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

Percentage Accurate: 71.0% → 94.0%

Time: 10.7s

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: 71.0% 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: 94.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{if}\;y \leq -2.9 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-200}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-285}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (*
          2.0
          (pow (exp (* 0.25 (- (log (- (- z) y)) (log (/ -1.0 x))))) 2.0))))
   (if (<= y -2.9e+42)
     t_0
     (if (<= y -2.55e-200)
       (* 2.0 (sqrt (* y x)))
       (if (<= y 7.8e-285) t_0 (* 2.0 (* (sqrt z) (sqrt y))))))))

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 tmp;
	if (y <= -2.9e+42) {
		tmp = t_0;
	} else if (y <= -2.55e-200) {
		tmp = 2.0 * sqrt((y * x));
	} else if (y <= 7.8e-285) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 * (exp((0.25d0 * (log((-z - y)) - log(((-1.0d0) / x))))) ** 2.0d0)
    if (y <= (-2.9d+42)) then
        tmp = t_0
    else if (y <= (-2.55d-200)) then
        tmp = 2.0d0 * sqrt((y * x))
    else if (y <= 7.8d-285) then
        tmp = t_0
    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 t_0 = 2.0 * Math.pow(Math.exp((0.25 * (Math.log((-z - y)) - Math.log((-1.0 / x))))), 2.0);
	double tmp;
	if (y <= -2.9e+42) {
		tmp = t_0;
	} else if (y <= -2.55e-200) {
		tmp = 2.0 * Math.sqrt((y * x));
	} else if (y <= 7.8e-285) {
		tmp = t_0;
	} 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):
	t_0 = 2.0 * math.pow(math.exp((0.25 * (math.log((-z - y)) - math.log((-1.0 / x))))), 2.0)
	tmp = 0
	if y <= -2.9e+42:
		tmp = t_0
	elif y <= -2.55e-200:
		tmp = 2.0 * math.sqrt((y * x))
	elif y <= 7.8e-285:
		tmp = t_0
	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)
	t_0 = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(-z) - y)) - log(Float64(-1.0 / x))))) ^ 2.0))
	tmp = 0.0
	if (y <= -2.9e+42)
		tmp = t_0;
	elseif (y <= -2.55e-200)
		tmp = Float64(2.0 * sqrt(Float64(y * x)));
	elseif (y <= 7.8e-285)
		tmp = t_0;
	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)
	t_0 = 2.0 * (exp((0.25 * (log((-z - y)) - log((-1.0 / x))))) ^ 2.0);
	tmp = 0.0;
	if (y <= -2.9e+42)
		tmp = t_0;
	elseif (y <= -2.55e-200)
		tmp = 2.0 * sqrt((y * x));
	elseif (y <= 7.8e-285)
		tmp = t_0;
	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_] := 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]}, If[LessEqual[y, -2.9e+42], t$95$0, If[LessEqual[y, -2.55e-200], N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7.8e-285], t$95$0, N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.89999999999999981e42 or -2.5499999999999999e-200 < y < 7.79999999999999972e-285

   1. Initial program 58.8%

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

      1. distribute-lft-out 59.0%

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

   3. Simplified 59.0%

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

   4. Taylor expanded in y around 0 58.9%

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

      1. add-sqr-sqrt 58.6%

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

      2. pow2 58.6%

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

      3. pow1/2 58.6%

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

      4. sqrt-pow1 58.7%

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

      5. fma-def 59.1%

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

      6. metadata-eval 59.1%

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

   6. Applied egg-rr 59.1%

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

   7. Taylor expanded in x around -inf 41.5%

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

   if -2.89999999999999981e42 < y < -2.5499999999999999e-200

   1. Initial program 90.5%

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

      1. distribute-lft-out 90.5%

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

   3. Simplified 90.5%

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

   4. Taylor expanded in z around 0 29.2%

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

   if 7.79999999999999972e-285 < y

   1. Initial program 72.6%

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

      1. distribute-lft-out 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around 0 24.1%

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

      1. pow1/2 24.3%

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

      2. *-commutative 24.3%

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

      3. metadata-eval 24.3%

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

      4. unpow-prod-down 34.6%

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

      5. metadata-eval 34.6%

         \[\leadsto 2 \cdot \left({z}^{\color{blue}{0.5}} \cdot {y}^{\left(\sqrt{0.25}\right)}\right) \]

      6. pow1/2 34.6%

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

      7. metadata-eval 34.6%

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

      8. pow1/2 34.6%

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

   6. Applied egg-rr 34.6%

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

4. Final simplification 35.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+42}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq -2.55 \cdot 10^{-200}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(-z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 2: 94.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} t_0 := 2 \cdot {\left(e^{0.25 \cdot \left(\log \left(-x\right) - \log \left(\frac{-1}{y}\right)\right)}\right)}^{2}\\ \mathbf{if}\;y \leq -1.06 \cdot 10^{+44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-239}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (* 2.0 (pow (exp (* 0.25 (- (log (- x)) (log (/ -1.0 y))))) 2.0))))
   (if (<= y -1.06e+44)
     t_0
     (if (<= y -2.4e-239)
       (* 2.0 (sqrt (* x (+ y z))))
       (if (<= y -5e-310) t_0 (* 2.0 (* (sqrt z) (sqrt y))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double t_0 = 2.0 * pow(exp((0.25 * (log(-x) - log((-1.0 / y))))), 2.0);
	double tmp;
	if (y <= -1.06e+44) {
		tmp = t_0;
	} else if (y <= -2.4e-239) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= -5e-310) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 2.0d0 * (exp((0.25d0 * (log(-x) - log(((-1.0d0) / y))))) ** 2.0d0)
    if (y <= (-1.06d+44)) then
        tmp = t_0
    else if (y <= (-2.4d-239)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= (-5d-310)) then
        tmp = t_0
    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 t_0 = 2.0 * Math.pow(Math.exp((0.25 * (Math.log(-x) - Math.log((-1.0 / y))))), 2.0);
	double tmp;
	if (y <= -1.06e+44) {
		tmp = t_0;
	} else if (y <= -2.4e-239) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= -5e-310) {
		tmp = t_0;
	} 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):
	t_0 = 2.0 * math.pow(math.exp((0.25 * (math.log(-x) - math.log((-1.0 / y))))), 2.0)
	tmp = 0
	if y <= -1.06e+44:
		tmp = t_0
	elif y <= -2.4e-239:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= -5e-310:
		tmp = t_0
	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)
	t_0 = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(-x)) - log(Float64(-1.0 / y))))) ^ 2.0))
	tmp = 0.0
	if (y <= -1.06e+44)
		tmp = t_0;
	elseif (y <= -2.4e-239)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= -5e-310)
		tmp = t_0;
	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)
	t_0 = 2.0 * (exp((0.25 * (log(-x) - log((-1.0 / y))))) ^ 2.0);
	tmp = 0.0;
	if (y <= -1.06e+44)
		tmp = t_0;
	elseif (y <= -2.4e-239)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= -5e-310)
		tmp = t_0;
	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_] := Block[{t$95$0 = N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[(-x)], $MachinePrecision] - N[Log[N[(-1.0 / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.06e+44], t$95$0, If[LessEqual[y, -2.4e-239], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5e-310], t$95$0, N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.06e44 or -2.39999999999999993e-239 < y < -4.999999999999985e-310

   1. Initial program 52.0%

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

      1. distribute-lft-out 52.2%

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

   3. Simplified 52.2%

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

   4. Taylor expanded in z around 0 23.8%

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

      1. add-sqr-sqrt 23.7%

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

      2. pow2 23.7%

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

      3. pow1/2 24.4%

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

      4. sqrt-pow1 24.4%

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

      5. *-commutative 24.4%

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

      6. metadata-eval 24.4%

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

   6. Applied egg-rr 24.4%

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

   7. Taylor expanded in y around -inf 38.6%

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

   if -1.06e44 < y < -2.39999999999999993e-239

   1. Initial program 88.0%

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

      1. distribute-lft-out 88.0%

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

   3. Simplified 88.0%

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

   4. Taylor expanded in x around inf 58.9%

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

   if -4.999999999999985e-310 < y

   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 x around 0 23.2%

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

      1. pow1/2 23.4%

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

      2. *-commutative 23.4%

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

      3. metadata-eval 23.4%

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

      4. unpow-prod-down 33.1%

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

      5. metadata-eval 33.1%

         \[\leadsto 2 \cdot \left({z}^{\color{blue}{0.5}} \cdot {y}^{\left(\sqrt{0.25}\right)}\right) \]

      6. pow1/2 33.1%

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

      7. metadata-eval 33.1%

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

      8. pow1/2 33.1%

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

   6. Applied egg-rr 33.1%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{+44}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(-x\right) - \log \left(\frac{-1}{y}\right)\right)}\right)}^{2}\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{-239}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-310}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(-x\right) - \log \left(\frac{-1}{y}\right)\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+155}:\\ \;\;\;\;2 \cdot \mathsf{hypot}\left(y \cdot \sqrt{\frac{x}{y - z}}, \sqrt{y \cdot z}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.8e+155)
   (* 2.0 (hypot (* y (sqrt (/ x (- y z)))) (sqrt (* y z))))
   (if (<= y 7e-284)
     (* 2.0 (sqrt (fma z (+ y x) (* y x))))
     (* 2.0 (* (sqrt z) (sqrt y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.8e+155) {
		tmp = 2.0 * hypot((y * sqrt((x / (y - z)))), sqrt((y * z)));
	} else if (y <= 7e-284) {
		tmp = 2.0 * sqrt(fma(z, (y + x), (y * x)));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.8e+155)
		tmp = Float64(2.0 * hypot(Float64(y * sqrt(Float64(x / Float64(y - z)))), sqrt(Float64(y * z))));
	elseif (y <= 7e-284)
		tmp = Float64(2.0 * sqrt(fma(z, Float64(y + x), Float64(y * x))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(y)));
	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, -1.8e+155], N[(2.0 * N[Sqrt[N[(y * N[Sqrt[N[(x / N[(y - z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] ^ 2 + N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision] ^ 2], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 7e-284], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.80000000000000004e155

   1. Initial program 39.7%

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

      1. distribute-lft-out 39.7%

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

   3. Simplified 39.7%

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

      1. flip-+ 3.1%

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

      2. associate-*r/ 3.1%

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

   5. Applied egg-rr 3.1%

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

      1. associate-/l* 3.1%

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

      2. associate-/r/ 2.5%

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

   7. Simplified 2.5%

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

   8. Taylor expanded in y around inf 2.6%

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

      1. unpow2 2.6%

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

   10. Simplified 2.6%

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

       1. add-sqr-sqrt 2.6%

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

       2. *-commutative 2.6%

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

       3. add-sqr-sqrt 1.2%

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

       4. add-sqr-sqrt 0.0%

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

       5. swap-sqr 0.0%

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

       6. hypot-def 2.6%

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

       7. *-commutative 2.6%

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

       8. sqrt-prod 2.6%

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

       9. sqrt-prod 0.0%

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

       10. add-sqr-sqrt 0.0%

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

       11. sqrt-unprod 39.0%

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

       12. *-commutative 39.0%

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

   12. Applied egg-rr 39.0%

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

   if -1.80000000000000004e155 < y < 6.99999999999999951e-284

   1. Initial program 79.8%

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

      1. associate-+l+ 79.8%

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

      2. +-commutative 79.8%

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

      3. distribute-rgt-out 79.8%

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

      4. fma-def 79.9%

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

   3. Simplified 79.9%

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

   if 6.99999999999999951e-284 < y

   1. Initial program 72.6%

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

      1. distribute-lft-out 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around 0 24.1%

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

      1. pow1/2 24.3%

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

      2. *-commutative 24.3%

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

      3. metadata-eval 24.3%

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

      4. unpow-prod-down 34.6%

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

      5. metadata-eval 34.6%

         \[\leadsto 2 \cdot \left({z}^{\color{blue}{0.5}} \cdot {y}^{\left(\sqrt{0.25}\right)}\right) \]

      6. pow1/2 34.6%

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

      7. metadata-eval 34.6%

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

      8. pow1/2 34.6%

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

   6. Applied egg-rr 34.6%

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

4. Final simplification 53.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+155}:\\ \;\;\;\;2 \cdot \mathsf{hypot}\left(y \cdot \sqrt{\frac{x}{y - z}}, \sqrt{y \cdot z}\right)\\ \mathbf{elif}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 4: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7e-284)
   (* 2.0 (sqrt (fma z (+ y x) (* y x))))
   (* 2.0 (* (sqrt z) (sqrt y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 7e-284) {
		tmp = 2.0 * sqrt(fma(z, (y + x), (y * x)));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 7e-284)
		tmp = Float64(2.0 * sqrt(fma(z, Float64(y + x), Float64(y * x))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(y)));
	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, 7e-284], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision] + N[(y * x), $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 < 6.99999999999999951e-284

   1. Initial program 70.8%

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

      1. associate-+l+ 70.8%

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

      2. +-commutative 70.8%

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

      3. distribute-rgt-out 70.8%

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

      4. fma-def 70.9%

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

   3. Simplified 70.9%

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

   if 6.99999999999999951e-284 < y

   1. Initial program 72.6%

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

      1. distribute-lft-out 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around 0 24.1%

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

      1. pow1/2 24.3%

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

      2. *-commutative 24.3%

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

      3. metadata-eval 24.3%

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

      4. unpow-prod-down 34.6%

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

      5. metadata-eval 34.6%

         \[\leadsto 2 \cdot \left({z}^{\color{blue}{0.5}} \cdot {y}^{\left(\sqrt{0.25}\right)}\right) \]

      6. pow1/2 34.6%

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

      7. metadata-eval 34.6%

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

      8. pow1/2 34.6%

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

   6. Applied egg-rr 34.6%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 5: 83.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7e-284)
   (* 2.0 (sqrt (+ (* y z) (* x (+ 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 <= 7e-284) {
		tmp = 2.0 * sqrt(((y * z) + (x * (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 <= 7d-284) then
        tmp = 2.0d0 * sqrt(((y * z) + (x * (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 <= 7e-284) {
		tmp = 2.0 * Math.sqrt(((y * z) + (x * (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 <= 7e-284:
		tmp = 2.0 * math.sqrt(((y * z) + (x * (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 <= 7e-284)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y * z) + Float64(x * 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 <= 7e-284)
		tmp = 2.0 * sqrt(((y * z) + (x * (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, 7e-284], N[(2.0 * N[Sqrt[N[(N[(y * z), $MachinePrecision] + N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.99999999999999951e-284

   1. Initial program 70.8%

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

      1. distribute-lft-out 71.0%

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

   3. Simplified 71.0%

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

   if 6.99999999999999951e-284 < y

   1. Initial program 72.6%

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

      1. distribute-lft-out 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around 0 24.1%

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

      1. pow1/2 24.3%

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

      2. *-commutative 24.3%

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

      3. metadata-eval 24.3%

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

      4. unpow-prod-down 34.6%

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

      5. metadata-eval 34.6%

         \[\leadsto 2 \cdot \left({z}^{\color{blue}{0.5}} \cdot {y}^{\left(\sqrt{0.25}\right)}\right) \]

      6. pow1/2 34.6%

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

      7. metadata-eval 34.6%

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

      8. pow1/2 34.6%

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

   6. Applied egg-rr 34.6%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]

Alternative 6: 71.1% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Derivation

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 71.8%

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

3. Simplified 71.8%

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

4. Final simplification 71.8%

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

Alternative 7: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -9.5e-273) (* 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 <= -9.5e-273) {
		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 <= (-9.5d-273)) 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 <= -9.5e-273) {
		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 <= -9.5e-273:
		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 <= -9.5e-273)
		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 <= -9.5e-273)
		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, -9.5e-273], 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 < -9.49999999999999925e-273

   1. Initial program 69.8%

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

      1. distribute-lft-out 69.9%

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

   3. Simplified 69.9%

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

   4. Taylor expanded in z around 0 27.2%

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

   if -9.49999999999999925e-273 < y

   1. Initial program 73.4%

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

      1. distribute-lft-out 73.5%

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

   3. Simplified 73.5%

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

   4. Taylor expanded in z around inf 51.8%

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

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-273}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 8: 71.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7.4e-284)
   (* 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 <= 7.4e-284) {
		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 <= 7.4d-284) 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 <= 7.4e-284) {
		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 <= 7.4e-284:
		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 <= 7.4e-284)
		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 <= 7.4e-284)
		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, 7.4e-284], 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 < 7.4000000000000001e-284

   1. Initial program 70.8%

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

      1. distribute-lft-out 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in x around inf 47.4%

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

   if 7.4000000000000001e-284 < y

   1. Initial program 72.6%

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

      1. distribute-lft-out 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in z around inf 49.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 9: 68.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7.4e-284) (* 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 <= 7.4e-284) {
		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 <= 7.4d-284) 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 <= 7.4e-284) {
		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 <= 7.4e-284:
		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 <= 7.4e-284)
		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 <= 7.4e-284)
		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, 7.4e-284], 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 < 7.4000000000000001e-284

   1. Initial program 70.8%

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

      1. distribute-lft-out 71.0%

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

   3. Simplified 71.0%

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

   4. Taylor expanded in z around 0 25.3%

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

   if 7.4000000000000001e-284 < y

   1. Initial program 72.6%

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

      1. distribute-lft-out 72.6%

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

   3. Simplified 72.6%

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

   4. Taylor expanded in x around 0 24.1%

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

4. Final simplification 24.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.4 \cdot 10^{-284}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 10: 36.4% 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 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 71.8%

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

3. Simplified 71.8%

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

4. Taylor expanded in z around 0 25.7%

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

5. Final simplification 25.7%

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

Developer target: 83.2% 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 2023215 
(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)))))