Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5

Percentage Accurate: 70.8% → 96.3%

Time: 13.3s

Alternatives: 11

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))

C

double code(double x, double y, double z) {
	return 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((x * y) + (x * z)) + (y * z)));
}

Python

def code(x, y, z):
	return 2.0 * math.sqrt((((x * y) + (x * z)) + (y * z)))

Julia

function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(x * y) + Float64(x * z)) + Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Initial Program: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))

C

double code(double x, double y, double z) {
	return 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((((x * y) + (x * z)) + (y * z)))
end function

Java

public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((((x * y) + (x * z)) + (y * z)));
}

Python

def code(x, y, z):
	return 2.0 * math.sqrt((((x * y) + (x * z)) + (y * z)))

Julia

function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(Float64(x * y) + Float64(x * z)) + Float64(y * z))))
end

MATLAB

function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((((x * y) + (x * z)) + (y * z)));
end

Wolfram

code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(N[(x * y), $MachinePrecision] + N[(x * z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Alternative 1: 96.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+55}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-306}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          2.0
          (pow (exp (* 0.25 (- (log (- (- y) z)) (log (/ -1.0 x))))) 2.0))))
   (if (<= y -8.5e+55)
     t_0
     (if (<= y -1.65e-204)
       (* 2.0 (sqrt (* x (+ y z))))
       (if (<= y 4e-306) t_0 (* 2.0 (* (sqrt (+ y x)) (sqrt z))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 2.0 * pow(exp((0.25 * (log((-y - z)) - log((-1.0 / x))))), 2.0);
	double tmp;
	if (y <= -8.5e+55) {
		tmp = t_0;
	} else if (y <= -1.65e-204) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= 4e-306) {
		tmp = t_0;
	} else {
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = 2.0d0 * (exp((0.25d0 * (log((-y - z)) - log(((-1.0d0) / x))))) ** 2.0d0)
    if (y <= (-8.5d+55)) then
        tmp = t_0
    else if (y <= (-1.65d-204)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= 4d-306) then
        tmp = t_0
    else
        tmp = 2.0d0 * (sqrt((y + x)) * sqrt(z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = 2.0 * Math.pow(Math.exp((0.25 * (Math.log((-y - z)) - Math.log((-1.0 / x))))), 2.0);
	double tmp;
	if (y <= -8.5e+55) {
		tmp = t_0;
	} else if (y <= -1.65e-204) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= 4e-306) {
		tmp = t_0;
	} else {
		tmp = 2.0 * (Math.sqrt((y + x)) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 2.0 * math.pow(math.exp((0.25 * (math.log((-y - z)) - math.log((-1.0 / x))))), 2.0)
	tmp = 0
	if y <= -8.5e+55:
		tmp = t_0
	elif y <= -1.65e-204:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= 4e-306:
		tmp = t_0
	else:
		tmp = 2.0 * (math.sqrt((y + x)) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(-y) - z)) - log(Float64(-1.0 / x))))) ^ 2.0))
	tmp = 0.0
	if (y <= -8.5e+55)
		tmp = t_0;
	elseif (y <= -1.65e-204)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= 4e-306)
		tmp = t_0;
	else
		tmp = Float64(2.0 * Float64(sqrt(Float64(y + x)) * sqrt(z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = 2.0 * (exp((0.25 * (log((-y - z)) - log((-1.0 / x))))) ^ 2.0);
	tmp = 0.0;
	if (y <= -8.5e+55)
		tmp = t_0;
	elseif (y <= -1.65e-204)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= 4e-306)
		tmp = t_0;
	else
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[((-y) - z), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+55], t$95$0, If[LessEqual[y, -1.65e-204], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4e-306], t$95$0, N[(2.0 * N[(N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.50000000000000002e55 or -1.65000000000000005e-204 < y < 4.00000000000000011e-306

   1. Initial program 66.9%

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

      1. +-commutative 66.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 66.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 66.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 66.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 66.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 66.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 66.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 66.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 66.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 66.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Step-by-step derivation

      1. add-sqr-sqrt 66.3%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{\sqrt{x \cdot y + z \cdot \left(y + x\right)}} \cdot \sqrt{\sqrt{x \cdot y + z \cdot \left(y + x\right)}}\right)} \]

      2. pow2 66.3%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt{\sqrt{x \cdot y + z \cdot \left(y + x\right)}}\right)}^{2}} \]

      3. pow1/2 66.3%

         \[\leadsto 2 \cdot {\left(\sqrt{\color{blue}{{\left(x \cdot y + z \cdot \left(y + x\right)\right)}^{0.5}}}\right)}^{2} \]

      4. sqrt-pow1 66.4%

         \[\leadsto 2 \cdot {\color{blue}{\left({\left(x \cdot y + z \cdot \left(y + x\right)\right)}^{\left(\frac{0.5}{2}\right)}\right)}}^{2} \]

      5. +-commutative 66.4%

         \[\leadsto 2 \cdot {\left({\color{blue}{\left(z \cdot \left(y + x\right) + x \cdot y\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2} \]

      6. +-commutative 66.4%

         \[\leadsto 2 \cdot {\left({\left(z \cdot \color{blue}{\left(x + y\right)} + x \cdot y\right)}^{\left(\frac{0.5}{2}\right)}\right)}^{2} \]

      7. fma-def 66.5%

         \[\leadsto 2 \cdot {\left({\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{\left(\frac{0.5}{2}\right)}\right)}^{2} \]

      8. metadata-eval 66.5%

         \[\leadsto 2 \cdot {\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{0.25}}\right)}^{2} \]

   5. Applied egg-rr 66.5%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \]

   6. Taylor expanded in x around -inf 46.2%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(-1 \cdot y + -1 \cdot z\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

   if -8.50000000000000002e55 < y < -1.65000000000000005e-204

   1. Initial program 84.1%

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

      1. +-commutative 84.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 84.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 84.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 84.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 84.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 84.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 84.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 84.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 84.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 84.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 55.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if 4.00000000000000011e-306 < y

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around inf 54.5%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + y\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 54.5%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(y + x\right)}} \]

   6. Simplified 54.5%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(y + x\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 54.5%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(x + y\right)}} \]

      2. *-commutative 54.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x + y\right) \cdot z}} \]

      3. sqrt-prod 53.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]

   8. Applied egg-rr 53.4%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+55}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 4 \cdot 10^{-306}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 2: 95.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \log \left(\frac{-1}{x}\right)\\ \mathbf{if}\;y \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(-y\right) - t_0\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot {\left(e^{\left(\log \left(\left(-y\right) - z\right) - t_0\right) \cdot 0.08333333333333333}\right)}^{6}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ -1.0 x))))
   (if (<= y -3.1e+54)
     (* 2.0 (pow (exp (* 0.16666666666666666 (- (log (- y)) t_0))) 3.0))
     (if (<= y -1.65e-204)
       (* 2.0 (sqrt (* x (+ y z))))
       (if (<= y -2.7e-285)
         (*
          2.0
          (pow (exp (* (- (log (- (- y) z)) t_0) 0.08333333333333333)) 6.0))
         (* 2.0 (* (sqrt (+ y x)) (sqrt z))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = log((-1.0 / x));
	double tmp;
	if (y <= -3.1e+54) {
		tmp = 2.0 * pow(exp((0.16666666666666666 * (log(-y) - t_0))), 3.0);
	} else if (y <= -1.65e-204) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= -2.7e-285) {
		tmp = 2.0 * pow(exp(((log((-y - z)) - t_0) * 0.08333333333333333)), 6.0);
	} else {
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = log(((-1.0d0) / x))
    if (y <= (-3.1d+54)) then
        tmp = 2.0d0 * (exp((0.16666666666666666d0 * (log(-y) - t_0))) ** 3.0d0)
    else if (y <= (-1.65d-204)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= (-2.7d-285)) then
        tmp = 2.0d0 * (exp(((log((-y - z)) - t_0) * 0.08333333333333333d0)) ** 6.0d0)
    else
        tmp = 2.0d0 * (sqrt((y + x)) * sqrt(z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = Math.log((-1.0 / x));
	double tmp;
	if (y <= -3.1e+54) {
		tmp = 2.0 * Math.pow(Math.exp((0.16666666666666666 * (Math.log(-y) - t_0))), 3.0);
	} else if (y <= -1.65e-204) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= -2.7e-285) {
		tmp = 2.0 * Math.pow(Math.exp(((Math.log((-y - z)) - t_0) * 0.08333333333333333)), 6.0);
	} else {
		tmp = 2.0 * (Math.sqrt((y + x)) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = math.log((-1.0 / x))
	tmp = 0
	if y <= -3.1e+54:
		tmp = 2.0 * math.pow(math.exp((0.16666666666666666 * (math.log(-y) - t_0))), 3.0)
	elif y <= -1.65e-204:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= -2.7e-285:
		tmp = 2.0 * math.pow(math.exp(((math.log((-y - z)) - t_0) * 0.08333333333333333)), 6.0)
	else:
		tmp = 2.0 * (math.sqrt((y + x)) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = log(Float64(-1.0 / x))
	tmp = 0.0
	if (y <= -3.1e+54)
		tmp = Float64(2.0 * (exp(Float64(0.16666666666666666 * Float64(log(Float64(-y)) - t_0))) ^ 3.0));
	elseif (y <= -1.65e-204)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= -2.7e-285)
		tmp = Float64(2.0 * (exp(Float64(Float64(log(Float64(Float64(-y) - z)) - t_0) * 0.08333333333333333)) ^ 6.0));
	else
		tmp = Float64(2.0 * Float64(sqrt(Float64(y + x)) * sqrt(z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = log((-1.0 / x));
	tmp = 0.0;
	if (y <= -3.1e+54)
		tmp = 2.0 * (exp((0.16666666666666666 * (log(-y) - t_0))) ^ 3.0);
	elseif (y <= -1.65e-204)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= -2.7e-285)
		tmp = 2.0 * (exp(((log((-y - z)) - t_0) * 0.08333333333333333)) ^ 6.0);
	else
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -3.1e+54], N[(2.0 * N[Power[N[Exp[N[(0.16666666666666666 * N[(N[Log[(-y)], $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.65e-204], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -2.7e-285], N[(2.0 * N[Power[N[Exp[N[(N[(N[Log[N[((-y) - z), $MachinePrecision]], $MachinePrecision] - t$95$0), $MachinePrecision] * 0.08333333333333333), $MachinePrecision]], $MachinePrecision], 6.0], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.0999999999999999e54

   1. Initial program 63.0%

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

      1. +-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 62.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}}} \]

      2. pow3 62.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right)}^{3}}} \]

      3. +-commutative 62.5%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{z \cdot \left(y + x\right) + x \cdot y}}\right)}^{3}} \]

      4. +-commutative 62.5%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{z \cdot \color{blue}{\left(x + y\right)} + x \cdot y}\right)}^{3}} \]

      5. fma-def 62.6%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, x + y, x \cdot y\right)}}\right)}^{3}} \]

   5. Applied egg-rr 62.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}}} \]
   6. Step-by-step derivation

      1. pow1/2 62.6%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}\right)}^{0.5}} \]

      2. rem-cube-cbrt 63.2%

         \[\leadsto 2 \cdot {\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{0.5} \]

      3. metadata-eval 63.2%

         \[\leadsto 2 \cdot {\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{\left(0.25 \cdot 2\right)}} \]

      4. pow-pow 62.7%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \]

      5. add-cube-cbrt 61.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)} \]

      6. pow3 61.8%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)}^{3}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}\right)}^{3}} \]

   8. Taylor expanded in z around 0 30.0%

      \[\leadsto 2 \cdot {\color{blue}{\left({\left(x \cdot y\right)}^{0.16666666666666666}\right)}}^{3} \]

   9. Taylor expanded in x around -inf 46.3%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.16666666666666666 \cdot \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{3} \]

   if -3.0999999999999999e54 < y < -1.65000000000000005e-204

   1. Initial program 83.9%

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

      1. +-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 54.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if -1.65000000000000005e-204 < y < -2.6999999999999998e-285

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}}} \]

      2. pow3 72.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right)}^{3}}} \]

      3. +-commutative 72.0%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{z \cdot \left(y + x\right) + x \cdot y}}\right)}^{3}} \]

      4. +-commutative 72.0%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{z \cdot \color{blue}{\left(x + y\right)} + x \cdot y}\right)}^{3}} \]

      5. fma-def 72.0%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, x + y, x \cdot y\right)}}\right)}^{3}} \]

   5. Applied egg-rr 72.0%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}}} \]
   6. Step-by-step derivation

      1. pow1/2 72.0%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}\right)}^{0.5}} \]

      2. rem-cube-cbrt 72.8%

         \[\leadsto 2 \cdot {\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{0.5} \]

      3. metadata-eval 72.8%

         \[\leadsto 2 \cdot {\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{\left(0.25 \cdot 2\right)}} \]

      4. pow-pow 72.5%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \]

      5. add-cube-cbrt 71.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)} \]

      6. pow3 71.5%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)}^{3}} \]

   7. Applied egg-rr 67.1%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}\right)}^{3}} \]
   8. Step-by-step derivation

      1. add-sqr-sqrt 67.1%

         \[\leadsto 2 \cdot {\color{blue}{\left(\sqrt{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}} \cdot \sqrt{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}}\right)}}^{3} \]

      2. unpow-prod-down 67.1%

         \[\leadsto 2 \cdot \color{blue}{\left({\left(\sqrt{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}}\right)}^{3} \cdot {\left(\sqrt{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}}\right)}^{3}\right)} \]

      3. sqrt-pow1 67.1%

         \[\leadsto 2 \cdot \left({\color{blue}{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\left(\frac{0.16666666666666666}{2}\right)}\right)}}^{3} \cdot {\left(\sqrt{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}}\right)}^{3}\right) \]

      4. metadata-eval 67.1%

         \[\leadsto 2 \cdot \left({\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{0.08333333333333333}}\right)}^{3} \cdot {\left(\sqrt{{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}}\right)}^{3}\right) \]

      5. sqrt-pow1 67.1%

         \[\leadsto 2 \cdot \left({\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{3} \cdot {\color{blue}{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\left(\frac{0.16666666666666666}{2}\right)}\right)}}^{3}\right) \]

      6. metadata-eval 67.1%

         \[\leadsto 2 \cdot \left({\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{3} \cdot {\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{0.08333333333333333}}\right)}^{3}\right) \]

   9. Applied egg-rr 67.1%

      \[\leadsto 2 \cdot \color{blue}{\left({\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{3} \cdot {\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{3}\right)} \]
   10. Step-by-step derivation

       1. pow-sqr 67.1%

          \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{\left(2 \cdot 3\right)}} \]

       2. metadata-eval 67.1%

          \[\leadsto 2 \cdot {\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{\color{blue}{6}} \]

   11. Simplified 67.1%

       \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.08333333333333333}\right)}^{6}} \]

   12. Taylor expanded in x around -inf 47.7%

       \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.08333333333333333 \cdot \left(\log \left(-1 \cdot y + -1 \cdot z\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{6} \]

   if -2.6999999999999998e-285 < y

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around inf 55.1%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + y\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(y + x\right)}} \]

   6. Simplified 55.1%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(y + x\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(x + y\right)}} \]

      2. *-commutative 55.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x + y\right) \cdot z}} \]

      3. sqrt-prod 54.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]

   8. Applied egg-rr 54.1%

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -2.7 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot {\left(e^{\left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.08333333333333333}\right)}^{6}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 3: 95.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := \log \left(\frac{-1}{x}\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(-y\right) - t_0\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot {\left(e^{\left(\log \left(\left(-y\right) - z\right) - t_0\right) \cdot 0.16666666666666666}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (log (/ -1.0 x))))
   (if (<= y -4.2e+53)
     (* 2.0 (pow (exp (* 0.16666666666666666 (- (log (- y)) t_0))) 3.0))
     (if (<= y -1.65e-204)
       (* 2.0 (sqrt (* x (+ y z))))
       (if (<= y -3.3e-292)
         (*
          2.0
          (pow (exp (* (- (log (- (- y) z)) t_0) 0.16666666666666666)) 3.0))
         (* 2.0 (* (sqrt (+ y x)) (sqrt z))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = log((-1.0 / x));
	double tmp;
	if (y <= -4.2e+53) {
		tmp = 2.0 * pow(exp((0.16666666666666666 * (log(-y) - t_0))), 3.0);
	} else if (y <= -1.65e-204) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= -3.3e-292) {
		tmp = 2.0 * pow(exp(((log((-y - z)) - t_0) * 0.16666666666666666)), 3.0);
	} else {
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 = log(((-1.0d0) / x))
    if (y <= (-4.2d+53)) then
        tmp = 2.0d0 * (exp((0.16666666666666666d0 * (log(-y) - t_0))) ** 3.0d0)
    else if (y <= (-1.65d-204)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= (-3.3d-292)) then
        tmp = 2.0d0 * (exp(((log((-y - z)) - t_0) * 0.16666666666666666d0)) ** 3.0d0)
    else
        tmp = 2.0d0 * (sqrt((y + x)) * sqrt(z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double t_0 = Math.log((-1.0 / x));
	double tmp;
	if (y <= -4.2e+53) {
		tmp = 2.0 * Math.pow(Math.exp((0.16666666666666666 * (Math.log(-y) - t_0))), 3.0);
	} else if (y <= -1.65e-204) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= -3.3e-292) {
		tmp = 2.0 * Math.pow(Math.exp(((Math.log((-y - z)) - t_0) * 0.16666666666666666)), 3.0);
	} else {
		tmp = 2.0 * (Math.sqrt((y + x)) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = math.log((-1.0 / x))
	tmp = 0
	if y <= -4.2e+53:
		tmp = 2.0 * math.pow(math.exp((0.16666666666666666 * (math.log(-y) - t_0))), 3.0)
	elif y <= -1.65e-204:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= -3.3e-292:
		tmp = 2.0 * math.pow(math.exp(((math.log((-y - z)) - t_0) * 0.16666666666666666)), 3.0)
	else:
		tmp = 2.0 * (math.sqrt((y + x)) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = log(Float64(-1.0 / x))
	tmp = 0.0
	if (y <= -4.2e+53)
		tmp = Float64(2.0 * (exp(Float64(0.16666666666666666 * Float64(log(Float64(-y)) - t_0))) ^ 3.0));
	elseif (y <= -1.65e-204)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= -3.3e-292)
		tmp = Float64(2.0 * (exp(Float64(Float64(log(Float64(Float64(-y) - z)) - t_0) * 0.16666666666666666)) ^ 3.0));
	else
		tmp = Float64(2.0 * Float64(sqrt(Float64(y + x)) * sqrt(z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	t_0 = log((-1.0 / x));
	tmp = 0.0;
	if (y <= -4.2e+53)
		tmp = 2.0 * (exp((0.16666666666666666 * (log(-y) - t_0))) ^ 3.0);
	elseif (y <= -1.65e-204)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= -3.3e-292)
		tmp = 2.0 * (exp(((log((-y - z)) - t_0) * 0.16666666666666666)) ^ 3.0);
	else
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := Block[{t$95$0 = N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[y, -4.2e+53], N[(2.0 * N[Power[N[Exp[N[(0.16666666666666666 * N[(N[Log[(-y)], $MachinePrecision] - t$95$0), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.65e-204], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.3e-292], N[(2.0 * N[Power[N[Exp[N[(N[(N[Log[N[((-y) - z), $MachinePrecision]], $MachinePrecision] - t$95$0), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.2000000000000004e53

   1. Initial program 63.0%

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

      1. +-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 62.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}}} \]

      2. pow3 62.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right)}^{3}}} \]

      3. +-commutative 62.5%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{z \cdot \left(y + x\right) + x \cdot y}}\right)}^{3}} \]

      4. +-commutative 62.5%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{z \cdot \color{blue}{\left(x + y\right)} + x \cdot y}\right)}^{3}} \]

      5. fma-def 62.6%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, x + y, x \cdot y\right)}}\right)}^{3}} \]

   5. Applied egg-rr 62.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}}} \]
   6. Step-by-step derivation

      1. pow1/2 62.6%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}\right)}^{0.5}} \]

      2. rem-cube-cbrt 63.2%

         \[\leadsto 2 \cdot {\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{0.5} \]

      3. metadata-eval 63.2%

         \[\leadsto 2 \cdot {\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{\left(0.25 \cdot 2\right)}} \]

      4. pow-pow 62.7%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \]

      5. add-cube-cbrt 61.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)} \]

      6. pow3 61.8%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)}^{3}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}\right)}^{3}} \]

   8. Taylor expanded in z around 0 30.0%

      \[\leadsto 2 \cdot {\color{blue}{\left({\left(x \cdot y\right)}^{0.16666666666666666}\right)}}^{3} \]

   9. Taylor expanded in x around -inf 46.3%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.16666666666666666 \cdot \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{3} \]

   if -4.2000000000000004e53 < y < -1.65000000000000005e-204

   1. Initial program 83.9%

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

      1. +-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 83.9%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 83.9%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 54.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if -1.65000000000000005e-204 < y < -3.29999999999999995e-292

   1. Initial program 72.8%

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

      1. +-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 72.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 72.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 72.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}}} \]

      2. pow3 72.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right)}^{3}}} \]

      3. +-commutative 72.0%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{z \cdot \left(y + x\right) + x \cdot y}}\right)}^{3}} \]

      4. +-commutative 72.0%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{z \cdot \color{blue}{\left(x + y\right)} + x \cdot y}\right)}^{3}} \]

      5. fma-def 72.0%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, x + y, x \cdot y\right)}}\right)}^{3}} \]

   5. Applied egg-rr 72.0%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}}} \]
   6. Step-by-step derivation

      1. pow1/2 72.0%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}\right)}^{0.5}} \]

      2. rem-cube-cbrt 72.8%

         \[\leadsto 2 \cdot {\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{0.5} \]

      3. metadata-eval 72.8%

         \[\leadsto 2 \cdot {\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{\left(0.25 \cdot 2\right)}} \]

      4. pow-pow 72.5%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \]

      5. add-cube-cbrt 71.4%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)} \]

      6. pow3 71.5%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)}^{3}} \]

   7. Applied egg-rr 67.1%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}\right)}^{3}} \]

   8. Taylor expanded in x around -inf 47.7%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.16666666666666666 \cdot \left(\log \left(-1 \cdot y + -1 \cdot z\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{3} \]

   if -3.29999999999999995e-292 < y

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around inf 55.1%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + y\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(y + x\right)}} \]

   6. Simplified 55.1%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(y + x\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 55.1%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(x + y\right)}} \]

      2. *-commutative 55.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x + y\right) \cdot z}} \]

      3. sqrt-prod 54.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]

   8. Applied egg-rr 54.1%

      \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+53}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq -1.65 \cdot 10^{-204}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot {\left(e^{\left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.16666666666666666}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 4: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-279}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e+54)
   (*
    2.0
    (pow (exp (* 0.16666666666666666 (- (log (- y)) (log (/ -1.0 x))))) 3.0))
   (if (<= y 6.1e-279)
     (* 2.0 (sqrt (* x (+ y z))))
     (* 2.0 (* (sqrt (+ y x)) (sqrt z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+54) {
		tmp = 2.0 * pow(exp((0.16666666666666666 * (log(-y) - log((-1.0 / x))))), 3.0);
	} else if (y <= 6.1e-279) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.1d+54)) then
        tmp = 2.0d0 * (exp((0.16666666666666666d0 * (log(-y) - log(((-1.0d0) / x))))) ** 3.0d0)
    else if (y <= 6.1d-279) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * (sqrt((y + x)) * sqrt(z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e+54) {
		tmp = 2.0 * Math.pow(Math.exp((0.16666666666666666 * (Math.log(-y) - Math.log((-1.0 / x))))), 3.0);
	} else if (y <= 6.1e-279) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * (Math.sqrt((y + x)) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.1e+54:
		tmp = 2.0 * math.pow(math.exp((0.16666666666666666 * (math.log(-y) - math.log((-1.0 / x))))), 3.0)
	elif y <= 6.1e-279:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * (math.sqrt((y + x)) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e+54)
		tmp = Float64(2.0 * (exp(Float64(0.16666666666666666 * Float64(log(Float64(-y)) - log(Float64(-1.0 / x))))) ^ 3.0));
	elseif (y <= 6.1e-279)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * Float64(sqrt(Float64(y + x)) * sqrt(z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.1e+54)
		tmp = 2.0 * (exp((0.16666666666666666 * (log(-y) - log((-1.0 / x))))) ^ 3.0);
	elseif (y <= 6.1e-279)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.1e+54], N[(2.0 * N[Power[N[Exp[N[(0.16666666666666666 * N[(N[Log[(-y)], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.1e-279], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.0999999999999999e54

   1. Initial program 63.0%

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

      1. +-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 63.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 63.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]
   4. Step-by-step derivation

      1. add-cube-cbrt 62.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)} \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right) \cdot \sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}}} \]

      2. pow3 62.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{x \cdot y + z \cdot \left(y + x\right)}\right)}^{3}}} \]

      3. +-commutative 62.5%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{z \cdot \left(y + x\right) + x \cdot y}}\right)}^{3}} \]

      4. +-commutative 62.5%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{z \cdot \color{blue}{\left(x + y\right)} + x \cdot y}\right)}^{3}} \]

      5. fma-def 62.6%

         \[\leadsto 2 \cdot \sqrt{{\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(z, x + y, x \cdot y\right)}}\right)}^{3}} \]

   5. Applied egg-rr 62.6%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}}} \]
   6. Step-by-step derivation

      1. pow1/2 62.6%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\sqrt[3]{\mathsf{fma}\left(z, x + y, x \cdot y\right)}\right)}^{3}\right)}^{0.5}} \]

      2. rem-cube-cbrt 63.2%

         \[\leadsto 2 \cdot {\color{blue}{\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}}^{0.5} \]

      3. metadata-eval 63.2%

         \[\leadsto 2 \cdot {\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{\color{blue}{\left(0.25 \cdot 2\right)}} \]

      4. pow-pow 62.7%

         \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \]

      5. add-cube-cbrt 61.8%

         \[\leadsto 2 \cdot \color{blue}{\left(\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}} \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right) \cdot \sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)} \]

      6. pow3 61.8%

         \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt[3]{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.25}\right)}^{2}}\right)}^{3}} \]

   7. Applied egg-rr 57.7%

      \[\leadsto 2 \cdot \color{blue}{{\left({\left(\mathsf{fma}\left(z, x + y, x \cdot y\right)\right)}^{0.16666666666666666}\right)}^{3}} \]

   8. Taylor expanded in z around 0 30.0%

      \[\leadsto 2 \cdot {\color{blue}{\left({\left(x \cdot y\right)}^{0.16666666666666666}\right)}}^{3} \]

   9. Taylor expanded in x around -inf 46.3%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.16666666666666666 \cdot \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}}^{3} \]

   if -3.0999999999999999e54 < y < 6.0999999999999999e-279

   1. Initial program 81.5%

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

      1. +-commutative 81.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 81.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 81.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 81.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 81.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 81.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 81.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 81.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 81.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 81.5%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 59.7%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if 6.0999999999999999e-279 < y

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around inf 53.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + y\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(y + x\right)}} \]

   6. Simplified 53.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(y + x\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(x + y\right)}} \]

      2. *-commutative 53.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x + y\right) \cdot z}} \]

      3. sqrt-prod 54.0%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]

   8. Applied egg-rr 54.0%

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

4. Final simplification 54.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{+54}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq 6.1 \cdot 10^{-279}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 5: 84.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.6e-280)
   (* 2.0 (sqrt (* x (+ y z))))
   (* 2.0 (* (sqrt (+ y x)) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.6e-280) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= 2.6d-280) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * (sqrt((y + x)) * sqrt(z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.6e-280) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * (Math.sqrt((y + x)) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 2.6e-280:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * (math.sqrt((y + x)) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2.6e-280)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * Float64(sqrt(Float64(y + x)) * sqrt(z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.6e-280)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 2.6e-280], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.6e-280

   1. Initial program 75.6%

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

      1. +-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.6%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.6%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 51.1%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if 2.6e-280 < y

   1. Initial program 75.0%

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

      1. +-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.0%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.0%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around inf 53.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + y\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(y + x\right)}} \]

   6. Simplified 53.4%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(y + x\right)}} \]
   7. Step-by-step derivation

      1. +-commutative 53.4%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(x + y\right)}} \]

      2. *-commutative 53.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x + y\right) \cdot z}} \]

      3. sqrt-prod 54.0%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{x + y} \cdot \sqrt{z}\right)} \]

   8. Applied egg-rr 54.0%

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

4. Final simplification 52.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.6 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 6: 83.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 3.6e-242)
   (* 2.0 (sqrt (+ (* y x) (* z (+ y x)))))
   (* 2.0 (* (sqrt z) (sqrt y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e-242) {
		tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 3.6d-242) then
        tmp = 2.0d0 * sqrt(((y * x) + (z * (y + x))))
    else
        tmp = 2.0d0 * (sqrt(z) * sqrt(y))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.6e-242) {
		tmp = 2.0 * Math.sqrt(((y * x) + (z * (y + x))));
	} else {
		tmp = 2.0 * (Math.sqrt(z) * Math.sqrt(y));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 3.6e-242:
		tmp = 2.0 * math.sqrt(((y * x) + (z * (y + x))))
	else:
		tmp = 2.0 * (math.sqrt(z) * math.sqrt(y))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 3.6e-242)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y * x) + Float64(z * Float64(y + x)))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(y)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 3.6e-242)
		tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
	else
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 3.6e-242], N[(2.0 * N[Sqrt[N[(N[(y * x), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.60000000000000014e-242

   1. Initial program 75.1%

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

      1. +-commutative 75.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.1%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.1%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   if 3.60000000000000014e-242 < y

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around 0 33.1%

      \[\leadsto 2 \cdot \color{blue}{\sqrt{y \cdot z}} \]
   5. Step-by-step derivation

      1. *-commutative 33.1%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot y}} \]

      2. sqrt-prod 41.1%

         \[\leadsto 2 \cdot \color{blue}{\left(\sqrt{z} \cdot \sqrt{y}\right)} \]

   6. Applied egg-rr 41.1%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.6 \cdot 10^{-242}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 7: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* 2.0 (sqrt (+ (* y x) (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 2.0 * sqrt(((y * x) + (z * (y + x))));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt(((y * x) + (z * (y + x))))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt(((y * x) + (z * (y + x))));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 2.0 * math.sqrt(((y * x) + (z * (y + x))))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(Float64(y * x) + Float64(z * Float64(y + x)))))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(N[(y * x), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.3%

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

   1. +-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

   2. associate-+r+ 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

   3. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

   4. +-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

   5. associate-+l+ 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

   6. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

   7. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

   8. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

   9. distribute-lft-out 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

3. Simplified 75.3%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

4. Final simplification 75.3%

   \[\leadsto 2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)} \]

Alternative 8: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.75e-277) (* 2.0 (sqrt (* x (+ y z)))) (* 2.0 (sqrt (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-277) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * sqrt((y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.75d-277)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * sqrt((y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-277) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * Math.sqrt((y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.75e-277:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * math.sqrt((y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.75e-277)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * sqrt(Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.75e-277)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * sqrt((y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -1.75e-277], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.74999999999999991e-277

   1. Initial program 74.8%

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

      1. +-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 47.8%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if -1.74999999999999991e-277 < y

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around 0 30.2%

      \[\leadsto 2 \cdot \color{blue}{\sqrt{y \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 9: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-271) (* 2.0 (sqrt (* x (+ y z)))) (* 2.0 (sqrt (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-271) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * sqrt((z * (y + x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
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 <= (-4d-271)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * sqrt((z * (y + x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-271) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * Math.sqrt((z * (y + x)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -4e-271:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * math.sqrt((z * (y + x)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -4e-271)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e-271)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * sqrt((z * (y + x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -4e-271], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999985e-271

   1. Initial program 75.2%

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

      1. +-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.2%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.2%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around inf 47.7%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot \left(y + z\right)}} \]

   if -3.99999999999999985e-271 < y

   1. Initial program 75.5%

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

      1. +-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.5%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.5%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around inf 56.0%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{z \cdot \left(x + y\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 56.0%

         \[\leadsto 2 \cdot \sqrt{z \cdot \color{blue}{\left(y + x\right)}} \]

   6. Simplified 56.0%

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

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 10: 68.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.75e-277) (* 2.0 (sqrt (* y x))) (* 2.0 (sqrt (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-277) {
		tmp = 2.0 * sqrt((y * x));
	} else {
		tmp = 2.0 * sqrt((y * z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.75d-277)) then
        tmp = 2.0d0 * sqrt((y * x))
    else
        tmp = 2.0d0 * sqrt((y * z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.75e-277) {
		tmp = 2.0 * Math.sqrt((y * x));
	} else {
		tmp = 2.0 * Math.sqrt((y * z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.75e-277:
		tmp = 2.0 * math.sqrt((y * x))
	else:
		tmp = 2.0 * math.sqrt((y * z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.75e-277)
		tmp = Float64(2.0 * sqrt(Float64(y * x)));
	else
		tmp = Float64(2.0 * sqrt(Float64(y * z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.75e-277)
		tmp = 2.0 * sqrt((y * x));
	else
		tmp = 2.0 * sqrt((y * z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -1.75e-277], N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.74999999999999991e-277

   1. Initial program 74.8%

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

      1. +-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 74.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 74.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in z around 0 28.8%

      \[\leadsto 2 \cdot \color{blue}{\sqrt{x \cdot y}} \]
   5. Step-by-step derivation

      1. *-commutative 28.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x}} \]

   6. Simplified 28.8%

      \[\leadsto 2 \cdot \color{blue}{\sqrt{y \cdot x}} \]

   if -1.74999999999999991e-277 < y

   1. Initial program 75.8%

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

      1. +-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

      2. associate-+r+ 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

      3. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

      4. +-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

      5. associate-+l+ 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

      6. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

      7. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

      8. *-commutative 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

      9. distribute-lft-out 75.8%

         \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

   3. Simplified 75.8%

      \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

   4. Taylor expanded in x around 0 30.2%

      \[\leadsto 2 \cdot \color{blue}{\sqrt{y \cdot z}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.75 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 11: 35.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ 2 \cdot \sqrt{y \cdot x} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z) :precision binary64 (* 2.0 (sqrt (* y x))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	return 2.0 * sqrt((y * x));
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((y * x))
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	return 2.0 * Math.sqrt((y * x));
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	return 2.0 * math.sqrt((y * x))

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	return Float64(2.0 * sqrt(Float64(y * x)))
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp = code(x, y, z)
	tmp = 2.0 * sqrt((y * x));
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 75.3%

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

   1. +-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(x \cdot z + x \cdot y\right)} + y \cdot z} \]

   2. associate-+r+ 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot z + \left(x \cdot y + y \cdot z\right)}} \]

   3. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot z + \left(\color{blue}{y \cdot x} + y \cdot z\right)} \]

   4. +-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{\left(y \cdot x + y \cdot z\right) + x \cdot z}} \]

   5. associate-+l+ 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x + \left(y \cdot z + x \cdot z\right)}} \]

   6. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{x \cdot y} + \left(y \cdot z + x \cdot z\right)} \]

   7. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(\color{blue}{z \cdot y} + x \cdot z\right)} \]

   8. *-commutative 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \left(z \cdot y + \color{blue}{z \cdot x}\right)} \]

   9. distribute-lft-out 75.3%

      \[\leadsto 2 \cdot \sqrt{x \cdot y + \color{blue}{z \cdot \left(y + x\right)}} \]

3. Simplified 75.3%

   \[\leadsto \color{blue}{2 \cdot \sqrt{x \cdot y + z \cdot \left(y + x\right)}} \]

4. Taylor expanded in z around 0 25.3%

   \[\leadsto 2 \cdot \color{blue}{\sqrt{x \cdot y}} \]
5. Step-by-step derivation

   1. *-commutative 25.3%

      \[\leadsto 2 \cdot \sqrt{\color{blue}{y \cdot x}} \]

6. Simplified 25.3%

   \[\leadsto 2 \cdot \color{blue}{\sqrt{y \cdot x}} \]

7. Final simplification 25.3%

   \[\leadsto 2 \cdot \sqrt{y \cdot x} \]

Developer target: 82.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\\ \mathbf{if}\;z < 7.636950090573675 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(t_0 \cdot t_0\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z)))
          (* (pow z 0.25) (pow y 0.25)))))
   (if (< z 7.636950090573675e+176)
     (* 2.0 (sqrt (+ (* (+ x y) z) (* x y))))
     (* (* t_0 t_0) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = (0.25 * ((pow(y, -0.75) * (pow(z, -0.75) * x)) * (y + z))) + (pow(z, 0.25) * pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	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 = (0.25d0 * (((y ** (-0.75d0)) * ((z ** (-0.75d0)) * x)) * (y + z))) + ((z ** 0.25d0) * (y ** 0.25d0))
    if (z < 7.636950090573675d+176) then
        tmp = 2.0d0 * sqrt((((x + y) * z) + (x * y)))
    else
        tmp = (t_0 * t_0) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.25 * ((Math.pow(y, -0.75) * (Math.pow(z, -0.75) * x)) * (y + z))) + (Math.pow(z, 0.25) * Math.pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * Math.sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.25 * ((math.pow(y, -0.75) * (math.pow(z, -0.75) * x)) * (y + z))) + (math.pow(z, 0.25) * math.pow(y, 0.25))
	tmp = 0
	if z < 7.636950090573675e+176:
		tmp = 2.0 * math.sqrt((((x + y) * z) + (x * y)))
	else:
		tmp = (t_0 * t_0) * 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.25 * Float64(Float64((y ^ -0.75) * Float64((z ^ -0.75) * x)) * Float64(y + z))) + Float64((z ^ 0.25) * (y ^ 0.25)))
	tmp = 0.0
	if (z < 7.636950090573675e+176)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(x + y) * z) + Float64(x * y))));
	else
		tmp = Float64(Float64(t_0 * t_0) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.25 * (((y ^ -0.75) * ((z ^ -0.75) * x)) * (y + z))) + ((z ^ 0.25) * (y ^ 0.25));
	tmp = 0.0;
	if (z < 7.636950090573675e+176)
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	else
		tmp = (t_0 * t_0) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.25 * N[(N[(N[Power[y, -0.75], $MachinePrecision] * N[(N[Power[z, -0.75], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 0.25], $MachinePrecision] * N[Power[y, 0.25], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, 7.636950090573675e+176], N[(2.0 * N[Sqrt[N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 * t$95$0), $MachinePrecision] * 2.0), $MachinePrecision]]]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :herbie-target
  (if (< z 7.636950090573675e+176) (* 2.0 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25))) (+ (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z))) (* (pow z 0.25) (pow y 0.25)))) 2.0))

  (* 2.0 (sqrt (+ (+ (* x y) (* x z)) (* y z)))))