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

Percentage Accurate: 99.7% → 99.8%

Time: 7.6s

Alternatives: 7

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 99.8%

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

Alternative 2: 85.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-55} \lor \neg \left(y \leq -9.5 \cdot 10^{-95}\right) \land \left(y \leq -5.3 \cdot 10^{-132} \lor \neg \left(y \leq 4.1 \cdot 10^{+42}\right)\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2e-55)
         (and (not (<= y -9.5e-95))
              (or (<= y -5.3e-132) (not (<= y 4.1e+42)))))
   (+ x (* 6.0 (* y z)))
   (+ x (* x (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-55) || (!(y <= -9.5e-95) && ((y <= -5.3e-132) || !(y <= 4.1e+42)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (x * (z * -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 <= (-2d-55)) .or. (.not. (y <= (-9.5d-95))) .and. (y <= (-5.3d-132)) .or. (.not. (y <= 4.1d+42))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + (x * (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2e-55) || (!(y <= -9.5e-95) && ((y <= -5.3e-132) || !(y <= 4.1e+42)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (x * (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2e-55) or (not (y <= -9.5e-95) and ((y <= -5.3e-132) or not (y <= 4.1e+42))):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (x * (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2e-55) || (!(y <= -9.5e-95) && ((y <= -5.3e-132) || !(y <= 4.1e+42))))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2e-55) || (~((y <= -9.5e-95)) && ((y <= -5.3e-132) || ~((y <= 4.1e+42)))))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (x * (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2e-55], And[N[Not[LessEqual[y, -9.5e-95]], $MachinePrecision], Or[LessEqual[y, -5.3e-132], N[Not[LessEqual[y, 4.1e+42]], $MachinePrecision]]]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999999e-55 or -9.49999999999999998e-95 < y < -5.3000000000000003e-132 or 4.1e42 < y

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. Taylor expanded in y around inf 91.2%

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

      1. *-commutative 91.2%

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

   7. Simplified 91.2%

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

   if -1.99999999999999999e-55 < y < -9.49999999999999998e-95 or -5.3000000000000003e-132 < y < 4.1e42

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r* 89.9%

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

      3. *-commutative 89.9%

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

   7. Simplified 89.9%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{-55} \lor \neg \left(y \leq -9.5 \cdot 10^{-95}\right) \land \left(y \leq -5.3 \cdot 10^{-132} \lor \neg \left(y \leq 4.1 \cdot 10^{+42}\right)\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;y \leq -1.65 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-132}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* x (* z -6.0)))))
   (if (<= y -1.65e-55)
     (+ x (* y (* 6.0 z)))
     (if (<= y -4e-97)
       t_0
       (if (<= y -9.2e-132)
         (+ x (* 6.0 (* y z)))
         (if (<= y 4e+42) t_0 (+ x (* z (* y 6.0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (x * (z * -6.0));
	double tmp;
	if (y <= -1.65e-55) {
		tmp = x + (y * (6.0 * z));
	} else if (y <= -4e-97) {
		tmp = t_0;
	} else if (y <= -9.2e-132) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 4e+42) {
		tmp = t_0;
	} else {
		tmp = x + (z * (y * 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) :: t_0
    real(8) :: tmp
    t_0 = x + (x * (z * (-6.0d0)))
    if (y <= (-1.65d-55)) then
        tmp = x + (y * (6.0d0 * z))
    else if (y <= (-4d-97)) then
        tmp = t_0
    else if (y <= (-9.2d-132)) then
        tmp = x + (6.0d0 * (y * z))
    else if (y <= 4d+42) then
        tmp = t_0
    else
        tmp = x + (z * (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (x * (z * -6.0));
	double tmp;
	if (y <= -1.65e-55) {
		tmp = x + (y * (6.0 * z));
	} else if (y <= -4e-97) {
		tmp = t_0;
	} else if (y <= -9.2e-132) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 4e+42) {
		tmp = t_0;
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (x * (z * -6.0))
	tmp = 0
	if y <= -1.65e-55:
		tmp = x + (y * (6.0 * z))
	elif y <= -4e-97:
		tmp = t_0
	elif y <= -9.2e-132:
		tmp = x + (6.0 * (y * z))
	elif y <= 4e+42:
		tmp = t_0
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(x * Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -1.65e-55)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	elseif (y <= -4e-97)
		tmp = t_0;
	elseif (y <= -9.2e-132)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (y <= 4e+42)
		tmp = t_0;
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (x * (z * -6.0));
	tmp = 0.0;
	if (y <= -1.65e-55)
		tmp = x + (y * (6.0 * z));
	elseif (y <= -4e-97)
		tmp = t_0;
	elseif (y <= -9.2e-132)
		tmp = x + (6.0 * (y * z));
	elseif (y <= 4e+42)
		tmp = t_0;
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.65e-55], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4e-97], t$95$0, If[LessEqual[y, -9.2e-132], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e+42], t$95$0, N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.65e-55

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 88.0%

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

   if -1.65e-55 < y < -4.00000000000000014e-97 or -9.20000000000000012e-132 < y < 4.00000000000000018e42

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r* 89.9%

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

      3. *-commutative 89.9%

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

   7. Simplified 89.9%

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

   if -4.00000000000000014e-97 < y < -9.20000000000000012e-132

   1. Initial program 99.6%

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

      1. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. *-commutative 92.6%

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

   7. Simplified 92.6%

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

   if 4.00000000000000018e42 < y

   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 94.5%

      \[\leadsto x + \left(\color{blue}{y} \cdot 6\right) \cdot z \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-97}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-132}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 4 \cdot 10^{+42}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + x \cdot \left(z \cdot -6\right)\\ t_1 := x + y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-97}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-132}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* x (* z -6.0)))) (t_1 (+ x (* y (* 6.0 z)))))
   (if (<= y -2.5e-55)
     t_1
     (if (<= y -4.4e-97)
       t_0
       (if (<= y -9.2e-132)
         (+ x (* 6.0 (* y z)))
         (if (<= y 3.6e+42) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (x * (z * -6.0));
	double t_1 = x + (y * (6.0 * z));
	double tmp;
	if (y <= -2.5e-55) {
		tmp = t_1;
	} else if (y <= -4.4e-97) {
		tmp = t_0;
	} else if (y <= -9.2e-132) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 3.6e+42) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (x * (z * (-6.0d0)))
    t_1 = x + (y * (6.0d0 * z))
    if (y <= (-2.5d-55)) then
        tmp = t_1
    else if (y <= (-4.4d-97)) then
        tmp = t_0
    else if (y <= (-9.2d-132)) then
        tmp = x + (6.0d0 * (y * z))
    else if (y <= 3.6d+42) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (x * (z * -6.0));
	double t_1 = x + (y * (6.0 * z));
	double tmp;
	if (y <= -2.5e-55) {
		tmp = t_1;
	} else if (y <= -4.4e-97) {
		tmp = t_0;
	} else if (y <= -9.2e-132) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 3.6e+42) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (x * (z * -6.0))
	t_1 = x + (y * (6.0 * z))
	tmp = 0
	if y <= -2.5e-55:
		tmp = t_1
	elif y <= -4.4e-97:
		tmp = t_0
	elif y <= -9.2e-132:
		tmp = x + (6.0 * (y * z))
	elif y <= 3.6e+42:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(x * Float64(z * -6.0)))
	t_1 = Float64(x + Float64(y * Float64(6.0 * z)))
	tmp = 0.0
	if (y <= -2.5e-55)
		tmp = t_1;
	elseif (y <= -4.4e-97)
		tmp = t_0;
	elseif (y <= -9.2e-132)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (y <= 3.6e+42)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (x * (z * -6.0));
	t_1 = x + (y * (6.0 * z));
	tmp = 0.0;
	if (y <= -2.5e-55)
		tmp = t_1;
	elseif (y <= -4.4e-97)
		tmp = t_0;
	elseif (y <= -9.2e-132)
		tmp = x + (6.0 * (y * z));
	elseif (y <= 3.6e+42)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.5e-55], t$95$1, If[LessEqual[y, -4.4e-97], t$95$0, If[LessEqual[y, -9.2e-132], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.6e+42], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.5000000000000001e-55 or 3.6000000000000001e42 < y

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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. Taylor expanded in y around inf 91.1%

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

   if -2.5000000000000001e-55 < y < -4.3999999999999998e-97 or -9.20000000000000012e-132 < y < 3.6000000000000001e42

   1. Initial program 99.9%

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

      1. associate-*l* 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 89.8%

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

      1. *-commutative 89.8%

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

      2. associate-*r* 89.9%

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

      3. *-commutative 89.9%

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

   7. Simplified 89.9%

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

   if -4.3999999999999998e-97 < y < -9.20000000000000012e-132

   1. Initial program 99.6%

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

      1. associate-*l* 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 92.6%

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

      1. *-commutative 92.6%

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

   7. Simplified 92.6%

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

4. Final simplification 90.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{-55}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-97}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{-132}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{+42}:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 1.0× speedup

Math

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

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 99.8%

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

3. Final simplification 99.8%

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

Alternative 6: 76.3% accurate, 1.3× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (6.0 * (y * 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 * (y * z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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. Taylor expanded in y around inf 75.3%

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

   1. *-commutative 75.3%

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

7. Simplified 75.3%

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

8. Final simplification 75.3%

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

Alternative 7: 36.7% 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 99.8%

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

   1. flip3-- 36.6%

      \[\leadsto x + \color{blue}{\frac{{y}^{3} - {x}^{3}}{y \cdot y + \left(x \cdot x + y \cdot x\right)}} \cdot \left(6 \cdot z\right) \]

   2. associate-*l/ 34.7%

      \[\leadsto x + \color{blue}{\frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{y \cdot y + \left(x \cdot x + y \cdot x\right)}} \]

   3. +-commutative 34.7%

      \[\leadsto x + \frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{\color{blue}{\left(x \cdot x + y \cdot x\right) + y \cdot y}} \]

   4. distribute-rgt-out 34.7%

      \[\leadsto x + \frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{\color{blue}{x \cdot \left(x + y\right)} + y \cdot y} \]

   5. +-commutative 34.7%

      \[\leadsto x + \frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{x \cdot \color{blue}{\left(y + x\right)} + y \cdot y} \]

   6. fma-define 34.7%

      \[\leadsto x + \frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{\color{blue}{\mathsf{fma}\left(x, y + x, y \cdot y\right)}} \]

   7. pow2 34.7%

      \[\leadsto x + \frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{\mathsf{fma}\left(x, y + x, \color{blue}{{y}^{2}}\right)} \]

6. Applied egg-rr 34.7%

   \[\leadsto x + \color{blue}{\frac{\left({y}^{3} - {x}^{3}\right) \cdot \left(6 \cdot z\right)}{\mathsf{fma}\left(x, y + x, {y}^{2}\right)}} \]

7. Taylor expanded in y around inf 35.7%

   \[\leadsto x + \frac{\color{blue}{{y}^{3}} \cdot \left(6 \cdot z\right)}{\mathsf{fma}\left(x, y + x, {y}^{2}\right)} \]

8. Taylor expanded in x around inf 36.4%

   \[\leadsto \color{blue}{x} \]
9. 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 2024111 
(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)))