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

Percentage Accurate: 99.6% → 99.8%

Time: 8.5s

Alternatives: 13

Speedup: 1.0×

• 20.9% 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: 99.6% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.5e-33)
   (* z (* y 6.0))
   (if (<= z 0.17) x (if (<= z 2.3e+114) (* -6.0 (* x z)) (* 6.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e-33) {
		tmp = z * (y * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 2.3e+114) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = 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 (z <= (-2.5d-33)) then
        tmp = z * (y * 6.0d0)
    else if (z <= 0.17d0) then
        tmp = x
    else if (z <= 2.3d+114) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.5e-33) {
		tmp = z * (y * 6.0);
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 2.3e+114) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.5e-33:
		tmp = z * (y * 6.0)
	elif z <= 0.17:
		tmp = x
	elif z <= 2.3e+114:
		tmp = -6.0 * (x * z)
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.5e-33)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 2.3e+114)
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.5e-33)
		tmp = z * (y * 6.0);
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 2.3e+114)
		tmp = -6.0 * (x * z);
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.5e-33], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, If[LessEqual[z, 2.3e+114], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.50000000000000014e-33

   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 93.7%

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

   4. Taylor expanded in z around 0 85.1%

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

   5. Taylor expanded in z around inf 82.7%

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

   6. Taylor expanded in y around inf 56.7%

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

      1. associate-*r* 56.8%

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

      2. *-commutative 56.8%

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

   8. Simplified 56.8%

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

   if -2.50000000000000014e-33 < z < 0.170000000000000012

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 77.4%

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

   if 0.170000000000000012 < z < 2.3e114

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 71.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 71.8%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 64.8%

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

   7. Taylor expanded in x around 0 64.8%

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

   if 2.3e114 < z

   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 inf 95.0%

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

   4. Taylor expanded in z around 0 90.2%

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

   5. Taylor expanded in z around inf 90.2%

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

   6. Taylor expanded in y around inf 75.8%

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

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{-33}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{+114}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-35}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+114}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -4.8e-35)
     t_0
     (if (<= z 0.17) x (if (<= z 1.8e+114) (* -6.0 (* x z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -4.8e-35) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 1.8e+114) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = t_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 = 6.0d0 * (y * z)
    if (z <= (-4.8d-35)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else if (z <= 1.8d+114) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -4.8e-35) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if (z <= 1.8e+114) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -4.8e-35:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	elif z <= 1.8e+114:
		tmp = -6.0 * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.8e-35)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 1.8e+114)
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.8e-35)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif (z <= 1.8e+114)
		tmp = -6.0 * (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-35], t$95$0, If[LessEqual[z, 0.17], x, If[LessEqual[z, 1.8e+114], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000003e-35 or 1.8e114 < 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 inf 94.1%

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

   4. Taylor expanded in z around 0 86.9%

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

   5. Taylor expanded in z around inf 85.2%

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

   6. Taylor expanded in y around inf 63.2%

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

   if -4.8000000000000003e-35 < z < 0.170000000000000012

   1. Initial program 99.2%

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

   3. Taylor expanded in z around 0 77.4%

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

   if 0.170000000000000012 < z < 1.8e114

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 71.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 71.8%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 71.8%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 64.8%

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

   7. Taylor expanded in x around 0 64.8%

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

Alternative 4: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-77} \lor \neg \left(y \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.9e-77) (not (<= y 4.5e-66)))
   (+ x (* y (* 6.0 z)))
   (+ x (* z (* x -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e-77) || !(y <= 4.5e-66)) {
		tmp = x + (y * (6.0 * 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 <= (-3.9d-77)) .or. (.not. (y <= 4.5d-66))) then
        tmp = x + (y * (6.0d0 * 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 <= -3.9e-77) || !(y <= 4.5e-66)) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = x + (z * (x * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.9e-77) or not (y <= 4.5e-66):
		tmp = x + (y * (6.0 * z))
	else:
		tmp = x + (z * (x * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.9e-77) || !(y <= 4.5e-66))
		tmp = Float64(x + Float64(y * Float64(6.0 * 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 <= -3.9e-77) || ~((y <= 4.5e-66)))
		tmp = x + (y * (6.0 * z));
	else
		tmp = x + (z * (x * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.9e-77], N[Not[LessEqual[y, 4.5e-66]], $MachinePrecision]], N[(x + N[(y * N[(6.0 * 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 < -3.89999999999999979e-77 or 4.4999999999999998e-66 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-*r* 92.2%

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

   5. Simplified 92.2%

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

   if -3.89999999999999979e-77 < y < 4.4999999999999998e-66

   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 87.0%

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

      1. associate-*r* 87.0%

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

   5. Simplified 87.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{-77} \lor \neg \left(y \leq 4.5 \cdot 10^{-66}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-85} \lor \neg \left(y \leq 5 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.4e-85) (not (<= y 5e-65)))
   (+ x (* y (* 6.0 z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.4e-85) || !(y <= 5e-65)) {
		tmp = x + (y * (6.0 * 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 <= (-7.4d-85)) .or. (.not. (y <= 5d-65))) then
        tmp = x + (y * (6.0d0 * 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 <= -7.4e-85) || !(y <= 5e-65)) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.4e-85) or not (y <= 5e-65):
		tmp = x + (y * (6.0 * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.4e-85) || !(y <= 5e-65))
		tmp = Float64(x + Float64(y * Float64(6.0 * 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 <= -7.4e-85) || ~((y <= 5e-65)))
		tmp = x + (y * (6.0 * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.4e-85], N[Not[LessEqual[y, 5e-65]], $MachinePrecision]], N[(x + N[(y * N[(6.0 * 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 < -7.39999999999999966e-85 or 4.99999999999999983e-65 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 92.2%

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

      1. *-commutative 92.2%

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

      2. associate-*r* 92.2%

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

   5. Simplified 92.2%

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

   if -7.39999999999999966e-85 < y < 4.99999999999999983e-65

   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 87.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-85} \lor \neg \left(y \leq 5 \cdot 10^{-65}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-81} \lor \neg \left(y \leq 6.6 \cdot 10^{-66}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.75e-81) (not (<= y 6.6e-66)))
   (+ x (* 6.0 (* y z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.75e-81) || !(y <= 6.6e-66)) {
		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 <= (-2.75d-81)) .or. (.not. (y <= 6.6d-66))) 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 <= -2.75e-81) || !(y <= 6.6e-66)) {
		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 <= -2.75e-81) or not (y <= 6.6e-66):
		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 <= -2.75e-81) || !(y <= 6.6e-66))
		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 <= -2.75e-81) || ~((y <= 6.6e-66)))
		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, -2.75e-81], N[Not[LessEqual[y, 6.6e-66]], $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 < -2.75000000000000013e-81 or 6.5999999999999998e-66 < y

   1. Initial program 99.3%

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

   3. Taylor expanded in y around inf 92.2%

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

      1. *-commutative 92.2%

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

   5. Simplified 92.2%

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

   if -2.75000000000000013e-81 < y < 6.5999999999999998e-66

   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 87.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.75 \cdot 10^{-81} \lor \neg \left(y \leq 6.6 \cdot 10^{-66}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e-78)
   (+ x (* y (* 6.0 z)))
   (if (<= y 8.2e-66) (+ x (* z (* x -6.0))) (+ x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e-78) {
		tmp = x + (y * (6.0 * z));
	} else if (y <= 8.2e-66) {
		tmp = x + (z * (x * -6.0));
	} 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) :: tmp
    if (y <= (-6.5d-78)) then
        tmp = x + (y * (6.0d0 * z))
    else if (y <= 8.2d-66) then
        tmp = x + (z * (x * (-6.0d0)))
    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 tmp;
	if (y <= -6.5e-78) {
		tmp = x + (y * (6.0 * z));
	} else if (y <= 8.2e-66) {
		tmp = x + (z * (x * -6.0));
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -6.5e-78:
		tmp = x + (y * (6.0 * z))
	elif y <= 8.2e-66:
		tmp = x + (z * (x * -6.0))
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e-78)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	elseif (y <= 8.2e-66)
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -6.5e-78)
		tmp = x + (y * (6.0 * z));
	elseif (y <= 8.2e-66)
		tmp = x + (z * (x * -6.0));
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -6.5e-78], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.2e-66], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.5000000000000003e-78

   1. Initial program 98.8%

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

   3. Taylor expanded in y around inf 90.8%

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

      1. *-commutative 90.8%

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

      2. associate-*r* 90.9%

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

   5. Simplified 90.9%

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

   if -6.5000000000000003e-78 < y < 8.19999999999999996e-66

   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 87.0%

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

      1. associate-*r* 87.0%

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

   5. Simplified 87.0%

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

   if 8.19999999999999996e-66 < 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 93.9%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{-78}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-66}:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-30}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e+161)
   (* y (* 6.0 z))
   (if (<= y 3.05e-30) (+ x (* -6.0 (* x z))) (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+161) {
		tmp = y * (6.0 * z);
	} else if (y <= 3.05e-30) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = 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) :: tmp
    if (y <= (-1.35d+161)) then
        tmp = y * (6.0d0 * z)
    else if (y <= 3.05d-30) then
        tmp = x + ((-6.0d0) * (x * z))
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e+161) {
		tmp = y * (6.0 * z);
	} else if (y <= 3.05e-30) {
		tmp = x + (-6.0 * (x * z));
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e+161:
		tmp = y * (6.0 * z)
	elif y <= 3.05e-30:
		tmp = x + (-6.0 * (x * z))
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e+161)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (y <= 3.05e-30)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.35e+161)
		tmp = y * (6.0 * z);
	elseif (y <= 3.05e-30)
		tmp = x + (-6.0 * (x * z));
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e+161], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.05e-30], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3499999999999999e161

   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 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 91.8%

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

   6. Taylor expanded in y around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*r* 91.8%

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

   8. Simplified 91.8%

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

   if -1.3499999999999999e161 < y < 3.0499999999999999e-30

   1. Initial program 99.3%

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

   3. Taylor expanded in y around 0 79.8%

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

   if 3.0499999999999999e-30 < 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 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 75.2%

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

   6. Taylor expanded in y around inf 70.2%

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

      1. associate-*r* 70.4%

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

      2. *-commutative 70.4%

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

   8. Simplified 70.4%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 3.05 \cdot 10^{-30}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -8e+160)
   (* y (* 6.0 z))
   (if (<= y 1.5e-46) (* x (+ (* z -6.0) 1.0)) (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+160) {
		tmp = y * (6.0 * z);
	} else if (y <= 1.5e-46) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = 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) :: tmp
    if (y <= (-8d+160)) then
        tmp = y * (6.0d0 * z)
    else if (y <= 1.5d-46) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8e+160) {
		tmp = y * (6.0 * z);
	} else if (y <= 1.5e-46) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -8e+160:
		tmp = y * (6.0 * z)
	elif y <= 1.5e-46:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -8e+160)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (y <= 1.5e-46)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8e+160)
		tmp = y * (6.0 * z);
	elseif (y <= 1.5e-46)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -8e+160], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e-46], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.00000000000000005e160

   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 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 91.8%

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

   6. Taylor expanded in y around inf 91.7%

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

      1. *-commutative 91.7%

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

      2. associate-*r* 91.8%

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

   8. Simplified 91.8%

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

   if -8.00000000000000005e160 < y < 1.49999999999999994e-46

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf 80.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 80.2%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 80.2%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   if 1.49999999999999994e-46 < 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 99.8%

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

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 76.0%

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

   6. Taylor expanded in y around inf 69.6%

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

      1. associate-*r* 69.7%

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

      2. *-commutative 69.7%

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

   8. Simplified 69.7%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+160}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{-46}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 59.6% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.17)) {
		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 <= 0.17d0))) 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 <= 0.17)) {
		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 <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 0.17))
		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 <= 0.17)))
		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, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in x around inf 50.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 50.9%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 50.9%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   6. Taylor expanded in z around inf 49.8%

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

   7. Taylor expanded in x around 0 49.9%

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

   if -0.170000000000000012 < z < 0.170000000000000012

   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 74.6%

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

4. Final simplification 62.0%

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

Alternative 11: 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. Add Preprocessing

Alternative 12: 99.6% 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 13: 35.7% 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 99.5%

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

3. Taylor expanded in z around 0 38.4%

   \[\leadsto \color{blue}{x} \]
4. 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 2024101 
(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)))