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

Percentage Accurate: 99.7% → 99.7%

Time: 9.2s

Alternatives: 12

Speedup: 1.0×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.8× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (((x * -6.0) + (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 + (((x * (-6.0d0)) + (6.0d0 * y)) * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in y around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 81.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-18} \lor \neg \left(z \leq -3.1 \cdot 10^{-83}\right) \land \left(z \leq -1.25 \cdot 10^{-177} \lor \neg \left(z \leq 3 \cdot 10^{-36}\right)\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.3e-18)
         (and (not (<= z -3.1e-83)) (or (<= z -1.25e-177) (not (<= z 3e-36)))))
   (* 6.0 (* z (- y x)))
   x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-18) || (!(z <= -3.1e-83) && ((z <= -1.25e-177) || !(z <= 3e-36)))) {
		tmp = 6.0 * (z * (y - x));
	} 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 <= (-1.3d-18)) .or. (.not. (z <= (-3.1d-83))) .and. (z <= (-1.25d-177)) .or. (.not. (z <= 3d-36))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.3e-18) || (!(z <= -3.1e-83) && ((z <= -1.25e-177) || !(z <= 3e-36)))) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.3e-18) or (not (z <= -3.1e-83) and ((z <= -1.25e-177) or not (z <= 3e-36))):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.3e-18) || (!(z <= -3.1e-83) && ((z <= -1.25e-177) || !(z <= 3e-36))))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.3e-18) || (~((z <= -3.1e-83)) && ((z <= -1.25e-177) || ~((z <= 3e-36)))))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.3e-18], And[N[Not[LessEqual[z, -3.1e-83]], $MachinePrecision], Or[LessEqual[z, -1.25e-177], N[Not[LessEqual[z, 3e-36]], $MachinePrecision]]]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.3e-18 or -3.09999999999999992e-83 < z < -1.25e-177 or 3.0000000000000002e-36 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 91.8%

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

   if -1.3e-18 < z < -3.09999999999999992e-83 or -1.25e-177 < z < 3.0000000000000002e-36

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 81.9%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{-18} \lor \neg \left(z \leq -3.1 \cdot 10^{-83}\right) \land \left(z \leq -1.25 \cdot 10^{-177} \lor \neg \left(z \leq 3 \cdot 10^{-36}\right)\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+101} \lor \neg \left(z \leq 4.1 \cdot 10^{+247}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -2.8e-17)
     t_0
     (if (<= z 1.3e-37)
       x
       (if (or (<= z 8.5e+101) (not (<= z 4.1e+247))) (* 6.0 (* y z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.8e-17) {
		tmp = t_0;
	} else if (z <= 1.3e-37) {
		tmp = x;
	} else if ((z <= 8.5e+101) || !(z <= 4.1e+247)) {
		tmp = 6.0 * (y * 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) * (x * z)
    if (z <= (-2.8d-17)) then
        tmp = t_0
    else if (z <= 1.3d-37) then
        tmp = x
    else if ((z <= 8.5d+101) .or. (.not. (z <= 4.1d+247))) then
        tmp = 6.0d0 * (y * 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 * (x * z);
	double tmp;
	if (z <= -2.8e-17) {
		tmp = t_0;
	} else if (z <= 1.3e-37) {
		tmp = x;
	} else if ((z <= 8.5e+101) || !(z <= 4.1e+247)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -2.8e-17:
		tmp = t_0
	elif z <= 1.3e-37:
		tmp = x
	elif (z <= 8.5e+101) or not (z <= 4.1e+247):
		tmp = 6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.8e-17)
		tmp = t_0;
	elseif (z <= 1.3e-37)
		tmp = x;
	elseif ((z <= 8.5e+101) || !(z <= 4.1e+247))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.8e-17)
		tmp = t_0;
	elseif (z <= 1.3e-37)
		tmp = x;
	elseif ((z <= 8.5e+101) || ~((z <= 4.1e+247)))
		tmp = 6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-17], t$95$0, If[LessEqual[z, 1.3e-37], x, If[Or[LessEqual[z, 8.5e+101], N[Not[LessEqual[z, 4.1e+247]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.7999999999999999e-17 or 8.5000000000000001e101 < z < 4.1000000000000002e247

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in y around 0 57.3%

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

   if -2.7999999999999999e-17 < z < 1.2999999999999999e-37

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.4%

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

   if 1.2999999999999999e-37 < z < 8.5000000000000001e101 or 4.1000000000000002e247 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 92.5%

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

   5. Taylor expanded in y around inf 75.0%

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

      1. *-commutative 75.0%

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

   7. Simplified 75.0%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-37}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+101} \lor \neg \left(z \leq 4.1 \cdot 10^{+247}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+102}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+245}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))))
   (if (<= z -2.8e-17)
     t_0
     (if (<= z 2.5e-39)
       x
       (if (<= z 2.15e+102)
         (* 6.0 (* y z))
         (if (<= z 2.15e+245) t_0 (* y (* 6.0 z))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.8e-17) {
		tmp = t_0;
	} else if (z <= 2.5e-39) {
		tmp = x;
	} else if (z <= 2.15e+102) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.15e+245) {
		tmp = t_0;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    if (z <= (-2.8d-17)) then
        tmp = t_0
    else if (z <= 2.5d-39) then
        tmp = x
    else if (z <= 2.15d+102) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 2.15d+245) then
        tmp = t_0
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double tmp;
	if (z <= -2.8e-17) {
		tmp = t_0;
	} else if (z <= 2.5e-39) {
		tmp = x;
	} else if (z <= 2.15e+102) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.15e+245) {
		tmp = t_0;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	tmp = 0
	if z <= -2.8e-17:
		tmp = t_0
	elif z <= 2.5e-39:
		tmp = x
	elif z <= 2.15e+102:
		tmp = 6.0 * (y * z)
	elif z <= 2.15e+245:
		tmp = t_0
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.8e-17)
		tmp = t_0;
	elseif (z <= 2.5e-39)
		tmp = x;
	elseif (z <= 2.15e+102)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 2.15e+245)
		tmp = t_0;
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.8e-17)
		tmp = t_0;
	elseif (z <= 2.5e-39)
		tmp = x;
	elseif (z <= 2.15e+102)
		tmp = 6.0 * (y * z);
	elseif (z <= 2.15e+245)
		tmp = t_0;
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e-17], t$95$0, If[LessEqual[z, 2.5e-39], x, If[LessEqual[z, 2.15e+102], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.15e+245], t$95$0, N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.7999999999999999e-17 or 2.15e102 < z < 2.1499999999999999e245

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 98.7%

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

   5. Taylor expanded in y around 0 57.3%

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

   if -2.7999999999999999e-17 < z < 2.4999999999999999e-39

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.4%

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

   if 2.4999999999999999e-39 < z < 2.15e102

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.5%

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

   4. Taylor expanded in z around inf 88.9%

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

   5. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

   7. Simplified 80.7%

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

   if 2.1499999999999999e245 < 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 inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in y around inf 62.6%

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

      1. fma-define 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in z around inf 63.7%

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

       1. *-commutative 63.7%

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

   11. Simplified 63.7%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+102}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{+245}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+101}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+244}:\\ \;\;\;\;\left(x \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.8e-17)
   (* -6.0 (* x z))
   (if (<= z 1.12e-38)
     x
     (if (<= z 4.8e+101)
       (* 6.0 (* y z))
       (if (<= z 3.2e+244) (* (* x -6.0) z) (* y (* 6.0 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e-17) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.12e-38) {
		tmp = x;
	} else if (z <= 4.8e+101) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3.2e+244) {
		tmp = (x * -6.0) * z;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.8d-17)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 1.12d-38) then
        tmp = x
    else if (z <= 4.8d+101) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 3.2d+244) then
        tmp = (x * (-6.0d0)) * z
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.8e-17) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.12e-38) {
		tmp = x;
	} else if (z <= 4.8e+101) {
		tmp = 6.0 * (y * z);
	} else if (z <= 3.2e+244) {
		tmp = (x * -6.0) * z;
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.8e-17:
		tmp = -6.0 * (x * z)
	elif z <= 1.12e-38:
		tmp = x
	elif z <= 4.8e+101:
		tmp = 6.0 * (y * z)
	elif z <= 3.2e+244:
		tmp = (x * -6.0) * z
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.8e-17)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 1.12e-38)
		tmp = x;
	elseif (z <= 4.8e+101)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 3.2e+244)
		tmp = Float64(Float64(x * -6.0) * z);
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.8e-17)
		tmp = -6.0 * (x * z);
	elseif (z <= 1.12e-38)
		tmp = x;
	elseif (z <= 4.8e+101)
		tmp = 6.0 * (y * z);
	elseif (z <= 3.2e+244)
		tmp = (x * -6.0) * z;
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.8e-17], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.12e-38], x, If[LessEqual[z, 4.8e+101], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+244], N[(N[(x * -6.0), $MachinePrecision] * z), $MachinePrecision], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.7999999999999999e-17

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 98.4%

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

   5. Taylor expanded in y around 0 56.5%

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

   if -2.7999999999999999e-17 < z < 1.1200000000000001e-38

   1. Initial program 99.9%

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

   3. Taylor expanded in z around 0 73.4%

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

   if 1.1200000000000001e-38 < z < 4.79999999999999977e101

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.5%

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

   4. Taylor expanded in z around inf 88.9%

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

   5. Taylor expanded in y around inf 80.7%

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

      1. *-commutative 80.7%

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

   7. Simplified 80.7%

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

   if 4.79999999999999977e101 < z < 3.2000000000000002e244

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 99.6%

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

   5. Taylor expanded in y around 0 59.3%

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

      1. associate-*r* 59.4%

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

   7. Simplified 59.4%

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

   if 3.2000000000000002e244 < 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 inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in y around inf 62.6%

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

      1. fma-define 62.6%

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

   8. Simplified 62.6%

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

   9. Taylor expanded in z around inf 63.7%

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

       1. *-commutative 63.7%

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

   11. Simplified 63.7%

       \[\leadsto y \cdot \color{blue}{\left(z \cdot 6\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.12 \cdot 10^{-38}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+101}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+244}:\\ \;\;\;\;\left(x \cdot -6\right) \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+45} \lor \neg \left(x \leq 1.3 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(-6 \cdot z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.9e+45) (not (<= x 1.3e+28)))
   (* x (+ (* -6.0 z) 1.0))
   (* 6.0 (* z (- y x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+45) || !(x <= 1.3e+28)) {
		tmp = x * ((-6.0 * z) + 1.0);
	} else {
		tmp = 6.0 * (z * (y - 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 ((x <= (-1.9d+45)) .or. (.not. (x <= 1.3d+28))) then
        tmp = x * (((-6.0d0) * z) + 1.0d0)
    else
        tmp = 6.0d0 * (z * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.9e+45) || !(x <= 1.3e+28)) {
		tmp = x * ((-6.0 * z) + 1.0);
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.9e+45) or not (x <= 1.3e+28):
		tmp = x * ((-6.0 * z) + 1.0)
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.9e+45) || !(x <= 1.3e+28))
		tmp = Float64(x * Float64(Float64(-6.0 * z) + 1.0));
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.9e+45) || ~((x <= 1.3e+28)))
		tmp = x * ((-6.0 * z) + 1.0);
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.9e+45], N[Not[LessEqual[x, 1.3e+28]], $MachinePrecision]], N[(x * N[(N[(-6.0 * z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.9000000000000001e45 or 1.3000000000000001e28 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 93.1%

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

      1. +-commutative 93.1%

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

   5. Simplified 93.1%

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

   if -1.9000000000000001e45 < x < 1.3000000000000001e28

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 80.1%

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

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.9 \cdot 10^{+45} \lor \neg \left(x \leq 1.3 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot \left(-6 \cdot z + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 80.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+45}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+32}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-6 \cdot z + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.95e+45)
   (+ x (* -6.0 (* x z)))
   (if (<= x 1.16e+32) (* 6.0 (* z (- y x))) (* x (+ (* -6.0 z) 1.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e+45) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 1.16e+32) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x * ((-6.0 * z) + 1.0);
	}
	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 (x <= (-1.95d+45)) then
        tmp = x + ((-6.0d0) * (x * z))
    else if (x <= 1.16d+32) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x * (((-6.0d0) * z) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.95e+45) {
		tmp = x + (-6.0 * (x * z));
	} else if (x <= 1.16e+32) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x * ((-6.0 * z) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.95e+45:
		tmp = x + (-6.0 * (x * z))
	elif x <= 1.16e+32:
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x * ((-6.0 * z) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.95e+45)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	elseif (x <= 1.16e+32)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x * Float64(Float64(-6.0 * z) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.95e+45)
		tmp = x + (-6.0 * (x * z));
	elseif (x <= 1.16e+32)
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x * ((-6.0 * z) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.95e+45], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e+32], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(-6.0 * z), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.95e45

   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 93.6%

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

   if -1.95e45 < x < 1.16e32

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 80.1%

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

   if 1.16e32 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 92.7%

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

      1. +-commutative 92.7%

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

   5. Simplified 92.7%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 85.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.95 \cdot 10^{+45}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+32}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-6 \cdot z + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-5}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.17)
   (* 6.0 (* z (- y x)))
   (if (<= z 5.8e-5) (+ x (* 6.0 (* y z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.17) {
		tmp = 6.0 * (z * (y - x));
	} else if (z <= 5.8e-5) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.17d0)) then
        tmp = 6.0d0 * (z * (y - x))
    else if (z <= 5.8d-5) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = (y - x) * (6.0d0 * 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 = 6.0 * (z * (y - x));
	} else if (z <= 5.8e-5) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.17:
		tmp = 6.0 * (z * (y - x))
	elif z <= 5.8e-5:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.17)
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 5.8e-5)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.17)
		tmp = 6.0 * (z * (y - x));
	elseif (z <= 5.8e-5)
		tmp = x + (6.0 * (y * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e-5], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.170000000000000012

   1. Initial program 99.6%

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

   3. Taylor expanded in z around 0 99.7%

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

   4. Taylor expanded in z around inf 98.4%

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

   if -0.170000000000000012 < z < 5.8e-5

   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 99.4%

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

      1. *-commutative 99.4%

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

   5. Simplified 99.4%

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

   if 5.8e-5 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 99.6%

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

   5. Taylor expanded in y around 0 96.6%

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

      1. metadata-eval 96.6%

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

      2. associate-*r* 96.6%

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

      3. mul-1-neg 96.6%

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

      4. distribute-lft-neg-out 96.6%

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

      5. *-commutative 96.6%

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

      6. associate-*r* 96.6%

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

      7. *-commutative 96.6%

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

      8. associate-*r* 96.7%

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

      9. *-commutative 96.7%

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

      10. associate-*r* 96.6%

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

      11. distribute-rgt-out 99.6%

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

      12. *-commutative 99.6%

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

      13. +-commutative 99.6%

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

      14. sub-neg 99.6%

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

   7. Simplified 99.6%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-5}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 6800\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.8e-17) (not (<= z 6800.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.8e-17) || !(z <= 6800.0)) {
		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 <= (-2.8d-17)) .or. (.not. (z <= 6800.0d0))) 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 <= -2.8e-17) || !(z <= 6800.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.8e-17) or not (z <= 6800.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.8e-17) || !(z <= 6800.0))
		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 <= -2.8e-17) || ~((z <= 6800.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.8e-17], N[Not[LessEqual[z, 6800.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.7999999999999999e-17 or 6800 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in z around 0 99.6%

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

   4. Taylor expanded in z around inf 99.0%

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

   5. Taylor expanded in y around 0 48.2%

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

   if -2.7999999999999999e-17 < z < 6800

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 66.0%

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

4. Final simplification 57.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{-17} \lor \neg \left(z \leq 6800\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (6.0 * (z * (y - 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 + (6.0d0 * (z * (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0 99.7%

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

4. Final simplification 99.7%

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

Alternative 11: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + (z * (6.0 * (y - 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 + (z * (6.0d0 * (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

Alternative 12: 36.3% 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. Add Preprocessing

3. Taylor expanded in z around 0 34.9%

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

4. Final simplification 34.9%

   \[\leadsto x \]
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 2024067 
(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)))