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

Percentage Accurate: 71.5% → 95.1%

Time: 10.8s

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: 71.5% 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: 95.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ t_1 := x \cdot \left(y + z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;2 \cdot \sqrt{t_1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-168} \lor \neg \left(y \leq 7.5 \cdot 10^{+20}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{t_1 + y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          2.0
          (pow (exp (* 0.25 (- (log (- (- z) y)) (log (/ -1.0 x))))) 2.0)))
        (t_1 (* x (+ y z))))
   (if (<= y -2.6e+43)
     t_0
     (if (<= y -2.5e-187)
       (* 2.0 (sqrt t_1))
       (if (<= y 4.5e-272)
         t_0
         (if (or (<= y 8.5e-168) (not (<= y 7.5e+20)))
           (* 2.0 (* (sqrt y) (sqrt z)))
           (* 2.0 (sqrt (+ t_1 (* y 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((-z - y)) - log((-1.0 / x))))), 2.0);
	double t_1 = x * (y + z);
	double tmp;
	if (y <= -2.6e+43) {
		tmp = t_0;
	} else if (y <= -2.5e-187) {
		tmp = 2.0 * sqrt(t_1);
	} else if (y <= 4.5e-272) {
		tmp = t_0;
	} else if ((y <= 8.5e-168) || !(y <= 7.5e+20)) {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	} else {
		tmp = 2.0 * sqrt((t_1 + (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 2.0d0 * (exp((0.25d0 * (log((-z - y)) - log(((-1.0d0) / x))))) ** 2.0d0)
    t_1 = x * (y + z)
    if (y <= (-2.6d+43)) then
        tmp = t_0
    else if (y <= (-2.5d-187)) then
        tmp = 2.0d0 * sqrt(t_1)
    else if (y <= 4.5d-272) then
        tmp = t_0
    else if ((y <= 8.5d-168) .or. (.not. (y <= 7.5d+20))) then
        tmp = 2.0d0 * (sqrt(y) * sqrt(z))
    else
        tmp = 2.0d0 * sqrt((t_1 + (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 t_0 = 2.0 * Math.pow(Math.exp((0.25 * (Math.log((-z - y)) - Math.log((-1.0 / x))))), 2.0);
	double t_1 = x * (y + z);
	double tmp;
	if (y <= -2.6e+43) {
		tmp = t_0;
	} else if (y <= -2.5e-187) {
		tmp = 2.0 * Math.sqrt(t_1);
	} else if (y <= 4.5e-272) {
		tmp = t_0;
	} else if ((y <= 8.5e-168) || !(y <= 7.5e+20)) {
		tmp = 2.0 * (Math.sqrt(y) * Math.sqrt(z));
	} else {
		tmp = 2.0 * Math.sqrt((t_1 + (y * 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((-z - y)) - math.log((-1.0 / x))))), 2.0)
	t_1 = x * (y + z)
	tmp = 0
	if y <= -2.6e+43:
		tmp = t_0
	elif y <= -2.5e-187:
		tmp = 2.0 * math.sqrt(t_1)
	elif y <= 4.5e-272:
		tmp = t_0
	elif (y <= 8.5e-168) or not (y <= 7.5e+20):
		tmp = 2.0 * (math.sqrt(y) * math.sqrt(z))
	else:
		tmp = 2.0 * math.sqrt((t_1 + (y * 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(-z) - y)) - log(Float64(-1.0 / x))))) ^ 2.0))
	t_1 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (y <= -2.6e+43)
		tmp = t_0;
	elseif (y <= -2.5e-187)
		tmp = Float64(2.0 * sqrt(t_1));
	elseif (y <= 4.5e-272)
		tmp = t_0;
	elseif ((y <= 8.5e-168) || !(y <= 7.5e+20))
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	else
		tmp = Float64(2.0 * sqrt(Float64(t_1 + Float64(y * 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((-z - y)) - log((-1.0 / x))))) ^ 2.0);
	t_1 = x * (y + z);
	tmp = 0.0;
	if (y <= -2.6e+43)
		tmp = t_0;
	elseif (y <= -2.5e-187)
		tmp = 2.0 * sqrt(t_1);
	elseif (y <= 4.5e-272)
		tmp = t_0;
	elseif ((y <= 8.5e-168) || ~((y <= 7.5e+20)))
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	else
		tmp = 2.0 * sqrt((t_1 + (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_] := Block[{t$95$0 = N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[((-z) - y), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+43], t$95$0, If[LessEqual[y, -2.5e-187], N[(2.0 * N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-272], t$95$0, If[Or[LessEqual[y, 8.5e-168], N[Not[LessEqual[y, 7.5e+20]], $MachinePrecision]], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(t$95$1 + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.60000000000000021e43 or -2.4999999999999998e-187 < y < 4.4999999999999998e-272

   1. Initial program 68.3%

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

      1. distribute-lft-out 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in y around 0 68.3%

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

      1. add-sqr-sqrt 67.7%

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

      2. pow2 67.7%

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

      3. pow1/2 67.7%

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

      4. sqrt-pow1 67.8%

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

      5. fma-def 68.2%

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

      6. metadata-eval 68.2%

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

   6. Applied egg-rr 68.2%

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

   7. Taylor expanded in x around -inf 44.2%

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

   if -2.60000000000000021e43 < y < -2.4999999999999998e-187

   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. distribute-lft-out 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 63.3%

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

   if 4.4999999999999998e-272 < y < 8.4999999999999994e-168 or 7.5e20 < y

   1. Initial program 62.2%

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

      1. distribute-lft-out 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in x around 0 25.7%

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

      1. sqrt-prod 36.1%

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

   6. Applied egg-rr 36.1%

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

   if 8.4999999999999994e-168 < y < 7.5e20

   1. Initial program 93.6%

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

      1. distribute-lft-out 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 50.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq -2.5 \cdot 10^{-187}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-168} \lor \neg \left(y \leq 7.5 \cdot 10^{+20}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \end{array} \]

Alternative 2: 94.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{\left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.16666666666666666}\right)}^{3}\\ t_1 := x \cdot \left(y + z\right)\\ \mathbf{if}\;y \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-187}:\\ \;\;\;\;2 \cdot \sqrt{t_1}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-168} \lor \neg \left(y \leq 1.45 \cdot 10^{+21}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{t_1 + y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          2.0
          (pow
           (exp (* (- (log (- (- z) y)) (log (/ -1.0 x))) 0.16666666666666666))
           3.0)))
        (t_1 (* x (+ y z))))
   (if (<= y -2.6e+43)
     t_0
     (if (<= y -2e-187)
       (* 2.0 (sqrt t_1))
       (if (<= y 4.5e-272)
         t_0
         (if (or (<= y 8.5e-168) (not (<= y 1.45e+21)))
           (* 2.0 (* (sqrt y) (sqrt z)))
           (* 2.0 (sqrt (+ t_1 (* y z))))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 2.0 * pow(exp(((log((-z - y)) - log((-1.0 / x))) * 0.16666666666666666)), 3.0);
	double t_1 = x * (y + z);
	double tmp;
	if (y <= -2.6e+43) {
		tmp = t_0;
	} else if (y <= -2e-187) {
		tmp = 2.0 * sqrt(t_1);
	} else if (y <= 4.5e-272) {
		tmp = t_0;
	} else if ((y <= 8.5e-168) || !(y <= 1.45e+21)) {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	} else {
		tmp = 2.0 * sqrt((t_1 + (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 2.0d0 * (exp(((log((-z - y)) - log(((-1.0d0) / x))) * 0.16666666666666666d0)) ** 3.0d0)
    t_1 = x * (y + z)
    if (y <= (-2.6d+43)) then
        tmp = t_0
    else if (y <= (-2d-187)) then
        tmp = 2.0d0 * sqrt(t_1)
    else if (y <= 4.5d-272) then
        tmp = t_0
    else if ((y <= 8.5d-168) .or. (.not. (y <= 1.45d+21))) then
        tmp = 2.0d0 * (sqrt(y) * sqrt(z))
    else
        tmp = 2.0d0 * sqrt((t_1 + (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 t_0 = 2.0 * Math.pow(Math.exp(((Math.log((-z - y)) - Math.log((-1.0 / x))) * 0.16666666666666666)), 3.0);
	double t_1 = x * (y + z);
	double tmp;
	if (y <= -2.6e+43) {
		tmp = t_0;
	} else if (y <= -2e-187) {
		tmp = 2.0 * Math.sqrt(t_1);
	} else if (y <= 4.5e-272) {
		tmp = t_0;
	} else if ((y <= 8.5e-168) || !(y <= 1.45e+21)) {
		tmp = 2.0 * (Math.sqrt(y) * Math.sqrt(z));
	} else {
		tmp = 2.0 * Math.sqrt((t_1 + (y * z)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	t_0 = 2.0 * math.pow(math.exp(((math.log((-z - y)) - math.log((-1.0 / x))) * 0.16666666666666666)), 3.0)
	t_1 = x * (y + z)
	tmp = 0
	if y <= -2.6e+43:
		tmp = t_0
	elif y <= -2e-187:
		tmp = 2.0 * math.sqrt(t_1)
	elif y <= 4.5e-272:
		tmp = t_0
	elif (y <= 8.5e-168) or not (y <= 1.45e+21):
		tmp = 2.0 * (math.sqrt(y) * math.sqrt(z))
	else:
		tmp = 2.0 * math.sqrt((t_1 + (y * z)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	t_0 = Float64(2.0 * (exp(Float64(Float64(log(Float64(Float64(-z) - y)) - log(Float64(-1.0 / x))) * 0.16666666666666666)) ^ 3.0))
	t_1 = Float64(x * Float64(y + z))
	tmp = 0.0
	if (y <= -2.6e+43)
		tmp = t_0;
	elseif (y <= -2e-187)
		tmp = Float64(2.0 * sqrt(t_1));
	elseif (y <= 4.5e-272)
		tmp = t_0;
	elseif ((y <= 8.5e-168) || !(y <= 1.45e+21))
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	else
		tmp = Float64(2.0 * sqrt(Float64(t_1 + Float64(y * 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(((log((-z - y)) - log((-1.0 / x))) * 0.16666666666666666)) ^ 3.0);
	t_1 = x * (y + z);
	tmp = 0.0;
	if (y <= -2.6e+43)
		tmp = t_0;
	elseif (y <= -2e-187)
		tmp = 2.0 * sqrt(t_1);
	elseif (y <= 4.5e-272)
		tmp = t_0;
	elseif ((y <= 8.5e-168) || ~((y <= 1.45e+21)))
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	else
		tmp = 2.0 * sqrt((t_1 + (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_] := Block[{t$95$0 = N[(2.0 * N[Power[N[Exp[N[(N[(N[Log[N[((-z) - y), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 0.16666666666666666), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2.6e+43], t$95$0, If[LessEqual[y, -2e-187], N[(2.0 * N[Sqrt[t$95$1], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.5e-272], t$95$0, If[Or[LessEqual[y, 8.5e-168], N[Not[LessEqual[y, 1.45e+21]], $MachinePrecision]], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(t$95$1 + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.60000000000000021e43 or -2e-187 < y < 4.4999999999999998e-272

   1. Initial program 68.3%

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

      1. distribute-lft-out 68.3%

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

   3. Simplified 68.3%

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

   4. Taylor expanded in y around 0 68.3%

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

      1. add-cube-cbrt 67.0%

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

      2. pow3 67.1%

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

      3. fma-def 67.3%

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

   6. Applied egg-rr 67.3%

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

   7. Taylor expanded in x around -inf 43.9%

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

   if -2.60000000000000021e43 < y < -2e-187

   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. distribute-lft-out 84.1%

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

   3. Simplified 84.1%

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

   4. Taylor expanded in x around inf 63.3%

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

   if 4.4999999999999998e-272 < y < 8.4999999999999994e-168 or 1.45e21 < y

   1. Initial program 62.2%

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

      1. distribute-lft-out 62.3%

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

   3. Simplified 62.3%

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

   4. Taylor expanded in x around 0 25.7%

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

      1. sqrt-prod 36.1%

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

   6. Applied egg-rr 36.1%

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

   if 8.4999999999999994e-168 < y < 1.45e21

   1. Initial program 93.6%

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

      1. distribute-lft-out 93.6%

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

   3. Simplified 93.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot {\left(e^{\left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.16666666666666666}\right)}^{3}\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-187}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{-272}:\\ \;\;\;\;2 \cdot {\left(e^{\left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.16666666666666666}\right)}^{3}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{-168} \lor \neg \left(y \leq 1.45 \cdot 10^{+21}\right):\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \end{array} \]

Alternative 3: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+44}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - x\right) - \log \left(\frac{-1}{y}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.4e+44)
   (* 2.0 (pow (exp (* 0.25 (- (log (- (- z) x)) (log (/ -1.0 y))))) 2.0))
   (if (<= y 7.5e+20)
     (* 2.0 (sqrt (fma x y (* z (+ y x)))))
     (* 2.0 (* (sqrt y) (sqrt z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.4e+44) {
		tmp = 2.0 * pow(exp((0.25 * (log((-z - x)) - log((-1.0 / y))))), 2.0);
	} else if (y <= 7.5e+20) {
		tmp = 2.0 * sqrt(fma(x, y, (z * (y + x))));
	} else {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.4e+44)
		tmp = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(-z) - x)) - log(Float64(-1.0 / y))))) ^ 2.0));
	elseif (y <= 7.5e+20)
		tmp = Float64(2.0 * sqrt(fma(x, y, Float64(z * Float64(y + x)))));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	end
	return 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, -1.4e+44], N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[((-z) - x), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.5e+20], N[(2.0 * N[Sqrt[N[(x * y + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.4e44

   1. Initial program 58.3%

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

      1. distribute-lft-out 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in y around 0 58.3%

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

      1. add-sqr-sqrt 57.8%

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

      2. pow2 57.8%

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

      3. pow1/2 57.8%

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

      4. sqrt-pow1 57.8%

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

      5. fma-def 58.5%

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

      6. metadata-eval 58.5%

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

   6. Applied egg-rr 58.5%

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

   7. Taylor expanded in y around -inf 85.1%

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

   if -1.4e44 < y < 7.5e20

   1. Initial program 85.8%

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

      1. associate-+l+ 85.8%

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

      2. fma-def 85.8%

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

      3. distribute-rgt-out 85.8%

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

   3. Simplified 85.8%

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

   if 7.5e20 < y

   1. Initial program 54.9%

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

      1. distribute-lft-out 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in x around 0 30.1%

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

      1. sqrt-prod 41.7%

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

   6. Applied egg-rr 41.7%

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

4. Final simplification 74.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.4 \cdot 10^{+44}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - x\right) - \log \left(\frac{-1}{y}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 4: 94.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot e^{\left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.5}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -6.5e+43)
   (* 2.0 (exp (* (- (log (- y)) (log (/ -1.0 x))) 0.5)))
   (if (<= y 5.5e+22)
     (* 2.0 (sqrt (fma x y (* z (+ y x)))))
     (* 2.0 (* (sqrt y) (sqrt z))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.5e+43) {
		tmp = 2.0 * exp(((log(-y) - log((-1.0 / x))) * 0.5));
	} else if (y <= 5.5e+22) {
		tmp = 2.0 * sqrt(fma(x, y, (z * (y + x))));
	} else {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -6.5e+43)
		tmp = Float64(2.0 * exp(Float64(Float64(log(Float64(-y)) - log(Float64(-1.0 / x))) * 0.5)));
	elseif (y <= 5.5e+22)
		tmp = Float64(2.0 * sqrt(fma(x, y, Float64(z * Float64(y + x)))));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	end
	return 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, -6.5e+43], N[(2.0 * N[Exp[N[(N[(N[Log[(-y)], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * 0.5), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5.5e+22], N[(2.0 * N[Sqrt[N[(x * y + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.4999999999999998e43

   1. Initial program 58.3%

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

      1. distribute-lft-out 58.3%

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

   3. Simplified 58.3%

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

   4. Taylor expanded in z around 0 26.6%

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

      1. pow1/2 26.9%

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

      2. pow-to-exp 25.0%

         \[\leadsto 2 \cdot \color{blue}{e^{\log \left(y \cdot x\right) \cdot 0.5}} \]

      3. *-commutative 25.0%

         \[\leadsto 2 \cdot e^{\log \color{blue}{\left(x \cdot y\right)} \cdot 0.5} \]

   6. Applied egg-rr 25.0%

      \[\leadsto 2 \cdot \color{blue}{e^{\log \left(x \cdot y\right) \cdot 0.5}} \]

   7. Taylor expanded in x around -inf 37.3%

      \[\leadsto 2 \cdot e^{\color{blue}{\left(-1 \cdot \log \left(\frac{-1}{x}\right) + \log \left(-1 \cdot y\right)\right)} \cdot 0.5} \]
   8. Step-by-step derivation

      1. +-commutative 37.3%

         \[\leadsto 2 \cdot e^{\color{blue}{\left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)} \cdot 0.5} \]

      2. mul-1-neg 37.3%

         \[\leadsto 2 \cdot e^{\left(\log \left(-1 \cdot y\right) + \color{blue}{\left(-\log \left(\frac{-1}{x}\right)\right)}\right) \cdot 0.5} \]

      3. unsub-neg 37.3%

         \[\leadsto 2 \cdot e^{\color{blue}{\left(\log \left(-1 \cdot y\right) - \log \left(\frac{-1}{x}\right)\right)} \cdot 0.5} \]

      4. mul-1-neg 37.3%

         \[\leadsto 2 \cdot e^{\left(\log \color{blue}{\left(-y\right)} - \log \left(\frac{-1}{x}\right)\right) \cdot 0.5} \]

   9. Simplified 37.3%

      \[\leadsto 2 \cdot e^{\color{blue}{\left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right)} \cdot 0.5} \]

   if -6.4999999999999998e43 < y < 5.50000000000000021e22

   1. Initial program 85.8%

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

      1. associate-+l+ 85.8%

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

      2. fma-def 85.8%

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

      3. distribute-rgt-out 85.8%

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

   3. Simplified 85.8%

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

   if 5.50000000000000021e22 < y

   1. Initial program 54.9%

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

      1. distribute-lft-out 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in x around 0 30.1%

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

      1. sqrt-prod 41.7%

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

   6. Applied egg-rr 41.7%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.5 \cdot 10^{+43}:\\ \;\;\;\;2 \cdot e^{\left(\log \left(-y\right) - \log \left(\frac{-1}{x}\right)\right) \cdot 0.5}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{+22}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(x, y, z \cdot \left(y + x\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 5: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2e+23)
   (* 2.0 (sqrt (fma z (+ y x) (* y x))))
   (* 2.0 (* (sqrt y) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2e+23) {
		tmp = 2.0 * sqrt(fma(z, (y + x), (y * x)));
	} else {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2e+23)
		tmp = Float64(2.0 * sqrt(fma(z, Float64(y + x), Float64(y * x))));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	end
	return 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, 2e+23], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.9999999999999998e23

   1. Initial program 78.1%

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

      1. associate-+l+ 78.1%

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

      2. +-commutative 78.1%

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

      3. distribute-rgt-out 78.1%

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

      4. fma-def 78.2%

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

   3. Simplified 78.2%

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

   if 1.9999999999999998e23 < y

   1. Initial program 53.5%

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

      1. distribute-lft-out 53.6%

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

   3. Simplified 53.6%

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

   4. Taylor expanded in x around 0 29.5%

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

      1. sqrt-prod 41.4%

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

   6. Applied egg-rr 41.4%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{+23}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 6: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.8e+20)
   (* 2.0 (sqrt (+ (* x (+ y z)) (* y z))))
   (* 2.0 (* (sqrt y) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.8e+20) {
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	} else {
		tmp = 2.0 * (sqrt(y) * 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 <= 2.8d+20) then
        tmp = 2.0d0 * sqrt(((x * (y + z)) + (y * z)))
    else
        tmp = 2.0d0 * (sqrt(y) * 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 <= 2.8e+20) {
		tmp = 2.0 * Math.sqrt(((x * (y + z)) + (y * z)));
	} else {
		tmp = 2.0 * (Math.sqrt(y) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 2.8e+20:
		tmp = 2.0 * math.sqrt(((x * (y + z)) + (y * z)))
	else:
		tmp = 2.0 * (math.sqrt(y) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2.8e+20)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * Float64(y + z)) + Float64(y * z))));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * 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 <= 2.8e+20)
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	else
		tmp = 2.0 * (sqrt(y) * 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, 2.8e+20], N[(2.0 * N[Sqrt[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.8e20

   1. Initial program 77.9%

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

      1. distribute-lft-out 77.9%

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

   3. Simplified 77.9%

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

   if 2.8e20 < y

   1. Initial program 54.9%

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

      1. distribute-lft-out 55.0%

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

   3. Simplified 55.0%

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

   4. Taylor expanded in x around 0 30.1%

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

      1. sqrt-prod 41.7%

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

   6. Applied egg-rr 41.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{+20}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 7: 71.5% accurate, 1.0× speedup

Math

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

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 (+ (* x (+ y z)) (* y z)))))

C

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

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(((x * (y + z)) + (y * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Derivation

1. Initial program 72.0%

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

   1. distribute-lft-out 72.1%

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

3. Simplified 72.1%

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

4. Final simplification 72.1%

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

Alternative 8: 70.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4.2e-271) (* 2.0 (sqrt (* y x))) (* 2.0 (sqrt (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.2e-271) {
		tmp = 2.0 * sqrt((y * x));
	} 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 <= (-4.2d-271)) then
        tmp = 2.0d0 * sqrt((y * x))
    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 <= -4.2e-271) {
		tmp = 2.0 * Math.sqrt((y * x));
	} 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 <= -4.2e-271:
		tmp = 2.0 * math.sqrt((y * x))
	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 <= -4.2e-271)
		tmp = Float64(2.0 * sqrt(Float64(y * x)));
	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 <= -4.2e-271)
		tmp = 2.0 * sqrt((y * x));
	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, -4.2e-271], N[(2.0 * N[Sqrt[N[(y * x), $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 < -4.2000000000000001e-271

   1. Initial program 73.6%

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

      1. distribute-lft-out 73.6%

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

   3. Simplified 73.6%

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

   4. Taylor expanded in z around 0 26.5%

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

   if -4.2000000000000001e-271 < y

   1. Initial program 70.6%

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

      1. distribute-lft-out 70.6%

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

   3. Simplified 70.6%

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

   4. Taylor expanded in z around inf 48.5%

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

4. Final simplification 37.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{-271}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 9: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-281}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-281) (* 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 <= -1e-281) {
		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 <= (-1d-281)) 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 <= -1e-281) {
		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 <= -1e-281:
		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 <= -1e-281)
		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 <= -1e-281)
		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, -1e-281], 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 < -1e-281

   1. Initial program 74.2%

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

      1. distribute-lft-out 74.2%

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

   3. Simplified 74.2%

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

   4. Taylor expanded in x around inf 51.2%

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

   if -1e-281 < y

   1. Initial program 69.9%

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

      1. distribute-lft-out 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in z around inf 47.3%

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

4. Final simplification 49.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-281}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 10: 69.2% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-310) (* 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 <= -5e-310) {
		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 <= (-5d-310)) 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 <= -5e-310) {
		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 <= -5e-310:
		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 <= -5e-310)
		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 <= -5e-310)
		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, -5e-310], 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 < -4.999999999999985e-310

   1. Initial program 74.1%

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

      1. distribute-lft-out 74.1%

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

   3. Simplified 74.1%

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

   4. Taylor expanded in z around 0 25.2%

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

   if -4.999999999999985e-310 < y

   1. Initial program 69.9%

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

      1. distribute-lft-out 70.0%

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

   3. Simplified 70.0%

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

   4. Taylor expanded in x around 0 26.0%

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

4. Final simplification 25.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 11: 35.7% 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 72.0%

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

   1. distribute-lft-out 72.1%

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

3. Simplified 72.1%

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

4. Taylor expanded in z around 0 25.1%

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

5. Final simplification 25.1%

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

Developer target: 83.3% 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 2023202 
(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)))))