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

Percentage Accurate: 70.7% → 97.5%

Time: 8.6s

Alternatives: 9

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: 70.7% 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: 97.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{-296}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{y + z} \cdot \sqrt[3]{x}\right)}^{1.5}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 1.05e-296)
   (* 2.0 (pow (* (cbrt (+ y z)) (cbrt x)) 1.5))
   (* 2.0 (* (sqrt y) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.05e-296) {
		tmp = 2.0 * pow((cbrt((y + z)) * cbrt(x)), 1.5);
	} else {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	}
	return tmp;
}

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 1.05e-296) {
		tmp = 2.0 * Math.pow((Math.cbrt((y + z)) * Math.cbrt(x)), 1.5);
	} else {
		tmp = 2.0 * (Math.sqrt(y) * Math.sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 1.05e-296)
		tmp = Float64(2.0 * (Float64(cbrt(Float64(y + z)) * cbrt(x)) ^ 1.5));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 1.05e-296], N[(2.0 * N[Power[N[(N[Power[N[(y + z), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[x, 1/3], $MachinePrecision]), $MachinePrecision], 1.5], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.05e-296

   1. Initial program 68.1%

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

      1. distribute-lft-out 68.1%

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

   3. Simplified 68.1%

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

   4. Taylor expanded in x around inf 45.6%

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

      1. *-commutative 45.6%

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

      2. add-cube-cbrt 45.2%

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

      3. unpow3 45.2%

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

      4. sqrt-pow1 45.2%

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

      5. rem-cbrt-cube 45.0%

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

      6. unpow3 45.1%

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

      7. add-cube-cbrt 45.2%

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

      8. +-commutative 45.2%

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

      9. metadata-eval 45.2%

         \[\leadsto 2 \cdot {\left(\sqrt[3]{x \cdot \left(z + y\right)}\right)}^{\color{blue}{1.5}} \]

   6. Applied egg-rr 45.2%

      \[\leadsto 2 \cdot \color{blue}{{\left(\sqrt[3]{x \cdot \left(z + y\right)}\right)}^{1.5}} \]
   7. Step-by-step derivation

      1. *-commutative 45.2%

         \[\leadsto 2 \cdot {\left(\sqrt[3]{\color{blue}{\left(z + y\right) \cdot x}}\right)}^{1.5} \]

      2. cbrt-prod 70.9%

         \[\leadsto 2 \cdot {\color{blue}{\left(\sqrt[3]{z + y} \cdot \sqrt[3]{x}\right)}}^{1.5} \]

      3. +-commutative 70.9%

         \[\leadsto 2 \cdot {\left(\sqrt[3]{\color{blue}{y + z}} \cdot \sqrt[3]{x}\right)}^{1.5} \]

   8. Applied egg-rr 70.9%

      \[\leadsto 2 \cdot {\color{blue}{\left(\sqrt[3]{y + z} \cdot \sqrt[3]{x}\right)}}^{1.5} \]

   if 1.05e-296 < y

   1. Initial program 71.1%

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

      1. distribute-lft-out 71.1%

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

   3. Simplified 71.1%

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

   4. Taylor expanded in x around 0 25.0%

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

      1. sqrt-prod 33.1%

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

   6. Applied egg-rr 33.1%

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

4. Final simplification 51.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.05 \cdot 10^{-296}:\\ \;\;\;\;2 \cdot {\left(\sqrt[3]{y + z} \cdot \sqrt[3]{x}\right)}^{1.5}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 2: 83.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7.5e+28)
   (* 2.0 (sqrt (fma z (+ y x) (* y x))))
   (* 2.0 (* (sqrt y) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.5e+28) {
		tmp = 2.0 * sqrt(fma(z, (y + x), (y * x)));
	} else {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 7.5e+28)
		tmp = Float64(2.0 * sqrt(fma(z, Float64(y + x), Float64(y * x))));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 7.5e+28], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.4999999999999998e28

   1. Initial program 74.8%

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

      1. associate-+l+ 74.8%

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

      2. +-commutative 74.8%

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

      3. distribute-rgt-out 74.9%

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

      4. fma-def 74.9%

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

   3. Simplified 74.9%

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

   if 7.4999999999999998e28 < y

   1. Initial program 53.1%

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

      1. distribute-lft-out 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in x around 0 24.1%

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

      1. sqrt-prod 42.4%

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

   6. Applied egg-rr 42.4%

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

4. Final simplification 67.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \sqrt{\mathsf{fma}\left(z, y + x, y \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 3: 83.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 7.7 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 7.7e+28)
   (* 2.0 (sqrt (+ (* (+ y z) x) (* y z))))
   (* 2.0 (* (sqrt y) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.7e+28) {
		tmp = 2.0 * sqrt((((y + z) * x) + (y * z)));
	} else {
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 7.7d+28) then
        tmp = 2.0d0 * sqrt((((y + z) * x) + (y * z)))
    else
        tmp = 2.0d0 * (sqrt(y) * sqrt(z))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 7.7e+28) {
		tmp = 2.0 * Math.sqrt((((y + z) * x) + (y * z)));
	} else {
		tmp = 2.0 * (Math.sqrt(y) * Math.sqrt(z));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 7.7e+28:
		tmp = 2.0 * math.sqrt((((y + z) * x) + (y * z)))
	else:
		tmp = 2.0 * (math.sqrt(y) * math.sqrt(z))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 7.7e+28)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(y + z) * x) + Float64(y * z))));
	else
		tmp = Float64(2.0 * Float64(sqrt(y) * sqrt(z)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 7.7e+28)
		tmp = 2.0 * sqrt((((y + z) * x) + (y * z)));
	else
		tmp = 2.0 * (sqrt(y) * sqrt(z));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 7.7e+28], N[(2.0 * N[Sqrt[N[(N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[y], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.6999999999999997e28

   1. Initial program 74.8%

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

      1. distribute-lft-out 74.8%

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

   3. Simplified 74.8%

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

   if 7.6999999999999997e28 < y

   1. Initial program 53.1%

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

      1. distribute-lft-out 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in x around 0 24.1%

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

      1. sqrt-prod 42.4%

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

   6. Applied egg-rr 42.4%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.7 \cdot 10^{+28}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x + y \cdot z}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{y} \cdot \sqrt{z}\right)\\ \end{array} \]

Alternative 4: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{\frac{z}{\frac{1}{y + x}}}\\ \end{array} \end{array} \]

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-303)
   (* 2.0 (sqrt (* (+ y z) x)))
   (* 2.0 (sqrt (/ z (/ 1.0 (+ y x)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-303) {
		tmp = 2.0 * sqrt(((y + z) * x));
	} else {
		tmp = 2.0 * sqrt((z / (1.0 / (y + x))));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-4d-303)) then
        tmp = 2.0d0 * sqrt(((y + z) * x))
    else
        tmp = 2.0d0 * sqrt((z / (1.0d0 / (y + x))))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-303) {
		tmp = 2.0 * Math.sqrt(((y + z) * x));
	} else {
		tmp = 2.0 * Math.sqrt((z / (1.0 / (y + x))));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -4e-303:
		tmp = 2.0 * math.sqrt(((y + z) * x))
	else:
		tmp = 2.0 * math.sqrt((z / (1.0 / (y + x))))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -4e-303)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y + z) * x)));
	else
		tmp = Float64(2.0 * sqrt(Float64(z / Float64(1.0 / Float64(y + x)))));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -4e-303)
		tmp = 2.0 * sqrt(((y + z) * x));
	else
		tmp = 2.0 * sqrt((z / (1.0 / (y + x))));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -4e-303], N[(2.0 * N[Sqrt[N[(N[(y + z), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(z / N[(1.0 / N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.99999999999999972e-303

   1. Initial program 67.9%

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

      1. distribute-lft-out 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around inf 44.6%

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

   if -3.99999999999999972e-303 < y

   1. Initial program 71.2%

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

      1. associate-+l+ 71.2%

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

      2. fma-def 71.2%

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

      3. distribute-rgt-out 71.6%

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

   3. Simplified 71.6%

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

      1. flip-+ 49.4%

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

      2. associate-*r/ 40.5%

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

   5. Applied egg-rr 40.5%

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

      1. associate-/l* 49.4%

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

   7. Simplified 49.4%

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

   8. Taylor expanded in z around -inf 30.6%

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

      1. associate-/l* 39.0%

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

      2. *-lft-identity 39.0%

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

      3. unpow2 39.0%

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

      4. unpow2 39.0%

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

      5. difference-of-squares 39.4%

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

      6. +-commutative 39.4%

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

      7. times-frac 48.8%

         \[\leadsto 2 \cdot \sqrt{\frac{z}{\color{blue}{\frac{1}{y + x} \cdot \frac{x - y}{x - y}}}} \]

      8. +-commutative 48.8%

         \[\leadsto 2 \cdot \sqrt{\frac{z}{\frac{1}{\color{blue}{x + y}} \cdot \frac{x - y}{x - y}}} \]

      9. *-inverses 48.8%

         \[\leadsto 2 \cdot \sqrt{\frac{z}{\frac{1}{x + y} \cdot \color{blue}{1}}} \]

      10. associate-*l/ 48.8%

          \[\leadsto 2 \cdot \sqrt{\frac{z}{\color{blue}{\frac{1 \cdot 1}{x + y}}}} \]

      11. metadata-eval 48.8%

          \[\leadsto 2 \cdot \sqrt{\frac{z}{\frac{\color{blue}{1}}{x + y}}} \]

      12. +-commutative 48.8%

          \[\leadsto 2 \cdot \sqrt{\frac{z}{\frac{1}{\color{blue}{y + x}}}} \]

   10. Simplified 48.8%

       \[\leadsto 2 \cdot \sqrt{\color{blue}{\frac{z}{\frac{1}{y + x}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{\frac{z}{\frac{1}{y + x}}}\\ \end{array} \]

Alternative 5: 70.7% accurate, 1.0× speedup

Math

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

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 (+ (* (+ 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(Float64(y + z) * 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[(N[(y + z), $MachinePrecision] * x), $MachinePrecision] + N[(y * z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

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 69.6%

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

3. Simplified 69.6%

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

4. Final simplification 69.6%

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

Alternative 6: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.65e-285) (* 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 <= -1.65e-285) {
		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 <= (-1.65d-285)) 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 <= -1.65e-285) {
		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 <= -1.65e-285:
		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 <= -1.65e-285)
		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 <= -1.65e-285)
		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, -1.65e-285], 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 < -1.64999999999999993e-285

   1. Initial program 67.6%

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

      1. distribute-lft-out 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in z around 0 17.7%

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

   if -1.64999999999999993e-285 < y

   1. Initial program 71.4%

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

      1. distribute-lft-out 71.4%

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

   3. Simplified 71.4%

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

   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 34.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-285}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 7: 70.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-303) (* 2.0 (sqrt (* (+ y z) 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 <= -4e-303) {
		tmp = 2.0 * sqrt(((y + z) * 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 <= (-4d-303)) then
        tmp = 2.0d0 * sqrt(((y + z) * 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 <= -4e-303) {
		tmp = 2.0 * Math.sqrt(((y + z) * 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 <= -4e-303:
		tmp = 2.0 * math.sqrt(((y + z) * 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 <= -4e-303)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y + z) * 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 <= -4e-303)
		tmp = 2.0 * sqrt(((y + z) * 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, -4e-303], N[(2.0 * N[Sqrt[N[(N[(y + z), $MachinePrecision] * 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 < -3.99999999999999972e-303

   1. Initial program 67.9%

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

      1. distribute-lft-out 67.9%

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

   3. Simplified 67.9%

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

   4. Taylor expanded in x around inf 44.6%

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

   if -3.99999999999999972e-303 < y

   1. Initial program 71.2%

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

      1. distribute-lft-out 71.2%

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

   3. Simplified 71.2%

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

   4. Taylor expanded in z around inf 48.8%

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

4. Final simplification 46.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot \sqrt{\left(y + z\right) \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]

Alternative 8: 68.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-309}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-309) (* 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 <= -1e-309) {
		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 <= (-1d-309)) 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 <= -1e-309) {
		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 <= -1e-309:
		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 <= -1e-309)
		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 <= -1e-309)
		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, -1e-309], N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.000000000000002e-309

   1. Initial program 67.6%

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

      1. distribute-lft-out 67.6%

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

   3. Simplified 67.6%

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

   4. Taylor expanded in z around 0 17.4%

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

   if -1.000000000000002e-309 < y

   1. Initial program 71.5%

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

      1. distribute-lft-out 71.5%

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

   3. Simplified 71.5%

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

   4. Taylor expanded in x around 0 24.7%

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

4. Final simplification 21.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-309}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]

Alternative 9: 35.8% 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 69.7%

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

   1. distribute-lft-out 69.6%

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

3. Simplified 69.6%

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

4. Taylor expanded in z around 0 21.4%

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

5. Final simplification 21.4%

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

Developer target: 83.4% 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 2023194 
(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)))))