z <= 6.2e+20)
		tmp = x;
	else
		tmp = Float64(z * Float64(x * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = x * (z * -6.0);
	elseif (z <= 6.2e+20)
		tmp = x;
	else
		tmp = z * (x * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.2e+20], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 45.9%

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

   4. Taylor expanded in z around inf 44.7%

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

      1. *-commutative 44.7%

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

      2. associate-*r* 44.8%

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

   6. Simplified 44.8%

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

   if -0.170000000000000012 < z < 6.2e20

   1. Initial program 99.3%

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

   3. Taylor expanded in z around 0 74.9%

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

   if 6.2e20 < z

   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 52.5%

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

   4. Taylor expanded in z around inf 52.5%

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

      1. *-commutative 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*l* 52.6%

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

   6. Simplified 52.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+20}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * ((y - x) * 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

3. Final simplification 99.5%

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

Alternative 9: 61.5% 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 99.5%

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

3. Taylor expanded in y around 0 64.5%

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

4. Final simplification 64.5%

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

Alternative 10: 36.4% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

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
end function

Java

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

Python

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

Julia

function code(x, y, z)
	return x
end

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

3. Taylor expanded in z around 0 45.1%

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

4. Final simplification 45.1%

   \[\leadsto x \]
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 2024053 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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