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

Percentage Accurate: 99.7% → 99.8%

Time: 9.0s

Alternatives: 13

Speedup: 1.0×

• 21.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

   1. associate-*l* 99.9%

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

3. Simplified 99.9%

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

Alternative 2: 59.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.52 \cdot 10^{+266}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+180}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+26} \lor \neg \left(z \leq 2.3 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -1.52e+266)
     t_0
     (if (<= z -5e+180)
       t_1
       (if (<= z -2.4e+96)
         t_0
         (if (<= z -6.6e-97)
           t_1
           (if (<= z 2e-118)
             x
             (if (or (<= z 1.26e+26) (not (<= z 2.3e+164)))
               (* y (* 6.0 z))
               t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.52e+266) {
		tmp = t_0;
	} else if (z <= -5e+180) {
		tmp = t_1;
	} else if (z <= -2.4e+96) {
		tmp = t_0;
	} else if (z <= -6.6e-97) {
		tmp = t_1;
	} else if (z <= 2e-118) {
		tmp = x;
	} else if ((z <= 1.26e+26) || !(z <= 2.3e+164)) {
		tmp = y * (6.0 * 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) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-1.52d+266)) then
        tmp = t_0
    else if (z <= (-5d+180)) then
        tmp = t_1
    else if (z <= (-2.4d+96)) then
        tmp = t_0
    else if (z <= (-6.6d-97)) then
        tmp = t_1
    else if (z <= 2d-118) then
        tmp = x
    else if ((z <= 1.26d+26) .or. (.not. (z <= 2.3d+164))) then
        tmp = y * (6.0d0 * 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 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.52e+266) {
		tmp = t_0;
	} else if (z <= -5e+180) {
		tmp = t_1;
	} else if (z <= -2.4e+96) {
		tmp = t_0;
	} else if (z <= -6.6e-97) {
		tmp = t_1;
	} else if (z <= 2e-118) {
		tmp = x;
	} else if ((z <= 1.26e+26) || !(z <= 2.3e+164)) {
		tmp = y * (6.0 * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.52e+266:
		tmp = t_0
	elif z <= -5e+180:
		tmp = t_1
	elif z <= -2.4e+96:
		tmp = t_0
	elif z <= -6.6e-97:
		tmp = t_1
	elif z <= 2e-118:
		tmp = x
	elif (z <= 1.26e+26) or not (z <= 2.3e+164):
		tmp = y * (6.0 * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.52e+266)
		tmp = t_0;
	elseif (z <= -5e+180)
		tmp = t_1;
	elseif (z <= -2.4e+96)
		tmp = t_0;
	elseif (z <= -6.6e-97)
		tmp = t_1;
	elseif (z <= 2e-118)
		tmp = x;
	elseif ((z <= 1.26e+26) || !(z <= 2.3e+164))
		tmp = Float64(y * Float64(6.0 * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.52e+266)
		tmp = t_0;
	elseif (z <= -5e+180)
		tmp = t_1;
	elseif (z <= -2.4e+96)
		tmp = t_0;
	elseif (z <= -6.6e-97)
		tmp = t_1;
	elseif (z <= 2e-118)
		tmp = x;
	elseif ((z <= 1.26e+26) || ~((z <= 2.3e+164)))
		tmp = y * (6.0 * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.52e+266], t$95$0, If[LessEqual[z, -5e+180], t$95$1, If[LessEqual[z, -2.4e+96], t$95$0, If[LessEqual[z, -6.6e-97], t$95$1, If[LessEqual[z, 2e-118], x, If[Or[LessEqual[z, 1.26e+26], N[Not[LessEqual[z, 2.3e+164]], $MachinePrecision]], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.52000000000000006e266 or -4.9999999999999996e180 < z < -2.39999999999999993e96 or 1.25999999999999995e26 < z < 2.3e164

   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 74.1%

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

   4. Taylor expanded in z around inf 74.1%

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

      1. associate-*r* 74.1%

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

      2. *-commutative 74.1%

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

      3. associate-*r* 74.2%

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

   6. Simplified 74.2%

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

   if -1.52000000000000006e266 < z < -4.9999999999999996e180 or -2.39999999999999993e96 < z < -6.6000000000000002e-97

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 99.8%

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

   4. Taylor expanded in y around inf 61.2%

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

   if -6.6000000000000002e-97 < z < 1.99999999999999997e-118

   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 79.9%

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

   if 1.99999999999999997e-118 < z < 1.25999999999999995e26 or 2.3e164 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.7%

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

   4. Taylor expanded in y around inf 60.5%

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

      1. *-commutative 60.5%

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

      2. associate-*r* 60.6%

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

      3. *-commutative 60.6%

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

   6. Simplified 60.6%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.52 \cdot 10^{+266}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{+180}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{+96}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-97}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.26 \cdot 10^{+26} \lor \neg \left(z \leq 2.3 \cdot 10^{+164}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 59.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.36 \cdot 10^{+265}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+179}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+25} \lor \neg \left(z \leq 1.15 \cdot 10^{+164}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* z -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -1.36e+265)
     t_0
     (if (<= z -8.5e+179)
       t_1
       (if (<= z -2.3e+94)
         t_0
         (if (<= z -7e-97)
           t_1
           (if (<= z 2e-118)
             x
             (if (or (<= z 4.2e+25) (not (<= z 1.15e+164))) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.36e+265) {
		tmp = t_0;
	} else if (z <= -8.5e+179) {
		tmp = t_1;
	} else if (z <= -2.3e+94) {
		tmp = t_0;
	} else if (z <= -7e-97) {
		tmp = t_1;
	} else if (z <= 2e-118) {
		tmp = x;
	} else if ((z <= 4.2e+25) || !(z <= 1.15e+164)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = x * (z * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-1.36d+265)) then
        tmp = t_0
    else if (z <= (-8.5d+179)) then
        tmp = t_1
    else if (z <= (-2.3d+94)) then
        tmp = t_0
    else if (z <= (-7d-97)) then
        tmp = t_1
    else if (z <= 2d-118) then
        tmp = x
    else if ((z <= 4.2d+25) .or. (.not. (z <= 1.15d+164))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (z * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -1.36e+265) {
		tmp = t_0;
	} else if (z <= -8.5e+179) {
		tmp = t_1;
	} else if (z <= -2.3e+94) {
		tmp = t_0;
	} else if (z <= -7e-97) {
		tmp = t_1;
	} else if (z <= 2e-118) {
		tmp = x;
	} else if ((z <= 4.2e+25) || !(z <= 1.15e+164)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (z * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -1.36e+265:
		tmp = t_0
	elif z <= -8.5e+179:
		tmp = t_1
	elif z <= -2.3e+94:
		tmp = t_0
	elif z <= -7e-97:
		tmp = t_1
	elif z <= 2e-118:
		tmp = x
	elif (z <= 4.2e+25) or not (z <= 1.15e+164):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(z * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.36e+265)
		tmp = t_0;
	elseif (z <= -8.5e+179)
		tmp = t_1;
	elseif (z <= -2.3e+94)
		tmp = t_0;
	elseif (z <= -7e-97)
		tmp = t_1;
	elseif (z <= 2e-118)
		tmp = x;
	elseif ((z <= 4.2e+25) || !(z <= 1.15e+164))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (z * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.36e+265)
		tmp = t_0;
	elseif (z <= -8.5e+179)
		tmp = t_1;
	elseif (z <= -2.3e+94)
		tmp = t_0;
	elseif (z <= -7e-97)
		tmp = t_1;
	elseif (z <= 2e-118)
		tmp = x;
	elseif ((z <= 4.2e+25) || ~((z <= 1.15e+164)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.36e+265], t$95$0, If[LessEqual[z, -8.5e+179], t$95$1, If[LessEqual[z, -2.3e+94], t$95$0, If[LessEqual[z, -7e-97], t$95$1, If[LessEqual[z, 2e-118], x, If[Or[LessEqual[z, 4.2e+25], N[Not[LessEqual[z, 1.15e+164]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.36e265 or -8.49999999999999962e179 < z < -2.3e94 or 4.1999999999999998e25 < z < 1.15e164

   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 74.1%

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

   4. Taylor expanded in z around inf 74.1%

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

      1. associate-*r* 74.1%

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

      2. *-commutative 74.1%

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

      3. associate-*r* 74.2%

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

   6. Simplified 74.2%

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

   if -1.36e265 < z < -8.49999999999999962e179 or -2.3e94 < z < -7.00000000000000038e-97 or 1.99999999999999997e-118 < z < 4.1999999999999998e25 or 1.15e164 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 97.2%

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

   4. Taylor expanded in y around inf 60.8%

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

   if -7.00000000000000038e-97 < z < 1.99999999999999997e-118

   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 79.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.36 \cdot 10^{+265}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+179}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{+94}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+25} \lor \neg \left(z \leq 1.15 \cdot 10^{+164}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.1 \cdot 10^{+264}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+177}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+24} \lor \neg \left(z \leq 2.5 \cdot 10^{+163}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -3.1e+264)
     t_0
     (if (<= z -1.8e+177)
       t_1
       (if (<= z -2.8e+95)
         t_0
         (if (<= z -7e-97)
           t_1
           (if (<= z 2e-118)
             x
             (if (or (<= z 8.2e+24) (not (<= z 2.5e+163))) t_1 t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (x * z);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.1e+264) {
		tmp = t_0;
	} else if (z <= -1.8e+177) {
		tmp = t_1;
	} else if (z <= -2.8e+95) {
		tmp = t_0;
	} else if (z <= -7e-97) {
		tmp = t_1;
	} else if (z <= 2e-118) {
		tmp = x;
	} else if ((z <= 8.2e+24) || !(z <= 2.5e+163)) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (x * z)
    t_1 = 6.0d0 * (y * z)
    if (z <= (-3.1d+264)) then
        tmp = t_0
    else if (z <= (-1.8d+177)) then
        tmp = t_1
    else if (z <= (-2.8d+95)) then
        tmp = t_0
    else if (z <= (-7d-97)) then
        tmp = t_1
    else if (z <= 2d-118) then
        tmp = x
    else if ((z <= 8.2d+24) .or. (.not. (z <= 2.5d+163))) then
        tmp = t_1
    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 t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.1e+264) {
		tmp = t_0;
	} else if (z <= -1.8e+177) {
		tmp = t_1;
	} else if (z <= -2.8e+95) {
		tmp = t_0;
	} else if (z <= -7e-97) {
		tmp = t_1;
	} else if (z <= 2e-118) {
		tmp = x;
	} else if ((z <= 8.2e+24) || !(z <= 2.5e+163)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (x * z)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -3.1e+264:
		tmp = t_0
	elif z <= -1.8e+177:
		tmp = t_1
	elif z <= -2.8e+95:
		tmp = t_0
	elif z <= -7e-97:
		tmp = t_1
	elif z <= 2e-118:
		tmp = x
	elif (z <= 8.2e+24) or not (z <= 2.5e+163):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(x * z))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.1e+264)
		tmp = t_0;
	elseif (z <= -1.8e+177)
		tmp = t_1;
	elseif (z <= -2.8e+95)
		tmp = t_0;
	elseif (z <= -7e-97)
		tmp = t_1;
	elseif (z <= 2e-118)
		tmp = x;
	elseif ((z <= 8.2e+24) || !(z <= 2.5e+163))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (x * z);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.1e+264)
		tmp = t_0;
	elseif (z <= -1.8e+177)
		tmp = t_1;
	elseif (z <= -2.8e+95)
		tmp = t_0;
	elseif (z <= -7e-97)
		tmp = t_1;
	elseif (z <= 2e-118)
		tmp = x;
	elseif ((z <= 8.2e+24) || ~((z <= 2.5e+163)))
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.1e+264], t$95$0, If[LessEqual[z, -1.8e+177], t$95$1, If[LessEqual[z, -2.8e+95], t$95$0, If[LessEqual[z, -7e-97], t$95$1, If[LessEqual[z, 2e-118], x, If[Or[LessEqual[z, 8.2e+24], N[Not[LessEqual[z, 2.5e+163]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.09999999999999981e264 or -1.80000000000000001e177 < z < -2.7999999999999998e95 or 8.2000000000000002e24 < z < 2.5e163

   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 74.1%

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

   4. Taylor expanded in z around inf 74.1%

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

   if -3.09999999999999981e264 < z < -1.80000000000000001e177 or -2.7999999999999998e95 < z < -7.00000000000000038e-97 or 1.99999999999999997e-118 < z < 8.2000000000000002e24 or 2.5e163 < z

   1. Initial program 99.6%

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

   3. Taylor expanded in x around 0 97.2%

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

   4. Taylor expanded in y around inf 60.8%

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

   if -7.00000000000000038e-97 < z < 1.99999999999999997e-118

   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 79.9%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+264}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{+177}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+95}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-97}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-118}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{+24} \lor \neg \left(z \leq 2.5 \cdot 10^{+163}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 83.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+106} \lor \neg \left(y \leq -500 \lor \neg \left(y \leq -5 \cdot 10^{-140}\right) \land y \leq 2.4 \cdot 10^{-9}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7.4e+106)
         (not (or (<= y -500.0) (and (not (<= y -5e-140)) (<= y 2.4e-9)))))
   (+ x (* 6.0 (* y z)))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.4e+106) || !((y <= -500.0) || (!(y <= -5e-140) && (y <= 2.4e-9)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-7.4d+106)) .or. (.not. (y <= (-500.0d0)) .or. (.not. (y <= (-5d-140))) .and. (y <= 2.4d-9))) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7.4e+106) || !((y <= -500.0) || (!(y <= -5e-140) && (y <= 2.4e-9)))) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7.4e+106) or not ((y <= -500.0) or (not (y <= -5e-140) and (y <= 2.4e-9))):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7.4e+106) || !((y <= -500.0) || (!(y <= -5e-140) && (y <= 2.4e-9))))
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7.4e+106) || ~(((y <= -500.0) || (~((y <= -5e-140)) && (y <= 2.4e-9)))))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7.4e+106], N[Not[Or[LessEqual[y, -500.0], And[N[Not[LessEqual[y, -5e-140]], $MachinePrecision], LessEqual[y, 2.4e-9]]]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.3999999999999999e106 or -500 < y < -5.00000000000000015e-140 or 2.4e-9 < y

   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 89.1%

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

   if -7.3999999999999999e106 < y < -500 or -5.00000000000000015e-140 < y < 2.4e-9

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 87.9%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+106} \lor \neg \left(y \leq -500 \lor \neg \left(y \leq -5 \cdot 10^{-140}\right) \land y \leq 2.4 \cdot 10^{-9}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+102} \lor \neg \left(y \leq 1800 \lor \neg \left(y \leq 6.5 \cdot 10^{+51}\right) \land y \leq 8 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.65e+102)
         (not (or (<= y 1800.0) (and (not (<= y 6.5e+51)) (<= y 8e+89)))))
   (* y (* 6.0 z))
   (+ x (* -6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e+102) || !((y <= 1800.0) || (!(y <= 6.5e+51) && (y <= 8e+89)))) {
		tmp = y * (6.0 * z);
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-2.65d+102)) .or. (.not. (y <= 1800.0d0) .or. (.not. (y <= 6.5d+51)) .and. (y <= 8d+89))) then
        tmp = y * (6.0d0 * z)
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.65e+102) || !((y <= 1800.0) || (!(y <= 6.5e+51) && (y <= 8e+89)))) {
		tmp = y * (6.0 * z);
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.65e+102) or not ((y <= 1800.0) or (not (y <= 6.5e+51) and (y <= 8e+89))):
		tmp = y * (6.0 * z)
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.65e+102) || !((y <= 1800.0) || (!(y <= 6.5e+51) && (y <= 8e+89))))
		tmp = Float64(y * Float64(6.0 * z));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.65e+102) || ~(((y <= 1800.0) || (~((y <= 6.5e+51)) && (y <= 8e+89)))))
		tmp = y * (6.0 * z);
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.65e+102], N[Not[Or[LessEqual[y, 1800.0], And[N[Not[LessEqual[y, 6.5e+51]], $MachinePrecision], LessEqual[y, 8e+89]]]], $MachinePrecision]], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.6499999999999998e102 or 1800 < y < 6.5e51 or 7.99999999999999996e89 < y

   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 0 93.7%

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

   4. Taylor expanded in y around inf 76.0%

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

      1. *-commutative 76.0%

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

      2. associate-*r* 76.1%

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

      3. *-commutative 76.1%

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

   6. Simplified 76.1%

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

   if -2.6499999999999998e102 < y < 1800 or 6.5e51 < y < 7.99999999999999996e89

   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 81.9%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.65 \cdot 10^{+102} \lor \neg \left(y \leq 1800 \lor \neg \left(y \leq 6.5 \cdot 10^{+51}\right) \land y \leq 8 \cdot 10^{+89}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 83.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -500:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-140} \lor \neg \left(y \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y (* 6.0 z)))))
   (if (<= y -7.4e+106)
     t_0
     (if (<= y -500.0)
       (+ x (* z (* x -6.0)))
       (if (or (<= y -5.5e-140) (not (<= y 1.8e-5)))
         t_0
         (+ x (* -6.0 (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * (6.0 * z));
	double tmp;
	if (y <= -7.4e+106) {
		tmp = t_0;
	} else if (y <= -500.0) {
		tmp = x + (z * (x * -6.0));
	} else if ((y <= -5.5e-140) || !(y <= 1.8e-5)) {
		tmp = t_0;
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (y * (6.0d0 * z))
    if (y <= (-7.4d+106)) then
        tmp = t_0
    else if (y <= (-500.0d0)) then
        tmp = x + (z * (x * (-6.0d0)))
    else if ((y <= (-5.5d-140)) .or. (.not. (y <= 1.8d-5))) then
        tmp = t_0
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * (6.0 * z));
	double tmp;
	if (y <= -7.4e+106) {
		tmp = t_0;
	} else if (y <= -500.0) {
		tmp = x + (z * (x * -6.0));
	} else if ((y <= -5.5e-140) || !(y <= 1.8e-5)) {
		tmp = t_0;
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * (6.0 * z))
	tmp = 0
	if y <= -7.4e+106:
		tmp = t_0
	elif y <= -500.0:
		tmp = x + (z * (x * -6.0))
	elif (y <= -5.5e-140) or not (y <= 1.8e-5):
		tmp = t_0
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * Float64(6.0 * z)))
	tmp = 0.0
	if (y <= -7.4e+106)
		tmp = t_0;
	elseif (y <= -500.0)
		tmp = Float64(x + Float64(z * Float64(x * -6.0)));
	elseif ((y <= -5.5e-140) || !(y <= 1.8e-5))
		tmp = t_0;
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * (6.0 * z));
	tmp = 0.0;
	if (y <= -7.4e+106)
		tmp = t_0;
	elseif (y <= -500.0)
		tmp = x + (z * (x * -6.0));
	elseif ((y <= -5.5e-140) || ~((y <= 1.8e-5)))
		tmp = t_0;
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e+106], t$95$0, If[LessEqual[y, -500.0], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.5e-140], N[Not[LessEqual[y, 1.8e-5]], $MachinePrecision]], t$95$0, N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3999999999999999e106 or -500 < y < -5.50000000000000026e-140 or 1.80000000000000005e-5 < y

   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 89.1%

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

      1. associate-*r* 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*r* 89.1%

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

   5. Simplified 89.1%

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

   if -7.3999999999999999e106 < y < -500

   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 78.9%

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

   if -5.50000000000000026e-140 < y < 1.80000000000000005e-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 0 90.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -500:\\ \;\;\;\;x + z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-140} \lor \neg \left(y \leq 1.8 \cdot 10^{-5}\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 83.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -65:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-140} \lor \neg \left(y \leq 0.000165\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y (* 6.0 z)))))
   (if (<= y -7.4e+106)
     t_0
     (if (<= y -65.0)
       (+ x (* x (* z -6.0)))
       (if (or (<= y -5.5e-140) (not (<= y 0.000165)))
         t_0
         (+ x (* -6.0 (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * (6.0 * z));
	double tmp;
	if (y <= -7.4e+106) {
		tmp = t_0;
	} else if (y <= -65.0) {
		tmp = x + (x * (z * -6.0));
	} else if ((y <= -5.5e-140) || !(y <= 0.000165)) {
		tmp = t_0;
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (y * (6.0d0 * z))
    if (y <= (-7.4d+106)) then
        tmp = t_0
    else if (y <= (-65.0d0)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if ((y <= (-5.5d-140)) .or. (.not. (y <= 0.000165d0))) then
        tmp = t_0
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * (6.0 * z));
	double tmp;
	if (y <= -7.4e+106) {
		tmp = t_0;
	} else if (y <= -65.0) {
		tmp = x + (x * (z * -6.0));
	} else if ((y <= -5.5e-140) || !(y <= 0.000165)) {
		tmp = t_0;
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * (6.0 * z))
	tmp = 0
	if y <= -7.4e+106:
		tmp = t_0
	elif y <= -65.0:
		tmp = x + (x * (z * -6.0))
	elif (y <= -5.5e-140) or not (y <= 0.000165):
		tmp = t_0
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * Float64(6.0 * z)))
	tmp = 0.0
	if (y <= -7.4e+106)
		tmp = t_0;
	elseif (y <= -65.0)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif ((y <= -5.5e-140) || !(y <= 0.000165))
		tmp = t_0;
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * (6.0 * z));
	tmp = 0.0;
	if (y <= -7.4e+106)
		tmp = t_0;
	elseif (y <= -65.0)
		tmp = x + (x * (z * -6.0));
	elseif ((y <= -5.5e-140) || ~((y <= 0.000165)))
		tmp = t_0;
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e+106], t$95$0, If[LessEqual[y, -65.0], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5.5e-140], N[Not[LessEqual[y, 0.000165]], $MachinePrecision]], t$95$0, N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3999999999999999e106 or -65 < y < -5.50000000000000026e-140 or 1.65e-4 < y

   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 89.1%

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

      1. associate-*r* 89.1%

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

      2. *-commutative 89.1%

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

      3. associate-*r* 89.1%

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

   5. Simplified 89.1%

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

   if -7.3999999999999999e106 < y < -65

   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 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*r* 78.8%

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

      3. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   if -5.50000000000000026e-140 < y < 1.65e-4

   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 90.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+106}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;y \leq -65:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-140} \lor \neg \left(y \leq 0.000165\right):\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 83.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;y \leq -7.4 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -500:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-140} \lor \neg \left(y \leq 1.1 \cdot 10^{-9}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* 6.0 (* y z)))))
   (if (<= y -7.4e+106)
     t_0
     (if (<= y -500.0)
       (+ x (* x (* z -6.0)))
       (if (or (<= y -5e-140) (not (<= y 1.1e-9)))
         t_0
         (+ x (* -6.0 (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (6.0 * (y * z));
	double tmp;
	if (y <= -7.4e+106) {
		tmp = t_0;
	} else if (y <= -500.0) {
		tmp = x + (x * (z * -6.0));
	} else if ((y <= -5e-140) || !(y <= 1.1e-9)) {
		tmp = t_0;
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x + (6.0d0 * (y * z))
    if (y <= (-7.4d+106)) then
        tmp = t_0
    else if (y <= (-500.0d0)) then
        tmp = x + (x * (z * (-6.0d0)))
    else if ((y <= (-5d-140)) .or. (.not. (y <= 1.1d-9))) then
        tmp = t_0
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (6.0 * (y * z));
	double tmp;
	if (y <= -7.4e+106) {
		tmp = t_0;
	} else if (y <= -500.0) {
		tmp = x + (x * (z * -6.0));
	} else if ((y <= -5e-140) || !(y <= 1.1e-9)) {
		tmp = t_0;
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (6.0 * (y * z))
	tmp = 0
	if y <= -7.4e+106:
		tmp = t_0
	elif y <= -500.0:
		tmp = x + (x * (z * -6.0))
	elif (y <= -5e-140) or not (y <= 1.1e-9):
		tmp = t_0
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(6.0 * Float64(y * z)))
	tmp = 0.0
	if (y <= -7.4e+106)
		tmp = t_0;
	elseif (y <= -500.0)
		tmp = Float64(x + Float64(x * Float64(z * -6.0)));
	elseif ((y <= -5e-140) || !(y <= 1.1e-9))
		tmp = t_0;
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (6.0 * (y * z));
	tmp = 0.0;
	if (y <= -7.4e+106)
		tmp = t_0;
	elseif (y <= -500.0)
		tmp = x + (x * (z * -6.0));
	elseif ((y <= -5e-140) || ~((y <= 1.1e-9)))
		tmp = t_0;
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.4e+106], t$95$0, If[LessEqual[y, -500.0], N[(x + N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[y, -5e-140], N[Not[LessEqual[y, 1.1e-9]], $MachinePrecision]], t$95$0, N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.3999999999999999e106 or -500 < y < -5.00000000000000015e-140 or 1.0999999999999999e-9 < y

   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 89.1%

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

   if -7.3999999999999999e106 < y < -500

   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 78.8%

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

      1. *-commutative 78.8%

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

      2. associate-*r* 78.8%

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

      3. *-commutative 78.8%

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

   5. Simplified 78.8%

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

   if -5.00000000000000015e-140 < y < 1.0999999999999999e-9

   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 90.1%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{+106}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq -500:\\ \;\;\;\;x + x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-140} \lor \neg \left(y \leq 1.1 \cdot 10^{-9}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;z \cdot \left(x \cdot -6 + y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.16) (not (<= z 0.166)))
   (* z (+ (* x -6.0) (* y 6.0)))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.16) || !(z <= 0.166)) {
		tmp = z * ((x * -6.0) + (y * 6.0));
	} else {
		tmp = x + (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 <= (-0.16d0)) .or. (.not. (z <= 0.166d0))) then
        tmp = z * ((x * (-6.0d0)) + (y * 6.0d0))
    else
        tmp = x + (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 <= -0.16) || !(z <= 0.166)) {
		tmp = z * ((x * -6.0) + (y * 6.0));
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.16) or not (z <= 0.166):
		tmp = z * ((x * -6.0) + (y * 6.0))
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.16) || !(z <= 0.166))
		tmp = Float64(z * Float64(Float64(x * -6.0) + Float64(y * 6.0)));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.16) || ~((z <= 0.166)))
		tmp = z * ((x * -6.0) + (y * 6.0));
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.16], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(z * N[(N[(x * -6.0), $MachinePrecision] + N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.160000000000000003 or 0.166000000000000009 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around 0 94.4%

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

   4. Taylor expanded in z around inf 97.7%

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

   if -0.160000000000000003 < z < 0.166000000000000009

   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 99.0%

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

      1. associate-*r* 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*r* 99.1%

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

   5. Simplified 99.1%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.16 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;z \cdot \left(x \cdot -6 + y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.17) (not (<= z 0.166))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.17d0)) .or. (.not. (z <= 0.166d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.17) || !(z <= 0.166)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.17) or not (z <= 0.166):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.17) || !(z <= 0.166))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.17) || ~((z <= 0.166)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 0.166]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.170000000000000012 or 0.166000000000000009 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in y around 0 57.3%

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

   4. Taylor expanded in z around inf 55.2%

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

   if -0.170000000000000012 < z < 0.166000000000000009

   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 64.3%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 0.166\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 13: 35.7% accurate, 9.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.8%

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

3. Taylor expanded in z around 0 33.3%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Developer target: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024103 
(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)))