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

Percentage Accurate: 99.7% → 99.7%

Time: 6.2s

Alternatives: 10

Speedup: 1.0×

• 20.5% 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: 99.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 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]

Derivation

1. Initial program 99.8%

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

2. Final simplification 99.8%

   \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]

Alternative 2: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(x \cdot z\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+64} \lor \neg \left(z \leq 5.2 \cdot 10^{+110}\right) \land z \leq 1.9 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* x z))) (t_1 (* 6.0 (* y z))))
   (if (<= z -2.2e+19)
     t_0
     (if (<= z -1.25e-75)
       t_1
       (if (<= z 2.65e-160)
         x
         (if (<= z 2.4e-116)
           t_1
           (if (<= z 5e-57)
             x
             (if (or (<= z 1.4e+64)
                     (and (not (<= z 5.2e+110)) (<= z 1.9e+216)))
               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 <= -2.2e+19) {
		tmp = t_0;
	} else if (z <= -1.25e-75) {
		tmp = t_1;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.4e-116) {
		tmp = t_1;
	} else if (z <= 5e-57) {
		tmp = x;
	} else if ((z <= 1.4e+64) || (!(z <= 5.2e+110) && (z <= 1.9e+216))) {
		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 <= (-2.2d+19)) then
        tmp = t_0
    else if (z <= (-1.25d-75)) then
        tmp = t_1
    else if (z <= 2.65d-160) then
        tmp = x
    else if (z <= 2.4d-116) then
        tmp = t_1
    else if (z <= 5d-57) then
        tmp = x
    else if ((z <= 1.4d+64) .or. (.not. (z <= 5.2d+110)) .and. (z <= 1.9d+216)) 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 <= -2.2e+19) {
		tmp = t_0;
	} else if (z <= -1.25e-75) {
		tmp = t_1;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.4e-116) {
		tmp = t_1;
	} else if (z <= 5e-57) {
		tmp = x;
	} else if ((z <= 1.4e+64) || (!(z <= 5.2e+110) && (z <= 1.9e+216))) {
		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 <= -2.2e+19:
		tmp = t_0
	elif z <= -1.25e-75:
		tmp = t_1
	elif z <= 2.65e-160:
		tmp = x
	elif z <= 2.4e-116:
		tmp = t_1
	elif z <= 5e-57:
		tmp = x
	elif (z <= 1.4e+64) or (not (z <= 5.2e+110) and (z <= 1.9e+216)):
		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 <= -2.2e+19)
		tmp = t_0;
	elseif (z <= -1.25e-75)
		tmp = t_1;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.4e-116)
		tmp = t_1;
	elseif (z <= 5e-57)
		tmp = x;
	elseif ((z <= 1.4e+64) || (!(z <= 5.2e+110) && (z <= 1.9e+216)))
		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 <= -2.2e+19)
		tmp = t_0;
	elseif (z <= -1.25e-75)
		tmp = t_1;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.4e-116)
		tmp = t_1;
	elseif (z <= 5e-57)
		tmp = x;
	elseif ((z <= 1.4e+64) || (~((z <= 5.2e+110)) && (z <= 1.9e+216)))
		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, -2.2e+19], t$95$0, If[LessEqual[z, -1.25e-75], t$95$1, If[LessEqual[z, 2.65e-160], x, If[LessEqual[z, 2.4e-116], t$95$1, If[LessEqual[z, 5e-57], x, If[Or[LessEqual[z, 1.4e+64], And[N[Not[LessEqual[z, 5.2e+110]], $MachinePrecision], LessEqual[z, 1.9e+216]]], t$95$1, t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.2e19 or 1.40000000000000012e64 < z < 5.2e110 or 1.90000000000000007e216 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 71.6%

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

   3. Taylor expanded in z around inf 71.6%

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

   4. Taylor expanded in z around 0 71.6%

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

   if -2.2e19 < z < -1.24999999999999995e-75 or 2.6500000000000001e-160 < z < 2.39999999999999993e-116 or 5.0000000000000002e-57 < z < 1.40000000000000012e64 or 5.2e110 < z < 1.90000000000000007e216

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 83.6%

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

   4. Taylor expanded in y around inf 64.5%

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

   if -1.24999999999999995e-75 < z < 2.6500000000000001e-160 or 2.39999999999999993e-116 < z < 5.0000000000000002e-57

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.2%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{+19}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-75}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-116}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+64} \lor \neg \left(z \leq 5.2 \cdot 10^{+110}\right) \land z \leq 1.9 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ t_1 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+110}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x -6.0))) (t_1 (* 6.0 (* y z))))
   (if (<= z -3.3e+18)
     t_0
     (if (<= z -1.25e-75)
       t_1
       (if (<= z 2.65e-160)
         x
         (if (<= z 2.2e-116)
           t_1
           (if (<= z 3.9e-57)
             x
             (if (<= z 1.5e+64)
               t_1
               (if (<= z 5.3e+110)
                 (* -6.0 (* x z))
                 (if (<= z 1.9e+216) t_1 t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.3e+18) {
		tmp = t_0;
	} else if (z <= -1.25e-75) {
		tmp = t_1;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = t_1;
	} else if (z <= 3.9e-57) {
		tmp = x;
	} else if (z <= 1.5e+64) {
		tmp = t_1;
	} else if (z <= 5.3e+110) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.9e+216) {
		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 = z * (x * (-6.0d0))
    t_1 = 6.0d0 * (y * z)
    if (z <= (-3.3d+18)) then
        tmp = t_0
    else if (z <= (-1.25d-75)) then
        tmp = t_1
    else if (z <= 2.65d-160) then
        tmp = x
    else if (z <= 2.2d-116) then
        tmp = t_1
    else if (z <= 3.9d-57) then
        tmp = x
    else if (z <= 1.5d+64) then
        tmp = t_1
    else if (z <= 5.3d+110) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 1.9d+216) 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 = z * (x * -6.0);
	double t_1 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.3e+18) {
		tmp = t_0;
	} else if (z <= -1.25e-75) {
		tmp = t_1;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = t_1;
	} else if (z <= 3.9e-57) {
		tmp = x;
	} else if (z <= 1.5e+64) {
		tmp = t_1;
	} else if (z <= 5.3e+110) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.9e+216) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -6.0)
	t_1 = 6.0 * (y * z)
	tmp = 0
	if z <= -3.3e+18:
		tmp = t_0
	elif z <= -1.25e-75:
		tmp = t_1
	elif z <= 2.65e-160:
		tmp = x
	elif z <= 2.2e-116:
		tmp = t_1
	elif z <= 3.9e-57:
		tmp = x
	elif z <= 1.5e+64:
		tmp = t_1
	elif z <= 5.3e+110:
		tmp = -6.0 * (x * z)
	elif z <= 1.9e+216:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * -6.0))
	t_1 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.3e+18)
		tmp = t_0;
	elseif (z <= -1.25e-75)
		tmp = t_1;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = t_1;
	elseif (z <= 3.9e-57)
		tmp = x;
	elseif (z <= 1.5e+64)
		tmp = t_1;
	elseif (z <= 5.3e+110)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 1.9e+216)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -6.0);
	t_1 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.3e+18)
		tmp = t_0;
	elseif (z <= -1.25e-75)
		tmp = t_1;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = t_1;
	elseif (z <= 3.9e-57)
		tmp = x;
	elseif (z <= 1.5e+64)
		tmp = t_1;
	elseif (z <= 5.3e+110)
		tmp = -6.0 * (x * z);
	elseif (z <= 1.9e+216)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+18], t$95$0, If[LessEqual[z, -1.25e-75], t$95$1, If[LessEqual[z, 2.65e-160], x, If[LessEqual[z, 2.2e-116], t$95$1, If[LessEqual[z, 3.9e-57], x, If[LessEqual[z, 1.5e+64], t$95$1, If[LessEqual[z, 5.3e+110], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+216], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3e18 or 1.90000000000000007e216 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

   6. Simplified 69.5%

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

   if -3.3e18 < z < -1.24999999999999995e-75 or 2.6500000000000001e-160 < z < 2.2000000000000001e-116 or 3.90000000000000006e-57 < z < 1.5000000000000001e64 or 5.2999999999999998e110 < z < 1.90000000000000007e216

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 83.6%

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

   4. Taylor expanded in y around inf 64.5%

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

   if -1.24999999999999995e-75 < z < 2.6500000000000001e-160 or 2.2000000000000001e-116 < z < 3.90000000000000006e-57

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.2%

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

   if 1.5000000000000001e64 < z < 5.2999999999999998e110

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 90.0%

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

   3. Taylor expanded in z around inf 90.0%

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

   4. Taylor expanded in z around 0 90.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-75}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+110}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 4: 59.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ t_1 := z \cdot \left(y \cdot 6\right)\\ t_2 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+110}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+216}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x -6.0))) (t_1 (* z (* y 6.0))) (t_2 (* 6.0 (* y z))))
   (if (<= z -4.3e+18)
     t_0
     (if (<= z -8e-76)
       t_2
       (if (<= z 2.65e-160)
         x
         (if (<= z 2.2e-116)
           t_1
           (if (<= z 8.4e-60)
             x
             (if (<= z 1.5e+64)
               t_2
               (if (<= z 5.2e+110)
                 (* -6.0 (* x z))
                 (if (<= z 3.2e+216) t_1 t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = z * (y * 6.0);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -4.3e+18) {
		tmp = t_0;
	} else if (z <= -8e-76) {
		tmp = t_2;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = t_1;
	} else if (z <= 8.4e-60) {
		tmp = x;
	} else if (z <= 1.5e+64) {
		tmp = t_2;
	} else if (z <= 5.2e+110) {
		tmp = -6.0 * (x * z);
	} else if (z <= 3.2e+216) {
		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) :: t_2
    real(8) :: tmp
    t_0 = z * (x * (-6.0d0))
    t_1 = z * (y * 6.0d0)
    t_2 = 6.0d0 * (y * z)
    if (z <= (-4.3d+18)) then
        tmp = t_0
    else if (z <= (-8d-76)) then
        tmp = t_2
    else if (z <= 2.65d-160) then
        tmp = x
    else if (z <= 2.2d-116) then
        tmp = t_1
    else if (z <= 8.4d-60) then
        tmp = x
    else if (z <= 1.5d+64) then
        tmp = t_2
    else if (z <= 5.2d+110) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 3.2d+216) 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 = z * (x * -6.0);
	double t_1 = z * (y * 6.0);
	double t_2 = 6.0 * (y * z);
	double tmp;
	if (z <= -4.3e+18) {
		tmp = t_0;
	} else if (z <= -8e-76) {
		tmp = t_2;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = t_1;
	} else if (z <= 8.4e-60) {
		tmp = x;
	} else if (z <= 1.5e+64) {
		tmp = t_2;
	} else if (z <= 5.2e+110) {
		tmp = -6.0 * (x * z);
	} else if (z <= 3.2e+216) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -6.0)
	t_1 = z * (y * 6.0)
	t_2 = 6.0 * (y * z)
	tmp = 0
	if z <= -4.3e+18:
		tmp = t_0
	elif z <= -8e-76:
		tmp = t_2
	elif z <= 2.65e-160:
		tmp = x
	elif z <= 2.2e-116:
		tmp = t_1
	elif z <= 8.4e-60:
		tmp = x
	elif z <= 1.5e+64:
		tmp = t_2
	elif z <= 5.2e+110:
		tmp = -6.0 * (x * z)
	elif z <= 3.2e+216:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * -6.0))
	t_1 = Float64(z * Float64(y * 6.0))
	t_2 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.3e+18)
		tmp = t_0;
	elseif (z <= -8e-76)
		tmp = t_2;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = t_1;
	elseif (z <= 8.4e-60)
		tmp = x;
	elseif (z <= 1.5e+64)
		tmp = t_2;
	elseif (z <= 5.2e+110)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 3.2e+216)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -6.0);
	t_1 = z * (y * 6.0);
	t_2 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.3e+18)
		tmp = t_0;
	elseif (z <= -8e-76)
		tmp = t_2;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = t_1;
	elseif (z <= 8.4e-60)
		tmp = x;
	elseif (z <= 1.5e+64)
		tmp = t_2;
	elseif (z <= 5.2e+110)
		tmp = -6.0 * (x * z);
	elseif (z <= 3.2e+216)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.3e+18], t$95$0, If[LessEqual[z, -8e-76], t$95$2, If[LessEqual[z, 2.65e-160], x, If[LessEqual[z, 2.2e-116], t$95$1, If[LessEqual[z, 8.4e-60], x, If[LessEqual[z, 1.5e+64], t$95$2, If[LessEqual[z, 5.2e+110], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.2e+216], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.3e18 or 3.1999999999999997e216 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

   6. Simplified 69.5%

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

   if -4.3e18 < z < -7.99999999999999942e-76 or 8.39999999999999964e-60 < z < 1.5000000000000001e64

   1. Initial program 99.6%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 75.2%

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

   4. Taylor expanded in y around inf 65.1%

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

   if -7.99999999999999942e-76 < z < 2.6500000000000001e-160 or 2.2000000000000001e-116 < z < 8.39999999999999964e-60

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.2%

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

   if 2.6500000000000001e-160 < z < 2.2000000000000001e-116 or 5.2e110 < z < 3.1999999999999997e216

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 92.0%

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

   4. Taylor expanded in y around inf 63.9%

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

      1. associate-*r* 64.0%

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

      2. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   if 1.5000000000000001e64 < z < 5.2e110

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 90.0%

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

   3. Taylor expanded in z around inf 90.0%

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

   4. Taylor expanded in z around 0 90.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.3 \cdot 10^{+18}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-76}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+64}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{+110}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+216}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 5: 59.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot -6\right)\\ t_1 := z \cdot \left(y \cdot 6\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-75}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+64}:\\ \;\;\;\;\frac{y \cdot z}{0.16666666666666666}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+110}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x -6.0))) (t_1 (* z (* y 6.0))))
   (if (<= z -1.15e+19)
     t_0
     (if (<= z -1.08e-75)
       (* 6.0 (* y z))
       (if (<= z 2.65e-160)
         x
         (if (<= z 2.2e-116)
           t_1
           (if (<= z 5e-57)
             x
             (if (<= z 1.35e+64)
               (/ (* y z) 0.16666666666666666)
               (if (<= z 5.3e+110)
                 (* -6.0 (* x z))
                 (if (<= z 1.22e+215) t_1 t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * -6.0);
	double t_1 = z * (y * 6.0);
	double tmp;
	if (z <= -1.15e+19) {
		tmp = t_0;
	} else if (z <= -1.08e-75) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = t_1;
	} else if (z <= 5e-57) {
		tmp = x;
	} else if (z <= 1.35e+64) {
		tmp = (y * z) / 0.16666666666666666;
	} else if (z <= 5.3e+110) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.22e+215) {
		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 = z * (x * (-6.0d0))
    t_1 = z * (y * 6.0d0)
    if (z <= (-1.15d+19)) then
        tmp = t_0
    else if (z <= (-1.08d-75)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 2.65d-160) then
        tmp = x
    else if (z <= 2.2d-116) then
        tmp = t_1
    else if (z <= 5d-57) then
        tmp = x
    else if (z <= 1.35d+64) then
        tmp = (y * z) / 0.16666666666666666d0
    else if (z <= 5.3d+110) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= 1.22d+215) 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 = z * (x * -6.0);
	double t_1 = z * (y * 6.0);
	double tmp;
	if (z <= -1.15e+19) {
		tmp = t_0;
	} else if (z <= -1.08e-75) {
		tmp = 6.0 * (y * z);
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = t_1;
	} else if (z <= 5e-57) {
		tmp = x;
	} else if (z <= 1.35e+64) {
		tmp = (y * z) / 0.16666666666666666;
	} else if (z <= 5.3e+110) {
		tmp = -6.0 * (x * z);
	} else if (z <= 1.22e+215) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * -6.0)
	t_1 = z * (y * 6.0)
	tmp = 0
	if z <= -1.15e+19:
		tmp = t_0
	elif z <= -1.08e-75:
		tmp = 6.0 * (y * z)
	elif z <= 2.65e-160:
		tmp = x
	elif z <= 2.2e-116:
		tmp = t_1
	elif z <= 5e-57:
		tmp = x
	elif z <= 1.35e+64:
		tmp = (y * z) / 0.16666666666666666
	elif z <= 5.3e+110:
		tmp = -6.0 * (x * z)
	elif z <= 1.22e+215:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * -6.0))
	t_1 = Float64(z * Float64(y * 6.0))
	tmp = 0.0
	if (z <= -1.15e+19)
		tmp = t_0;
	elseif (z <= -1.08e-75)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = t_1;
	elseif (z <= 5e-57)
		tmp = x;
	elseif (z <= 1.35e+64)
		tmp = Float64(Float64(y * z) / 0.16666666666666666);
	elseif (z <= 5.3e+110)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= 1.22e+215)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * -6.0);
	t_1 = z * (y * 6.0);
	tmp = 0.0;
	if (z <= -1.15e+19)
		tmp = t_0;
	elseif (z <= -1.08e-75)
		tmp = 6.0 * (y * z);
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = t_1;
	elseif (z <= 5e-57)
		tmp = x;
	elseif (z <= 1.35e+64)
		tmp = (y * z) / 0.16666666666666666;
	elseif (z <= 5.3e+110)
		tmp = -6.0 * (x * z);
	elseif (z <= 1.22e+215)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+19], t$95$0, If[LessEqual[z, -1.08e-75], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.65e-160], x, If[LessEqual[z, 2.2e-116], t$95$1, If[LessEqual[z, 5e-57], x, If[LessEqual[z, 1.35e+64], N[(N[(y * z), $MachinePrecision] / 0.16666666666666666), $MachinePrecision], If[LessEqual[z, 5.3e+110], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.22e+215], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.15e19 or 1.22000000000000007e215 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   4. Taylor expanded in y around 0 69.4%

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

      1. *-commutative 69.4%

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

      2. associate-*r* 69.5%

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

      3. *-commutative 69.5%

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

   6. Simplified 69.5%

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

   if -1.15e19 < z < -1.08e-75

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.9%

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

   3. Taylor expanded in z around inf 71.4%

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

   4. Taylor expanded in y around inf 64.3%

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

   if -1.08e-75 < z < 2.6500000000000001e-160 or 2.2000000000000001e-116 < z < 5.0000000000000002e-57

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.2%

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

   if 2.6500000000000001e-160 < z < 2.2000000000000001e-116 or 5.2999999999999998e110 < z < 1.22000000000000007e215

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 92.0%

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

   4. Taylor expanded in y around inf 63.9%

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

      1. associate-*r* 64.0%

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

      2. *-commutative 64.0%

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

   6. Simplified 64.0%

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

   if 5.0000000000000002e-57 < z < 1.35e64

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in z around inf 78.2%

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

   4. Taylor expanded in y around inf 65.8%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

   6. Simplified 65.7%

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

      1. associate-*r* 65.7%

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

      2. metadata-eval 65.7%

         \[\leadsto \left(z \cdot \color{blue}{\frac{1}{0.16666666666666666}}\right) \cdot y \]

      3. div-inv 65.7%

         \[\leadsto \color{blue}{\frac{z}{0.16666666666666666}} \cdot y \]

      4. associate-*l/ 65.9%

         \[\leadsto \color{blue}{\frac{z \cdot y}{0.16666666666666666}} \]

   8. Applied egg-rr 65.9%

      \[\leadsto \color{blue}{\frac{z \cdot y}{0.16666666666666666}} \]

   if 1.35e64 < z < 5.2999999999999998e110

   1. Initial program 99.7%

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

   2. Taylor expanded in x around inf 90.0%

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

   3. Taylor expanded in z around inf 90.0%

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

   4. Taylor expanded in z around 0 90.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+19}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-75}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{+64}:\\ \;\;\;\;\frac{y \cdot z}{0.16666666666666666}\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{+110}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{+215}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \end{array} \]

Alternative 6: 82.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* (- y x) z))))
   (if (<= z -5.6e-86)
     t_0
     (if (<= z 2.65e-160)
       x
       (if (<= z 2.2e-116) (* z (* y 6.0)) (if (<= z 1.15e-60) x t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.6e-86) {
		tmp = t_0;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = z * (y * 6.0);
	} else if (z <= 1.15e-60) {
		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 * ((y - x) * z)
    if (z <= (-5.6d-86)) then
        tmp = t_0
    else if (z <= 2.65d-160) then
        tmp = x
    else if (z <= 2.2d-116) then
        tmp = z * (y * 6.0d0)
    else if (z <= 1.15d-60) 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 * ((y - x) * z);
	double tmp;
	if (z <= -5.6e-86) {
		tmp = t_0;
	} else if (z <= 2.65e-160) {
		tmp = x;
	} else if (z <= 2.2e-116) {
		tmp = z * (y * 6.0);
	} else if (z <= 1.15e-60) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * ((y - x) * z)
	tmp = 0
	if z <= -5.6e-86:
		tmp = t_0
	elif z <= 2.65e-160:
		tmp = x
	elif z <= 2.2e-116:
		tmp = z * (y * 6.0)
	elif z <= 1.15e-60:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -5.6e-86)
		tmp = t_0;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= 1.15e-60)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -5.6e-86)
		tmp = t_0;
	elseif (z <= 2.65e-160)
		tmp = x;
	elseif (z <= 2.2e-116)
		tmp = z * (y * 6.0);
	elseif (z <= 1.15e-60)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.6e-86], t$95$0, If[LessEqual[z, 2.65e-160], x, If[LessEqual[z, 2.2e-116], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.15e-60], x, t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.60000000000000019e-86 or 1.1500000000000001e-60 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 93.5%

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

   if -5.60000000000000019e-86 < z < 2.6500000000000001e-160 or 2.2000000000000001e-116 < z < 1.1500000000000001e-60

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 82.8%

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

   if 2.6500000000000001e-160 < z < 2.2000000000000001e-116

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 71.5%

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

   4. Taylor expanded in y around inf 71.5%

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

      1. associate-*r* 71.7%

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

      2. *-commutative 71.7%

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

   6. Simplified 71.7%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{-86}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 2.65 \cdot 10^{-160}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-116}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-60}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -48000000000000.0) (not (<= z 0.17)))
   (* 6.0 (* (- y x) z))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000000000000.0) || !(z <= 0.17)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-48000000000000.0d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000000000000.0) || !(z <= 0.17)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -48000000000000.0) or not (z <= 0.17):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -48000000000000.0) || !(z <= 0.17))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -48000000000000.0) || ~((z <= 0.17)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -48000000000000.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e13 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.4%

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

   if -4.8e13 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.7%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -48000000000000.0) (not (<= z 0.17)))
   (* 6.0 (* (- y x) z))
   (+ x (* z (* y 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000000000000.0) || !(z <= 0.17)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-48000000000000.0d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = 6.0d0 * ((y - x) * z)
    else
        tmp = x + (z * (y * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -48000000000000.0) || !(z <= 0.17)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x + (z * (y * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -48000000000000.0) or not (z <= 0.17):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x + (z * (y * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -48000000000000.0) || !(z <= 0.17))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(z * Float64(y * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -48000000000000.0) || ~((z <= 0.17)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x + (z * (y * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -48000000000000.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.8e13 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.4%

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

   if -4.8e13 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 98.7%

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

      1. associate-*r* 98.8%

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

   4. Simplified 98.8%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -48000000000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(y \cdot 6\right)\\ \end{array} \]

Alternative 9: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 0.17d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.17)) {
		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 <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.17))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 0.17)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around inf 62.4%

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

   3. Taylor expanded in z around inf 62.2%

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

   4. Taylor expanded in z around 0 62.2%

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

   if -0.165000000000000008 < z < 0.170000000000000012

   1. Initial program 99.9%

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

   2. Taylor expanded in z around 0 68.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 36.9% 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. Taylor expanded in z around 0 35.3%

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

3. Final simplification 35.3%

   \[\leadsto x \]

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 2023178 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

  (+ x (* (* (- y x) 6.0) z)))