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

Percentage Accurate: 99.8% → 99.8%

Time: 8.6s

Alternatives: 13

Speedup: 1.0×

• 21.5% 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: 99.8% 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

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

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 99.5%

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

3. Taylor expanded in z around 0 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 59.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-133}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+109} \lor \neg \left(z \leq 5.6 \cdot 10^{+228}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))))
   (if (<= z -2.7e-12)
     t_0
     (if (<= z 5.1e-169)
       x
       (if (<= z 5.7e-133)
         t_0
         (if (<= z 1860.0)
           x
           (if (or (<= z 2.95e+109) (not (<= z 5.6e+228)))
             (* -6.0 (* x z))
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -2.7e-12) {
		tmp = t_0;
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.7e-133) {
		tmp = t_0;
	} else if (z <= 1860.0) {
		tmp = x;
	} else if ((z <= 2.95e+109) || !(z <= 5.6e+228)) {
		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 * (z * y)
    if (z <= (-2.7d-12)) then
        tmp = t_0
    else if (z <= 5.1d-169) then
        tmp = x
    else if (z <= 5.7d-133) then
        tmp = t_0
    else if (z <= 1860.0d0) then
        tmp = x
    else if ((z <= 2.95d+109) .or. (.not. (z <= 5.6d+228))) 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 * (z * y);
	double tmp;
	if (z <= -2.7e-12) {
		tmp = t_0;
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.7e-133) {
		tmp = t_0;
	} else if (z <= 1860.0) {
		tmp = x;
	} else if ((z <= 2.95e+109) || !(z <= 5.6e+228)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	tmp = 0
	if z <= -2.7e-12:
		tmp = t_0
	elif z <= 5.1e-169:
		tmp = x
	elif z <= 5.7e-133:
		tmp = t_0
	elif z <= 1860.0:
		tmp = x
	elif (z <= 2.95e+109) or not (z <= 5.6e+228):
		tmp = -6.0 * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -2.7e-12)
		tmp = t_0;
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.7e-133)
		tmp = t_0;
	elseif (z <= 1860.0)
		tmp = x;
	elseif ((z <= 2.95e+109) || !(z <= 5.6e+228))
		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 * (z * y);
	tmp = 0.0;
	if (z <= -2.7e-12)
		tmp = t_0;
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.7e-133)
		tmp = t_0;
	elseif (z <= 1860.0)
		tmp = x;
	elseif ((z <= 2.95e+109) || ~((z <= 5.6e+228)))
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e-12], t$95$0, If[LessEqual[z, 5.1e-169], x, If[LessEqual[z, 5.7e-133], t$95$0, If[LessEqual[z, 1860.0], x, If[Or[LessEqual[z, 2.95e+109], N[Not[LessEqual[z, 5.6e+228]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.6999999999999998e-12 or 5.09999999999999997e-169 < z < 5.6999999999999997e-133 or 2.9499999999999999e109 < z < 5.5999999999999998e228

   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. Taylor expanded in z around inf 96.6%

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

   5. Taylor expanded in y around inf 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -2.6999999999999998e-12 < z < 5.09999999999999997e-169 or 5.6999999999999997e-133 < z < 1860

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 1860 < z < 2.9499999999999999e109 or 5.5999999999999998e228 < z

   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 99.7%

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

   4. Taylor expanded in z around inf 98.1%

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

   5. Taylor expanded in y around 0 70.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{-12}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-133}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.95 \cdot 10^{+109} \lor \neg \left(z \leq 5.6 \cdot 10^{+228}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+107} \lor \neg \left(z \leq 2.45 \cdot 10^{+229}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))))
   (if (<= z -1.45e-13)
     (* y (* 6.0 z))
     (if (<= z 5.1e-169)
       x
       (if (<= z 5.5e-131)
         t_0
         (if (<= z 1860.0)
           x
           (if (or (<= z 4.2e+107) (not (<= z 2.45e+229)))
             (* -6.0 (* x z))
             t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -1.45e-13) {
		tmp = y * (6.0 * z);
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.5e-131) {
		tmp = t_0;
	} else if (z <= 1860.0) {
		tmp = x;
	} else if ((z <= 4.2e+107) || !(z <= 2.45e+229)) {
		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 * (z * y)
    if (z <= (-1.45d-13)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 5.1d-169) then
        tmp = x
    else if (z <= 5.5d-131) then
        tmp = t_0
    else if (z <= 1860.0d0) then
        tmp = x
    else if ((z <= 4.2d+107) .or. (.not. (z <= 2.45d+229))) 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 * (z * y);
	double tmp;
	if (z <= -1.45e-13) {
		tmp = y * (6.0 * z);
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.5e-131) {
		tmp = t_0;
	} else if (z <= 1860.0) {
		tmp = x;
	} else if ((z <= 4.2e+107) || !(z <= 2.45e+229)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	tmp = 0
	if z <= -1.45e-13:
		tmp = y * (6.0 * z)
	elif z <= 5.1e-169:
		tmp = x
	elif z <= 5.5e-131:
		tmp = t_0
	elif z <= 1860.0:
		tmp = x
	elif (z <= 4.2e+107) or not (z <= 2.45e+229):
		tmp = -6.0 * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -1.45e-13)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.5e-131)
		tmp = t_0;
	elseif (z <= 1860.0)
		tmp = x;
	elseif ((z <= 4.2e+107) || !(z <= 2.45e+229))
		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 * (z * y);
	tmp = 0.0;
	if (z <= -1.45e-13)
		tmp = y * (6.0 * z);
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.5e-131)
		tmp = t_0;
	elseif (z <= 1860.0)
		tmp = x;
	elseif ((z <= 4.2e+107) || ~((z <= 2.45e+229)))
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.45e-13], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-169], x, If[LessEqual[z, 5.5e-131], t$95$0, If[LessEqual[z, 1860.0], x, If[Or[LessEqual[z, 4.2e+107], N[Not[LessEqual[z, 2.45e+229]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4499999999999999e-13

   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 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*r* 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in x around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. associate-/l* 43.9%

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

   8. Simplified 43.9%

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

   9. Taylor expanded in x around 0 66.9%

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

       1. *-commutative 66.9%

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

       2. associate-*l* 66.9%

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

       3. *-commutative 66.9%

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

   11. Simplified 66.9%

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

   if -1.4499999999999999e-13 < z < 5.09999999999999997e-169 or 5.4999999999999997e-131 < z < 1860

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 5.09999999999999997e-169 < z < 5.4999999999999997e-131 or 4.1999999999999999e107 < z < 2.45000000000000017e229

   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 99.8%

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

   4. Taylor expanded in z around inf 92.1%

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

   5. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 1860 < z < 4.1999999999999999e107 or 2.45000000000000017e229 < z

   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 99.7%

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

   4. Taylor expanded in z around inf 98.1%

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

   5. Taylor expanded in y around 0 70.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.45 \cdot 10^{-13}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+107} \lor \neg \left(z \leq 2.45 \cdot 10^{+229}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+229}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z y))))
   (if (<= z -3.8e-15)
     (* y (* 6.0 z))
     (if (<= z 5.1e-169)
       x
       (if (<= z 5.5e-135)
         t_0
         (if (<= z 1860.0)
           x
           (if (<= z 1.5e+108)
             (* z (* x -6.0))
             (if (<= z 1.75e+229) t_0 (* -6.0 (* x z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -3.8e-15) {
		tmp = y * (6.0 * z);
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.5e-135) {
		tmp = t_0;
	} else if (z <= 1860.0) {
		tmp = x;
	} else if (z <= 1.5e+108) {
		tmp = z * (x * -6.0);
	} else if (z <= 1.75e+229) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (z * y)
    if (z <= (-3.8d-15)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 5.1d-169) then
        tmp = x
    else if (z <= 5.5d-135) then
        tmp = t_0
    else if (z <= 1860.0d0) then
        tmp = x
    else if (z <= 1.5d+108) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 1.75d+229) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * y);
	double tmp;
	if (z <= -3.8e-15) {
		tmp = y * (6.0 * z);
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.5e-135) {
		tmp = t_0;
	} else if (z <= 1860.0) {
		tmp = x;
	} else if (z <= 1.5e+108) {
		tmp = z * (x * -6.0);
	} else if (z <= 1.75e+229) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * y)
	tmp = 0
	if z <= -3.8e-15:
		tmp = y * (6.0 * z)
	elif z <= 5.1e-169:
		tmp = x
	elif z <= 5.5e-135:
		tmp = t_0
	elif z <= 1860.0:
		tmp = x
	elif z <= 1.5e+108:
		tmp = z * (x * -6.0)
	elif z <= 1.75e+229:
		tmp = t_0
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -3.8e-15)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.5e-135)
		tmp = t_0;
	elseif (z <= 1860.0)
		tmp = x;
	elseif (z <= 1.5e+108)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 1.75e+229)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * y);
	tmp = 0.0;
	if (z <= -3.8e-15)
		tmp = y * (6.0 * z);
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.5e-135)
		tmp = t_0;
	elseif (z <= 1860.0)
		tmp = x;
	elseif (z <= 1.5e+108)
		tmp = z * (x * -6.0);
	elseif (z <= 1.75e+229)
		tmp = t_0;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.8e-15], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-169], x, If[LessEqual[z, 5.5e-135], t$95$0, If[LessEqual[z, 1860.0], x, If[LessEqual[z, 1.5e+108], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.75e+229], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.8000000000000002e-15

   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 67.8%

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

      1. *-commutative 67.8%

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

      2. associate-*r* 67.8%

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

   5. Simplified 67.8%

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

   6. Taylor expanded in x around inf 49.7%

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

      1. +-commutative 49.7%

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

      2. associate-/l* 43.9%

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

   8. Simplified 43.9%

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

   9. Taylor expanded in x around 0 66.9%

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

       1. *-commutative 66.9%

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

       2. associate-*l* 66.9%

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

       3. *-commutative 66.9%

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

   11. Simplified 66.9%

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

   if -3.8000000000000002e-15 < z < 5.09999999999999997e-169 or 5.4999999999999999e-135 < z < 1860

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 5.09999999999999997e-169 < z < 5.4999999999999999e-135 or 1.49999999999999992e108 < z < 1.7500000000000001e229

   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 99.8%

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

   4. Taylor expanded in z around inf 92.1%

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

   5. Taylor expanded in y around inf 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 1860 < z < 1.49999999999999992e108

   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 99.6%

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

   4. Taylor expanded in z around inf 96.6%

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

   5. Taylor expanded in y around 0 67.1%

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

      1. associate-*r* 67.1%

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

      2. *-commutative 67.1%

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

      3. *-commutative 67.1%

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

      4. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if 1.7500000000000001e229 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in y around 0 75.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+108}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+229}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(6 \cdot y\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+228}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* 6.0 y))))
   (if (<= z -1.12e-13)
     t_0
     (if (<= z 5.1e-169)
       x
       (if (<= z 5.5e-135)
         (* 6.0 (* z y))
         (if (<= z 1860.0)
           x
           (if (<= z 3.1e+107)
             (* z (* x -6.0))
             (if (<= z 6.6e+228) t_0 (* -6.0 (* x z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (z <= -1.12e-13) {
		tmp = t_0;
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 1860.0) {
		tmp = x;
	} else if (z <= 3.1e+107) {
		tmp = z * (x * -6.0);
	} else if (z <= 6.6e+228) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (6.0d0 * y)
    if (z <= (-1.12d-13)) then
        tmp = t_0
    else if (z <= 5.1d-169) then
        tmp = x
    else if (z <= 5.5d-135) then
        tmp = 6.0d0 * (z * y)
    else if (z <= 1860.0d0) then
        tmp = x
    else if (z <= 3.1d+107) then
        tmp = z * (x * (-6.0d0))
    else if (z <= 6.6d+228) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (6.0 * y);
	double tmp;
	if (z <= -1.12e-13) {
		tmp = t_0;
	} else if (z <= 5.1e-169) {
		tmp = x;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 1860.0) {
		tmp = x;
	} else if (z <= 3.1e+107) {
		tmp = z * (x * -6.0);
	} else if (z <= 6.6e+228) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (6.0 * y)
	tmp = 0
	if z <= -1.12e-13:
		tmp = t_0
	elif z <= 5.1e-169:
		tmp = x
	elif z <= 5.5e-135:
		tmp = 6.0 * (z * y)
	elif z <= 1860.0:
		tmp = x
	elif z <= 3.1e+107:
		tmp = z * (x * -6.0)
	elif z <= 6.6e+228:
		tmp = t_0
	else:
		tmp = -6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * y))
	tmp = 0.0
	if (z <= -1.12e-13)
		tmp = t_0;
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.5e-135)
		tmp = Float64(6.0 * Float64(z * y));
	elseif (z <= 1860.0)
		tmp = x;
	elseif (z <= 3.1e+107)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= 6.6e+228)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (6.0 * y);
	tmp = 0.0;
	if (z <= -1.12e-13)
		tmp = t_0;
	elseif (z <= 5.1e-169)
		tmp = x;
	elseif (z <= 5.5e-135)
		tmp = 6.0 * (z * y);
	elseif (z <= 1860.0)
		tmp = x;
	elseif (z <= 3.1e+107)
		tmp = z * (x * -6.0);
	elseif (z <= 6.6e+228)
		tmp = t_0;
	else
		tmp = -6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e-13], t$95$0, If[LessEqual[z, 5.1e-169], x, If[LessEqual[z, 5.5e-135], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1860.0], x, If[LessEqual[z, 3.1e+107], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6.6e+228], t$95$0, N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.12e-13 or 3.10000000000000026e107 < z < 6.60000000000000011e228

   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 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*r* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in x around inf 49.2%

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

      1. +-commutative 49.2%

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

      2. associate-/l* 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in x around 0 66.4%

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

       1. associate-*r* 66.4%

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

       2. *-commutative 66.4%

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

   11. Simplified 66.4%

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

   if -1.12e-13 < z < 5.09999999999999997e-169 or 5.4999999999999999e-135 < z < 1860

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 72.3%

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

   if 5.09999999999999997e-169 < z < 5.4999999999999999e-135

   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 72.5%

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

   5. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

   if 1860 < z < 3.10000000000000026e107

   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 99.6%

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

   4. Taylor expanded in z around inf 96.6%

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

   5. Taylor expanded in y around 0 67.1%

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

      1. associate-*r* 67.1%

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

      2. *-commutative 67.1%

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

      3. *-commutative 67.1%

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

      4. *-commutative 67.1%

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

   7. Simplified 67.1%

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

   if 6.60000000000000011e228 < z

   1. Initial program 100.0%

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

   3. Taylor expanded in z around 0 99.9%

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

   4. Taylor expanded in z around inf 99.9%

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

   5. Taylor expanded in y around 0 75.2%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{-13}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+228}:\\ \;\;\;\;z \cdot \left(6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{-13}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* z (- y x)))))
   (if (<= z -3e-13)
     t_0
     (if (<= z 4.7e-169)
       x
       (if (<= z 5.5e-135) (* 6.0 (* z y)) (if (<= z 8.2e-19) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (z * (y - x));
	double tmp;
	if (z <= -3e-13) {
		tmp = t_0;
	} else if (z <= 4.7e-169) {
		tmp = x;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 8.2e-19) {
		tmp = x;
	} 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 * (z * (y - x))
    if (z <= (-3d-13)) then
        tmp = t_0
    else if (z <= 4.7d-169) then
        tmp = x
    else if (z <= 5.5d-135) then
        tmp = 6.0d0 * (z * y)
    else if (z <= 8.2d-19) then
        tmp = x
    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 * (z * (y - x));
	double tmp;
	if (z <= -3e-13) {
		tmp = t_0;
	} else if (z <= 4.7e-169) {
		tmp = x;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 8.2e-19) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (z * (y - x))
	tmp = 0
	if z <= -3e-13:
		tmp = t_0
	elif z <= 4.7e-169:
		tmp = x
	elif z <= 5.5e-135:
		tmp = 6.0 * (z * y)
	elif z <= 8.2e-19:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -3e-13)
		tmp = t_0;
	elseif (z <= 4.7e-169)
		tmp = x;
	elseif (z <= 5.5e-135)
		tmp = Float64(6.0 * Float64(z * y));
	elseif (z <= 8.2e-19)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -3e-13)
		tmp = t_0;
	elseif (z <= 4.7e-169)
		tmp = x;
	elseif (z <= 5.5e-135)
		tmp = 6.0 * (z * y);
	elseif (z <= 8.2e-19)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e-13], t$95$0, If[LessEqual[z, 4.7e-169], x, If[LessEqual[z, 5.5e-135], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 8.2e-19], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.99999999999999984e-13 or 8.1999999999999997e-19 < 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 99.7%

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

   4. Taylor expanded in z around inf 97.7%

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

   if -2.99999999999999984e-13 < z < 4.6999999999999999e-169 or 5.4999999999999999e-135 < z < 8.1999999999999997e-19

   1. Initial program 99.1%

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

   3. Taylor expanded in z around 0 75.0%

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

   if 4.6999999999999999e-169 < z < 5.4999999999999999e-135

   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 72.5%

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

   5. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 87.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{-13}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 4.7 \cdot 10^{-169}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 84.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6 + 1\right)\\ t_1 := 6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -9.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.000185:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (* z -6.0) 1.0))) (t_1 (* 6.0 (* z (- y x)))))
   (if (<= z -9.6e-15)
     t_1
     (if (<= z 5.1e-169)
       t_0
       (if (<= z 5.5e-135) (* 6.0 (* z y)) (if (<= z 0.000185) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * -6.0) + 1.0);
	double t_1 = 6.0 * (z * (y - x));
	double tmp;
	if (z <= -9.6e-15) {
		tmp = t_1;
	} else if (z <= 5.1e-169) {
		tmp = t_0;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 0.000185) {
		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 * ((z * (-6.0d0)) + 1.0d0)
    t_1 = 6.0d0 * (z * (y - x))
    if (z <= (-9.6d-15)) then
        tmp = t_1
    else if (z <= 5.1d-169) then
        tmp = t_0
    else if (z <= 5.5d-135) then
        tmp = 6.0d0 * (z * y)
    else if (z <= 0.000185d0) 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 * ((z * -6.0) + 1.0);
	double t_1 = 6.0 * (z * (y - x));
	double tmp;
	if (z <= -9.6e-15) {
		tmp = t_1;
	} else if (z <= 5.1e-169) {
		tmp = t_0;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 0.000185) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * -6.0) + 1.0)
	t_1 = 6.0 * (z * (y - x))
	tmp = 0
	if z <= -9.6e-15:
		tmp = t_1
	elif z <= 5.1e-169:
		tmp = t_0
	elif z <= 5.5e-135:
		tmp = 6.0 * (z * y)
	elif z <= 0.000185:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * -6.0) + 1.0))
	t_1 = Float64(6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -9.6e-15)
		tmp = t_1;
	elseif (z <= 5.1e-169)
		tmp = t_0;
	elseif (z <= 5.5e-135)
		tmp = Float64(6.0 * Float64(z * y));
	elseif (z <= 0.000185)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * -6.0) + 1.0);
	t_1 = 6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -9.6e-15)
		tmp = t_1;
	elseif (z <= 5.1e-169)
		tmp = t_0;
	elseif (z <= 5.5e-135)
		tmp = 6.0 * (z * y);
	elseif (z <= 0.000185)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -9.6e-15], t$95$1, If[LessEqual[z, 5.1e-169], t$95$0, If[LessEqual[z, 5.5e-135], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.000185], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -9.5999999999999998e-15 or 1.85e-4 < 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 99.7%

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

   4. Taylor expanded in z around inf 99.0%

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

   if -9.5999999999999998e-15 < z < 5.09999999999999997e-169 or 5.4999999999999999e-135 < z < 1.85e-4

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if 5.09999999999999997e-169 < z < 5.4999999999999999e-135

   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 72.5%

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

   5. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.6 \cdot 10^{-15}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.000185:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.0016:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (* z -6.0) 1.0))))
   (if (<= z -1.8e-14)
     (* (- y x) (* 6.0 z))
     (if (<= z 5.1e-169)
       t_0
       (if (<= z 5.5e-135)
         (* 6.0 (* z y))
         (if (<= z 0.0016) t_0 (* 6.0 (* z (- y x)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * -6.0) + 1.0);
	double tmp;
	if (z <= -1.8e-14) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 5.1e-169) {
		tmp = t_0;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 0.0016) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x * ((z * (-6.0d0)) + 1.0d0)
    if (z <= (-1.8d-14)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 5.1d-169) then
        tmp = t_0
    else if (z <= 5.5d-135) then
        tmp = 6.0d0 * (z * y)
    else if (z <= 0.0016d0) then
        tmp = t_0
    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 t_0 = x * ((z * -6.0) + 1.0);
	double tmp;
	if (z <= -1.8e-14) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 5.1e-169) {
		tmp = t_0;
	} else if (z <= 5.5e-135) {
		tmp = 6.0 * (z * y);
	} else if (z <= 0.0016) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * -6.0) + 1.0)
	tmp = 0
	if z <= -1.8e-14:
		tmp = (y - x) * (6.0 * z)
	elif z <= 5.1e-169:
		tmp = t_0
	elif z <= 5.5e-135:
		tmp = 6.0 * (z * y)
	elif z <= 0.0016:
		tmp = t_0
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * -6.0) + 1.0))
	tmp = 0.0
	if (z <= -1.8e-14)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 5.1e-169)
		tmp = t_0;
	elseif (z <= 5.5e-135)
		tmp = Float64(6.0 * Float64(z * y));
	elseif (z <= 0.0016)
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * -6.0) + 1.0);
	tmp = 0.0;
	if (z <= -1.8e-14)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 5.1e-169)
		tmp = t_0;
	elseif (z <= 5.5e-135)
		tmp = 6.0 * (z * y);
	elseif (z <= 0.0016)
		tmp = t_0;
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.8e-14], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.1e-169], t$95$0, If[LessEqual[z, 5.5e-135], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.0016], t$95$0, N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.7999999999999999e-14

   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 99.7%

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

   4. Taylor expanded in z around inf 99.2%

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

   5. Taylor expanded in y around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*r* 96.3%

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

      3. metadata-eval 96.3%

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

      4. distribute-lft-neg-in 96.3%

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

      5. distribute-lft-neg-in 96.3%

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

      6. distribute-rgt-neg-out 96.3%

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

      7. *-commutative 96.3%

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

      8. associate-*r* 96.3%

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

      9. distribute-lft-out 99.2%

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

      10. *-commutative 99.2%

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

      11. +-commutative 99.2%

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

      12. sub-neg 99.2%

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

   7. Simplified 99.2%

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

   if -1.7999999999999999e-14 < z < 5.09999999999999997e-169 or 5.4999999999999999e-135 < z < 0.00160000000000000008

   1. Initial program 99.1%

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

   3. Taylor expanded in x around inf 74.7%

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

      1. +-commutative 74.7%

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

   5. Simplified 74.7%

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

   if 5.09999999999999997e-169 < z < 5.4999999999999999e-135

   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 72.5%

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

   5. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

   if 0.00160000000000000008 < z

   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 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{-14}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-169}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.0016:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-172}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.00023:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.3e-15)
   (* (- y x) (* 6.0 z))
   (if (<= z 5.2e-172)
     (+ x (* -6.0 (* x z)))
     (if (<= z 5.4e-129)
       (* 6.0 (* z y))
       (if (<= z 0.00023) (* x (+ (* z -6.0) 1.0)) (* 6.0 (* z (- y x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.3e-15) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 5.2e-172) {
		tmp = x + (-6.0 * (x * z));
	} else if (z <= 5.4e-129) {
		tmp = 6.0 * (z * y);
	} else if (z <= 0.00023) {
		tmp = x * ((z * -6.0) + 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 (z <= (-2.3d-15)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 5.2d-172) then
        tmp = x + ((-6.0d0) * (x * z))
    else if (z <= 5.4d-129) then
        tmp = 6.0d0 * (z * y)
    else if (z <= 0.00023d0) then
        tmp = x * ((z * (-6.0d0)) + 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 (z <= -2.3e-15) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 5.2e-172) {
		tmp = x + (-6.0 * (x * z));
	} else if (z <= 5.4e-129) {
		tmp = 6.0 * (z * y);
	} else if (z <= 0.00023) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.3e-15:
		tmp = (y - x) * (6.0 * z)
	elif z <= 5.2e-172:
		tmp = x + (-6.0 * (x * z))
	elif z <= 5.4e-129:
		tmp = 6.0 * (z * y)
	elif z <= 0.00023:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.3e-15)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 5.2e-172)
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	elseif (z <= 5.4e-129)
		tmp = Float64(6.0 * Float64(z * y));
	elseif (z <= 0.00023)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 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 (z <= -2.3e-15)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 5.2e-172)
		tmp = x + (-6.0 * (x * z));
	elseif (z <= 5.4e-129)
		tmp = 6.0 * (z * y);
	elseif (z <= 0.00023)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.3e-15], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.2e-172], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.4e-129], N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.00023], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.2999999999999999e-15

   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 99.7%

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

   4. Taylor expanded in z around inf 99.2%

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

   5. Taylor expanded in y around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*r* 96.3%

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

      3. metadata-eval 96.3%

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

      4. distribute-lft-neg-in 96.3%

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

      5. distribute-lft-neg-in 96.3%

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

      6. distribute-rgt-neg-out 96.3%

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

      7. *-commutative 96.3%

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

      8. associate-*r* 96.3%

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

      9. distribute-lft-out 99.2%

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

      10. *-commutative 99.2%

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

      11. +-commutative 99.2%

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

      12. sub-neg 99.2%

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

   7. Simplified 99.2%

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

   if -2.2999999999999999e-15 < z < 5.1999999999999996e-172

   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 0 74.5%

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

   if 5.1999999999999996e-172 < z < 5.39999999999999998e-129

   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 72.5%

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

   5. Taylor expanded in y around inf 72.6%

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

      1. *-commutative 72.6%

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

   7. Simplified 72.6%

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

   if 5.39999999999999998e-129 < z < 2.3000000000000001e-4

   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 75.4%

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

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

   if 2.3000000000000001e-4 < z

   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 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.3 \cdot 10^{-15}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-172}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-129}:\\ \;\;\;\;6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.00023:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 1.5\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 1.5)))
   (* 6.0 (* z (- y x)))
   (+ x (* z (* 6.0 y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 1.5)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x + (z * (6.0 * y));
	}
	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 <= 1.5d0))) then
        tmp = 6.0d0 * (z * (y - x))
    else
        tmp = x + (z * (6.0d0 * y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 1.5)) {
		tmp = 6.0 * (z * (y - x));
	} else {
		tmp = x + (z * (6.0 * y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 1.5):
		tmp = 6.0 * (z * (y - x))
	else:
		tmp = x + (z * (6.0 * y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 1.5))
		tmp = Float64(6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 1.5)))
		tmp = 6.0 * (z * (y - x));
	else
		tmp = x + (z * (6.0 * y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 1.5]], $MachinePrecision]], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 1.5 < 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 99.8%

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

   4. Taylor expanded in z around inf 99.0%

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

   if -0.170000000000000012 < z < 1.5

   1. Initial program 99.2%

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

   3. Taylor expanded in y around inf 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 1.5\right):\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.16:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.4e-12)
   (* (- y x) (* 6.0 z))
   (if (<= z 0.16) (+ x (* 6.0 (* z y))) (* 6.0 (* z (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.4e-12) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.16) {
		tmp = x + (6.0 * (z * y));
	} 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 (z <= (-5.4d-12)) then
        tmp = (y - x) * (6.0d0 * z)
    else if (z <= 0.16d0) then
        tmp = x + (6.0d0 * (z * y))
    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 (z <= -5.4e-12) {
		tmp = (y - x) * (6.0 * z);
	} else if (z <= 0.16) {
		tmp = x + (6.0 * (z * y));
	} else {
		tmp = 6.0 * (z * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.4e-12:
		tmp = (y - x) * (6.0 * z)
	elif z <= 0.16:
		tmp = x + (6.0 * (z * y))
	else:
		tmp = 6.0 * (z * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.4e-12)
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	elseif (z <= 0.16)
		tmp = Float64(x + Float64(6.0 * Float64(z * y)));
	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 (z <= -5.4e-12)
		tmp = (y - x) * (6.0 * z);
	elseif (z <= 0.16)
		tmp = x + (6.0 * (z * y));
	else
		tmp = 6.0 * (z * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.4e-12], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.16], N[(x + N[(6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999961e-12

   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 99.7%

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

   4. Taylor expanded in z around inf 99.2%

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

   5. Taylor expanded in y around 0 96.3%

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

      1. *-commutative 96.3%

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

      2. associate-*r* 96.3%

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

      3. metadata-eval 96.3%

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

      4. distribute-lft-neg-in 96.3%

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

      5. distribute-lft-neg-in 96.3%

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

      6. distribute-rgt-neg-out 96.3%

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

      7. *-commutative 96.3%

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

      8. associate-*r* 96.3%

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

      9. distribute-lft-out 99.2%

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

      10. *-commutative 99.2%

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

      11. +-commutative 99.2%

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

      12. sub-neg 99.2%

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

   7. Simplified 99.2%

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

   if -5.39999999999999961e-12 < z < 0.160000000000000003

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. *-commutative 98.7%

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

   5. Simplified 98.7%

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

   if 0.160000000000000003 < z

   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 99.8%

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

   4. Taylor expanded in z around inf 98.8%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 0.16:\\ \;\;\;\;x + 6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 61.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1860\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 1860.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 1860.0)) {
		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 <= (-0.165d0)) .or. (.not. (z <= 1860.0d0))) 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 <= -0.165) || !(z <= 1860.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 1860.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 1860.0))
		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 <= -0.165) || ~((z <= 1860.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 1860.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 1860 < 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 99.8%

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

   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 46.3%

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

   if -0.165000000000000008 < z < 1860

   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 67.9%

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

4. Final simplification 56.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 1860\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 36.5% 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 32.7%

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

4. Final simplification 32.7%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 99.7% 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 2024080 
(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)))