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

Percentage Accurate: 70.2% → 96.4%

Time: 12.2s

Alternatives: 10

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: 70.2% 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: 96.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{if}\;y \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-212}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-287}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

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 -6.8e+39)
     t_0
     (if (<= y -1.75e-212)
       (* 2.0 (sqrt (+ (* x (+ y z)) (* y z))))
       (if (<= y 1.6e-287) 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 <= -6.8e+39) {
		tmp = t_0;
	} else if (y <= -1.75e-212) {
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	} else if (y <= 1.6e-287) {
		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 <= (-6.8d+39)) then
        tmp = t_0
    else if (y <= (-1.75d-212)) then
        tmp = 2.0d0 * sqrt(((x * (y + z)) + (y * z)))
    else if (y <= 1.6d-287) 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 <= -6.8e+39) {
		tmp = t_0;
	} else if (y <= -1.75e-212) {
		tmp = 2.0 * Math.sqrt(((x * (y + z)) + (y * z)));
	} else if (y <= 1.6e-287) {
		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 <= -6.8e+39:
		tmp = t_0
	elif y <= -1.75e-212:
		tmp = 2.0 * math.sqrt(((x * (y + z)) + (y * z)))
	elif y <= 1.6e-287:
		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 <= -6.8e+39)
		tmp = t_0;
	elseif (y <= -1.75e-212)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * Float64(y + z)) + Float64(y * z))));
	elseif (y <= 1.6e-287)
		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 <= -6.8e+39)
		tmp = t_0;
	elseif (y <= -1.75e-212)
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	elseif (y <= 1.6e-287)
		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, -6.8e+39], t$95$0, If[LessEqual[y, -1.75e-212], N[(2.0 * N[Sqrt[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.6e-287], 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 < -6.7999999999999998e39 or -1.7499999999999999e-212 < y < 1.60000000000000009e-287

   1. Initial program 61.7%

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

      1. distribute-lft-out 61.7%

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

   3. Simplified 61.7%

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

      1. add-sqr-sqrt 61.4%

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

      2. pow2 61.4%

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

      3. pow1/2 61.4%

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

      4. sqrt-pow1 61.4%

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

      5. distribute-lft-in 61.4%

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

      6. associate-+l+ 61.4%

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

      7. fma-def 61.4%

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

      8. distribute-rgt-out 61.5%

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

      9. metadata-eval 61.5%

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

   5. Applied egg-rr 61.5%

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

   6. Taylor expanded in x around -inf 47.2%

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

   if -6.7999999999999998e39 < y < -1.7499999999999999e-212

   1. Initial program 80.6%

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

      1. distribute-lft-out 80.6%

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

   3. Simplified 80.6%

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

   if 1.60000000000000009e-287 < y

   1. Initial program 70.9%

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

      1. distribute-lft-out 70.9%

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

   3. Simplified 70.9%

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

      1. add-sqr-sqrt 70.5%

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

      2. pow2 70.5%

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

      3. pow1/2 70.5%

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

      4. sqrt-pow1 70.6%

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

      5. distribute-lft-in 70.6%

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

      6. associate-+l+ 70.6%

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

      7. fma-def 70.6%

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

      8. distribute-rgt-out 70.6%

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

      9. metadata-eval 70.6%

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

   5. Applied egg-rr 70.6%

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

   6. Taylor expanded in z around inf 45.8%

      \[\leadsto 2 \cdot {\left({\color{blue}{\left(\left(y + x\right) \cdot z\right)}}^{0.25}\right)}^{2} \]
   7. Step-by-step derivation

      1. pow-pow 45.9%

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

      2. metadata-eval 45.9%

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

      3. pow1/2 45.9%

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

      4. sqrt-prod 47.7%

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

   8. Applied egg-rr 47.7%

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

4. Final simplification 53.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-212}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{-287}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 2: 95.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.25}\right)}^{\left(2 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)\right)}\\ \mathbf{if}\;y \leq -4.4 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-212}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-293}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

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) (* 2.0 (- (log (- (- y) z)) (log (/ -1.0 x))))))))
   (if (<= y -4.4e+39)
     t_0
     (if (<= y -1.75e-212)
       (* 2.0 (sqrt (+ (* x (+ y z)) (* y z))))
       (if (<= y -1.6e-293) 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), (2.0 * (log((-y - z)) - log((-1.0 / x)))));
	double tmp;
	if (y <= -4.4e+39) {
		tmp = t_0;
	} else if (y <= -1.75e-212) {
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	} else if (y <= -1.6e-293) {
		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) ** (2.0d0 * (log((-y - z)) - log(((-1.0d0) / x)))))
    if (y <= (-4.4d+39)) then
        tmp = t_0
    else if (y <= (-1.75d-212)) then
        tmp = 2.0d0 * sqrt(((x * (y + z)) + (y * z)))
    else if (y <= (-1.6d-293)) 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), (2.0 * (Math.log((-y - z)) - Math.log((-1.0 / x)))));
	double tmp;
	if (y <= -4.4e+39) {
		tmp = t_0;
	} else if (y <= -1.75e-212) {
		tmp = 2.0 * Math.sqrt(((x * (y + z)) + (y * z)));
	} else if (y <= -1.6e-293) {
		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), (2.0 * (math.log((-y - z)) - math.log((-1.0 / x)))))
	tmp = 0
	if y <= -4.4e+39:
		tmp = t_0
	elif y <= -1.75e-212:
		tmp = 2.0 * math.sqrt(((x * (y + z)) + (y * z)))
	elif y <= -1.6e-293:
		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(0.25) ^ Float64(2.0 * Float64(log(Float64(Float64(-y) - z)) - log(Float64(-1.0 / x))))))
	tmp = 0.0
	if (y <= -4.4e+39)
		tmp = t_0;
	elseif (y <= -1.75e-212)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * Float64(y + z)) + Float64(y * z))));
	elseif (y <= -1.6e-293)
		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) ^ (2.0 * (log((-y - z)) - log((-1.0 / x)))));
	tmp = 0.0;
	if (y <= -4.4e+39)
		tmp = t_0;
	elseif (y <= -1.75e-212)
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	elseif (y <= -1.6e-293)
		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[0.25], $MachinePrecision], N[(2.0 * N[(N[Log[N[((-y) - z), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.4e+39], t$95$0, If[LessEqual[y, -1.75e-212], N[(2.0 * N[Sqrt[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.6e-293], 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 < -4.4000000000000003e39 or -1.7499999999999999e-212 < y < -1.60000000000000003e-293

   1. Initial program 59.2%

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

      1. distribute-lft-out 59.2%

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

   3. Simplified 59.2%

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

      1. add-sqr-sqrt 58.9%

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

      2. pow2 58.9%

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

      3. pow1/2 58.9%

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

      4. sqrt-pow1 58.9%

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

      5. distribute-lft-in 58.9%

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

      6. associate-+l+ 58.9%

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

      7. fma-def 58.9%

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

      8. distribute-rgt-out 59.0%

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

      9. metadata-eval 59.0%

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

   5. Applied egg-rr 59.0%

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

   6. Taylor expanded in x around -inf 47.5%

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

      1. unpow2 47.5%

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

      2. exp-prod 46.1%

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

      3. exp-prod 45.3%

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

      4. pow-sqr 45.3%

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

      5. +-commutative 45.3%

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

      6. mul-1-neg 45.3%

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

      7. unsub-neg 45.3%

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

   8. Simplified 45.3%

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

   if -4.4000000000000003e39 < y < -1.7499999999999999e-212

   1. Initial program 80.6%

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

      1. distribute-lft-out 80.6%

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

   3. Simplified 80.6%

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

   if -1.60000000000000003e-293 < y

   1. Initial program 71.7%

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

      1. distribute-lft-out 71.7%

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

   3. Simplified 71.7%

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

      1. add-sqr-sqrt 71.3%

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

      2. pow2 71.3%

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

      3. pow1/2 71.3%

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

      4. sqrt-pow1 71.4%

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

      5. distribute-lft-in 71.4%

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

      6. associate-+l+ 71.4%

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

      7. fma-def 71.4%

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

      8. distribute-rgt-out 71.4%

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

      9. metadata-eval 71.4%

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

   5. Applied egg-rr 71.4%

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

   6. Taylor expanded in z around inf 48.4%

      \[\leadsto 2 \cdot {\left({\color{blue}{\left(\left(y + x\right) \cdot z\right)}}^{0.25}\right)}^{2} \]
   7. Step-by-step derivation

      1. pow-pow 48.6%

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

      2. metadata-eval 48.6%

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

      3. pow1/2 48.6%

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

      4. sqrt-prod 47.9%

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

   8. Applied egg-rr 47.9%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot {\left(e^{0.25}\right)}^{\left(2 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)\right)}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-212}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-293}:\\ \;\;\;\;2 \cdot {\left(e^{0.25}\right)}^{\left(2 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 3: 96.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{if}\;y \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-212}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-280}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

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 (* 0.16666666666666666 (- (log (- (- y) z)) (log (/ -1.0 x)))))
           3.0))))
   (if (<= y -3.8e+39)
     t_0
     (if (<= y -1.75e-212)
       (* 2.0 (sqrt (+ (* x (+ y z)) (* y z))))
       (if (<= y 2.5e-280) 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((0.16666666666666666 * (log((-y - z)) - log((-1.0 / x))))), 3.0);
	double tmp;
	if (y <= -3.8e+39) {
		tmp = t_0;
	} else if (y <= -1.75e-212) {
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	} else if (y <= 2.5e-280) {
		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((0.16666666666666666d0 * (log((-y - z)) - log(((-1.0d0) / x))))) ** 3.0d0)
    if (y <= (-3.8d+39)) then
        tmp = t_0
    else if (y <= (-1.75d-212)) then
        tmp = 2.0d0 * sqrt(((x * (y + z)) + (y * z)))
    else if (y <= 2.5d-280) 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((0.16666666666666666 * (Math.log((-y - z)) - Math.log((-1.0 / x))))), 3.0);
	double tmp;
	if (y <= -3.8e+39) {
		tmp = t_0;
	} else if (y <= -1.75e-212) {
		tmp = 2.0 * Math.sqrt(((x * (y + z)) + (y * z)));
	} else if (y <= 2.5e-280) {
		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((0.16666666666666666 * (math.log((-y - z)) - math.log((-1.0 / x))))), 3.0)
	tmp = 0
	if y <= -3.8e+39:
		tmp = t_0
	elif y <= -1.75e-212:
		tmp = 2.0 * math.sqrt(((x * (y + z)) + (y * z)))
	elif y <= 2.5e-280:
		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(0.16666666666666666 * Float64(log(Float64(Float64(-y) - z)) - log(Float64(-1.0 / x))))) ^ 3.0))
	tmp = 0.0
	if (y <= -3.8e+39)
		tmp = t_0;
	elseif (y <= -1.75e-212)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * Float64(y + z)) + Float64(y * z))));
	elseif (y <= 2.5e-280)
		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((0.16666666666666666 * (log((-y - z)) - log((-1.0 / x))))) ^ 3.0);
	tmp = 0.0;
	if (y <= -3.8e+39)
		tmp = t_0;
	elseif (y <= -1.75e-212)
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	elseif (y <= 2.5e-280)
		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[(0.16666666666666666 * N[(N[Log[N[((-y) - z), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.8e+39], t$95$0, If[LessEqual[y, -1.75e-212], N[(2.0 * N[Sqrt[N[(N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e-280], 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 < -3.7999999999999998e39 or -1.7499999999999999e-212 < y < 2.50000000000000014e-280

   1. Initial program 62.1%

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

      1. distribute-lft-out 62.1%

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

   3. Simplified 62.1%

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

      1. add-cube-cbrt 61.5%

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

      2. pow3 61.5%

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

   5. Applied egg-rr 61.5%

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

      1. add-cube-cbrt 60.8%

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

      2. pow3 60.9%

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

   7. Applied egg-rr 61.0%

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

   8. Taylor expanded in x around -inf 47.5%

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

   if -3.7999999999999998e39 < y < -1.7499999999999999e-212

   1. Initial program 80.6%

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

      1. distribute-lft-out 80.6%

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

   3. Simplified 80.6%

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

   if 2.50000000000000014e-280 < y

   1. Initial program 70.7%

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

      1. distribute-lft-out 70.7%

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

   3. Simplified 70.7%

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

      1. add-sqr-sqrt 70.3%

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

      2. pow2 70.3%

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

      3. pow1/2 70.3%

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

      4. sqrt-pow1 70.4%

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

      5. distribute-lft-in 70.4%

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

      6. associate-+l+ 70.4%

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

      7. fma-def 70.4%

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

      8. distribute-rgt-out 70.4%

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

      9. metadata-eval 70.4%

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

   5. Applied egg-rr 70.4%

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

   6. Taylor expanded in z around inf 45.3%

      \[\leadsto 2 \cdot {\left({\color{blue}{\left(\left(y + x\right) \cdot z\right)}}^{0.25}\right)}^{2} \]
   7. Step-by-step derivation

      1. pow-pow 45.5%

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

      2. metadata-eval 45.5%

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

      3. pow1/2 45.5%

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

      4. sqrt-prod 48.1%

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

   8. Applied egg-rr 48.1%

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

4. Final simplification 53.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{elif}\;y \leq -1.75 \cdot 10^{-212}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-280}:\\ \;\;\;\;2 \cdot {\left(e^{0.16666666666666666 \cdot \left(\log \left(\left(-y\right) - z\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{3}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 4: 87.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+120}:\\ \;\;\;\;2 \cdot \mathsf{hypot}\left(\frac{y}{\sqrt{\frac{y - z}{x}}}, \sqrt{y \cdot z}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot z + y \cdot \left(x + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -6e+120)
   (* 2.0 (hypot (/ y (sqrt (/ (- y z) x))) (sqrt (* y z))))
   (if (<= y 2.7e-229)
     (* 2.0 (sqrt (+ (* x z) (* y (+ x 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 <= -6e+120) {
		tmp = 2.0 * hypot((y / sqrt(((y - z) / x))), sqrt((y * z)));
	} else if (y <= 2.7e-229) {
		tmp = 2.0 * sqrt(((x * z) + (y * (x + z))));
	} else {
		tmp = 2.0 * (sqrt((y + x)) * sqrt(z));
	}
	return tmp;
}

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -6e+120) {
		tmp = 2.0 * Math.hypot((y / Math.sqrt(((y - z) / x))), Math.sqrt((y * z)));
	} else if (y <= 2.7e-229) {
		tmp = 2.0 * Math.sqrt(((x * z) + (y * (x + 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 <= -6e+120:
		tmp = 2.0 * math.hypot((y / math.sqrt(((y - z) / x))), math.sqrt((y * z)))
	elif y <= 2.7e-229:
		tmp = 2.0 * math.sqrt(((x * z) + (y * (x + 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 <= -6e+120)
		tmp = Float64(2.0 * hypot(Float64(y / sqrt(Float64(Float64(y - z) / x))), sqrt(Float64(y * z))));
	elseif (y <= 2.7e-229)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * z) + Float64(y * Float64(x + 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 <= -6e+120)
		tmp = 2.0 * hypot((y / sqrt(((y - z) / x))), sqrt((y * z)));
	elseif (y <= 2.7e-229)
		tmp = 2.0 * sqrt(((x * z) + (y * (x + 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, -6e+120], N[(2.0 * N[Sqrt[N[(y / N[Sqrt[N[(N[(y - z), $MachinePrecision] / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-229], N[(2.0 * N[Sqrt[N[(N[(x * z), $MachinePrecision] + N[(y * N[(x + z), $MachinePrecision]), $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 < -6e120

   1. Initial program 48.7%

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

      1. distribute-lft-out 48.7%

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

   3. Simplified 48.7%

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

      1. *-commutative 48.7%

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

      2. flip-+ 11.0%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{y \cdot y - z \cdot z}{y - z}} \cdot x + y \cdot z} \]

      3. associate-*l/ 5.0%

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

   5. Applied egg-rr 5.0%

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

   6. Taylor expanded in y around inf 6.2%

      \[\leadsto 2 \cdot \sqrt{\frac{\color{blue}{{y}^{2}} \cdot x}{y - z} + y \cdot z} \]
   7. Step-by-step derivation

      1. unpow2 6.2%

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

   8. Simplified 6.2%

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

      1. add-sqr-sqrt 6.2%

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

      2. add-sqr-sqrt 5.0%

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

      3. hypot-def 6.8%

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

      4. associate-/l* 8.2%

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

      5. sqrt-div 8.1%

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

      6. sqrt-prod 1.9%

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

      7. add-sqr-sqrt 33.1%

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

   10. Applied egg-rr 33.1%

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

   if -6e120 < y < 2.6999999999999998e-229

   1. Initial program 80.0%

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

      1. distribute-lft-out 80.0%

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

   3. Simplified 80.0%

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

      1. *-commutative 80.0%

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

      2. flip-+ 60.4%

         \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{y \cdot y - z \cdot z}{y - z}} \cdot x + y \cdot z} \]

      3. associate-*l/ 51.5%

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

   5. Applied egg-rr 51.5%

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

   6. Taylor expanded in y around inf 32.0%

      \[\leadsto 2 \cdot \sqrt{\frac{\color{blue}{{y}^{2}} \cdot x}{y - z} + y \cdot z} \]
   7. Step-by-step derivation

      1. unpow2 32.0%

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

   8. Simplified 32.0%

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

   9. Taylor expanded in y around inf 80.0%

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

   if 2.6999999999999998e-229 < y

   1. Initial program 69.2%

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

      1. distribute-lft-out 69.2%

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

   3. Simplified 69.2%

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

      1. add-sqr-sqrt 68.7%

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

      2. pow2 68.7%

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

      3. pow1/2 68.7%

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

      4. sqrt-pow1 68.8%

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

      5. distribute-lft-in 68.8%

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

      6. associate-+l+ 68.8%

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

      7. fma-def 68.8%

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

      8. distribute-rgt-out 68.8%

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

      9. metadata-eval 68.8%

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

   5. Applied egg-rr 68.8%

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

   6. Taylor expanded in z around inf 42.7%

      \[\leadsto 2 \cdot {\left({\color{blue}{\left(\left(y + x\right) \cdot z\right)}}^{0.25}\right)}^{2} \]
   7. Step-by-step derivation

      1. pow-pow 42.8%

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

      2. metadata-eval 42.8%

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

      3. pow1/2 42.8%

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

      4. sqrt-prod 50.2%

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

   8. Applied egg-rr 50.2%

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

4. Final simplification 58.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{+120}:\\ \;\;\;\;2 \cdot \mathsf{hypot}\left(\frac{y}{\sqrt{\frac{y - z}{x}}}, \sqrt{y \cdot z}\right)\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot z + y \cdot \left(x + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 5: 83.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.7e-229)
   (* 2.0 (sqrt (+ (* x (+ y z)) (* 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 <= 2.7e-229) {
		tmp = 2.0 * sqrt(((x * (y + z)) + (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 <= 2.7d-229) then
        tmp = 2.0d0 * sqrt(((x * (y + z)) + (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 <= 2.7e-229) {
		tmp = 2.0 * Math.sqrt(((x * (y + z)) + (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 <= 2.7e-229:
		tmp = 2.0 * math.sqrt(((x * (y + z)) + (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 <= 2.7e-229)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * Float64(y + z)) + 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 <= 2.7e-229)
		tmp = 2.0 * sqrt(((x * (y + z)) + (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, 2.7e-229], 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[N[(y + x), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.6999999999999998e-229

   1. Initial program 69.7%

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

      1. distribute-lft-out 69.7%

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

   3. Simplified 69.7%

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

   if 2.6999999999999998e-229 < y

   1. Initial program 69.2%

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

      1. distribute-lft-out 69.2%

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

   3. Simplified 69.2%

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

      1. add-sqr-sqrt 68.7%

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

      2. pow2 68.7%

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

      3. pow1/2 68.7%

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

      4. sqrt-pow1 68.8%

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

      5. distribute-lft-in 68.8%

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

      6. associate-+l+ 68.8%

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

      7. fma-def 68.8%

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

      8. distribute-rgt-out 68.8%

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

      9. metadata-eval 68.8%

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

   5. Applied egg-rr 68.8%

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

   6. Taylor expanded in z around inf 42.7%

      \[\leadsto 2 \cdot {\left({\color{blue}{\left(\left(y + x\right) \cdot z\right)}}^{0.25}\right)}^{2} \]
   7. Step-by-step derivation

      1. pow-pow 42.8%

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

      2. metadata-eval 42.8%

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

      3. pow1/2 42.8%

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

      4. sqrt-prod 50.2%

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

   8. Applied egg-rr 50.2%

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

4. Final simplification 61.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.7 \cdot 10^{-229}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y + x} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 6: 82.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-223}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 8e-223)
   (* 2.0 (sqrt (+ (* x (+ y z)) (* y z))))
   (* 2.0 (* (sqrt z) (sqrt y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e-223) {
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	} 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 <= 8d-223) then
        tmp = 2.0d0 * sqrt(((x * (y + z)) + (y * z)))
    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 <= 8e-223) {
		tmp = 2.0 * Math.sqrt(((x * (y + z)) + (y * z)));
	} 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 <= 8e-223:
		tmp = 2.0 * math.sqrt(((x * (y + z)) + (y * z)))
	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 <= 8e-223)
		tmp = Float64(2.0 * sqrt(Float64(Float64(x * Float64(y + z)) + Float64(y * z))));
	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 <= 8e-223)
		tmp = 2.0 * sqrt(((x * (y + z)) + (y * z)));
	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, 8e-223], 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[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.9999999999999998e-223

   1. Initial program 69.3%

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

      1. distribute-lft-out 69.2%

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

   3. Simplified 69.2%

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

   if 7.9999999999999998e-223 < y

   1. Initial program 69.7%

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

      1. distribute-lft-out 69.7%

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

   3. Simplified 69.7%

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

   4. Taylor expanded in x around 0 27.1%

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

      1. *-commutative 27.1%

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

      2. sqrt-prod 39.8%

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

   6. Applied egg-rr 39.8%

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

4. Final simplification 56.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-223}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right) + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 7: 70.3% 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 69.4%

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

   1. distribute-lft-out 69.4%

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

3. Simplified 69.4%

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

4. Final simplification 69.4%

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

Alternative 8: 69.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-289}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -8.2e-289) (* 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 <= -8.2e-289) {
		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 <= (-8.2d-289)) 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 <= -8.2e-289) {
		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 <= -8.2e-289:
		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 <= -8.2e-289)
		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 <= -8.2e-289)
		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, -8.2e-289], 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 < -8.1999999999999996e-289

   1. Initial program 66.8%

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

      1. distribute-lft-out 66.8%

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

   3. Simplified 66.8%

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

   4. Taylor expanded in z around 0 24.4%

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

   if -8.1999999999999996e-289 < y

   1. Initial program 71.9%

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

      1. distribute-lft-out 71.9%

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

   3. Simplified 71.9%

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

      1. add-sqr-sqrt 71.5%

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

      2. pow2 71.5%

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

      3. pow1/2 71.5%

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

      4. sqrt-pow1 71.6%

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

      5. distribute-lft-in 71.6%

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

      6. associate-+l+ 71.6%

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

      7. fma-def 71.6%

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

      8. distribute-rgt-out 71.6%

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

      9. metadata-eval 71.6%

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

   5. Applied egg-rr 71.6%

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

   6. Taylor expanded in z around inf 48.8%

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

   7. Taylor expanded in z around 0 44.2%

      \[\leadsto 2 \cdot \color{blue}{{\left(e^{0.25 \cdot \left(\log \left(y + x\right) + \log z\right)}\right)}^{2}} \]
   8. Step-by-step derivation

      1. +-commutative 44.2%

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

      2. log-prod 45.7%

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

      3. *-commutative 45.7%

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

      4. exp-to-pow 48.8%

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

      5. unpow2 48.8%

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

      6. pow-sqr 49.0%

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

      7. metadata-eval 49.0%

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

      8. unpow1/2 49.0%

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

   9. Simplified 49.0%

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

4. Final simplification 37.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.2 \cdot 10^{-289}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 9: 68.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-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 <= -4e-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 <= (-4d-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 <= -4e-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 <= -4e-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 <= -4e-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 <= -4e-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, -4e-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 < -3.999999999999988e-310

   1. Initial program 66.6%

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

      1. distribute-lft-out 66.6%

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

   3. Simplified 66.6%

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

   4. Taylor expanded in z around 0 23.6%

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

   if -3.999999999999988e-310 < y

   1. Initial program 72.3%

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

      1. distribute-lft-out 72.3%

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

   3. Simplified 72.3%

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

   4. Taylor expanded in x around 0 23.7%

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

4. Final simplification 23.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 10: 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 69.4%

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

   1. distribute-lft-out 69.4%

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

3. Simplified 69.4%

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

4. Taylor expanded in z around 0 24.8%

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

5. Final simplification 24.8%

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

Developer target: 82.7% 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 2023207 
(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)))))