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

Percentage Accurate: 69.9% → 96.4%

Time: 10.6s

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: 69.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 96.4% accurate, 0.6× speedup

Math

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

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -4e-310)
   (* (* (- 2.0) (/ (sqrt (- (+ z x))) (sqrt (- y)))) y)
   (* (/ (* (sqrt z) 2.0) (sqrt y)) y)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -4e-310) {
		tmp = (-2.0 * (sqrt(-(z + x)) / sqrt(-y))) * y;
	} else {
		tmp = ((sqrt(z) * 2.0) / sqrt(y)) * 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 <= (-4d-310)) then
        tmp = (-2.0d0 * (sqrt(-(z + x)) / sqrt(-y))) * y
    else
        tmp = ((sqrt(z) * 2.0d0) / sqrt(y)) * 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 <= -4e-310) {
		tmp = (-2.0 * (Math.sqrt(-(z + x)) / Math.sqrt(-y))) * y;
	} else {
		tmp = ((Math.sqrt(z) * 2.0) / Math.sqrt(y)) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -4e-310:
		tmp = (-2.0 * (math.sqrt(-(z + x)) / math.sqrt(-y))) * y
	else:
		tmp = ((math.sqrt(z) * 2.0) / math.sqrt(y)) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -4e-310)
		tmp = Float64(Float64(Float64(-2.0) * Float64(sqrt(Float64(-Float64(z + x))) / sqrt(Float64(-y)))) * y);
	else
		tmp = Float64(Float64(Float64(sqrt(z) * 2.0) / sqrt(y)) * 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 <= -4e-310)
		tmp = (-2.0 * (sqrt(-(z + x)) / sqrt(-y))) * y;
	else
		tmp = ((sqrt(z) * 2.0) / sqrt(y)) * 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, -4e-310], N[(N[((-2.0) * N[(N[Sqrt[(-N[(z + x), $MachinePrecision])], $MachinePrecision] / N[Sqrt[(-y)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], N[(N[(N[(N[Sqrt[z], $MachinePrecision] * 2.0), $MachinePrecision] / N[Sqrt[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.999999999999988e-310

   1. Initial program 67.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 0.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 54.3%

      \[\leadsto \left(\left(\sqrt{\frac{z + x}{y}} \cdot -1\right) \cdot 2\right) \cdot y \]
   9. Step-by-step derivation

   10. Applied rewrites 62.7%

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

   if -3.999999999999988e-310 < y

   1. Initial program 64.6%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 43.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 30.5%

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

   10. Applied rewrites 34.0%

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

4. Final simplification 47.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{-310}:\\ \;\;\;\;\left(\left(-2\right) \cdot \frac{\sqrt{-\left(z + x\right)}}{\sqrt{-y}}\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{z} \cdot 2}{\sqrt{y}} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-295}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{z} \cdot 2}{\sqrt{y}} \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+42)
   (* (* (sqrt (/ x y)) -2.0) y)
   (if (<= y 3.4e-295)
     (* (sqrt (* (+ z y) x)) 2.0)
     (* (/ (* (sqrt z) 2.0) (sqrt y)) y))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (sqrt((x / y)) * -2.0) * y;
	} else if (y <= 3.4e-295) {
		tmp = sqrt(((z + y) * x)) * 2.0;
	} else {
		tmp = ((sqrt(z) * 2.0) / sqrt(y)) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.4d+42)) then
        tmp = (sqrt((x / y)) * (-2.0d0)) * y
    else if (y <= 3.4d-295) then
        tmp = sqrt(((z + y) * x)) * 2.0d0
    else
        tmp = ((sqrt(z) * 2.0d0) / sqrt(y)) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (Math.sqrt((x / y)) * -2.0) * y;
	} else if (y <= 3.4e-295) {
		tmp = Math.sqrt(((z + y) * x)) * 2.0;
	} else {
		tmp = ((Math.sqrt(z) * 2.0) / Math.sqrt(y)) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.4e+42:
		tmp = (math.sqrt((x / y)) * -2.0) * y
	elif y <= 3.4e-295:
		tmp = math.sqrt(((z + y) * x)) * 2.0
	else:
		tmp = ((math.sqrt(z) * 2.0) / math.sqrt(y)) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+42)
		tmp = Float64(Float64(sqrt(Float64(x / y)) * -2.0) * y);
	elseif (y <= 3.4e-295)
		tmp = Float64(sqrt(Float64(Float64(z + y) * x)) * 2.0);
	else
		tmp = Float64(Float64(Float64(sqrt(z) * 2.0) / sqrt(y)) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+42)
		tmp = (sqrt((x / y)) * -2.0) * y;
	elseif (y <= 3.4e-295)
		tmp = sqrt(((z + y) * x)) * 2.0;
	else
		tmp = ((sqrt(z) * 2.0) / sqrt(y)) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.4e+42], N[(N[(N[Sqrt[N[(x / y), $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 3.4e-295], N[(N[Sqrt[N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[(N[Sqrt[z], $MachinePrecision] * 2.0), $MachinePrecision] / N[Sqrt[y], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999975e42

   1. Initial program 55.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 1.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 46.9%

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

   if -3.39999999999999975e42 < y < 3.40000000000000007e-295

   1. Initial program 75.1%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 58.3

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

   5. Applied rewrites 58.3%

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

   if 3.40000000000000007e-295 < y

   1. Initial program 65.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 44.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 31.6%

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

   10. Applied rewrites 35.2%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{-295}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt{z} \cdot 2}{\sqrt{y}} \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-269}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;\sqrt{z \cdot x + z \cdot y} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{z}{y}} \cdot 2\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+42)
   (* (* (sqrt (/ x y)) -2.0) y)
   (if (<= y -2e-269)
     (* (sqrt (* (+ z y) x)) 2.0)
     (if (<= y 1.8e+36)
       (* (sqrt (+ (* z x) (* z y))) 2.0)
       (* (* (sqrt (/ z y)) 2.0) y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (sqrt((x / y)) * -2.0) * y;
	} else if (y <= -2e-269) {
		tmp = sqrt(((z + y) * x)) * 2.0;
	} else if (y <= 1.8e+36) {
		tmp = sqrt(((z * x) + (z * y))) * 2.0;
	} else {
		tmp = (sqrt((z / y)) * 2.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.4d+42)) then
        tmp = (sqrt((x / y)) * (-2.0d0)) * y
    else if (y <= (-2d-269)) then
        tmp = sqrt(((z + y) * x)) * 2.0d0
    else if (y <= 1.8d+36) then
        tmp = sqrt(((z * x) + (z * y))) * 2.0d0
    else
        tmp = (sqrt((z / y)) * 2.0d0) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (Math.sqrt((x / y)) * -2.0) * y;
	} else if (y <= -2e-269) {
		tmp = Math.sqrt(((z + y) * x)) * 2.0;
	} else if (y <= 1.8e+36) {
		tmp = Math.sqrt(((z * x) + (z * y))) * 2.0;
	} else {
		tmp = (Math.sqrt((z / y)) * 2.0) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.4e+42:
		tmp = (math.sqrt((x / y)) * -2.0) * y
	elif y <= -2e-269:
		tmp = math.sqrt(((z + y) * x)) * 2.0
	elif y <= 1.8e+36:
		tmp = math.sqrt(((z * x) + (z * y))) * 2.0
	else:
		tmp = (math.sqrt((z / y)) * 2.0) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+42)
		tmp = Float64(Float64(sqrt(Float64(x / y)) * -2.0) * y);
	elseif (y <= -2e-269)
		tmp = Float64(sqrt(Float64(Float64(z + y) * x)) * 2.0);
	elseif (y <= 1.8e+36)
		tmp = Float64(sqrt(Float64(Float64(z * x) + Float64(z * y))) * 2.0);
	else
		tmp = Float64(Float64(sqrt(Float64(z / y)) * 2.0) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+42)
		tmp = (sqrt((x / y)) * -2.0) * y;
	elseif (y <= -2e-269)
		tmp = sqrt(((z + y) * x)) * 2.0;
	elseif (y <= 1.8e+36)
		tmp = sqrt(((z * x) + (z * y))) * 2.0;
	else
		tmp = (sqrt((z / y)) * 2.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.4e+42], N[(N[(N[Sqrt[N[(x / y), $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, -2e-269], N[(N[Sqrt[N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], If[LessEqual[y, 1.8e+36], N[(N[Sqrt[N[(N[(z * x), $MachinePrecision] + N[(z * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision] * y), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.39999999999999975e42

   1. Initial program 55.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 1.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 46.9%

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

   if -3.39999999999999975e42 < y < -1.9999999999999999e-269

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 60.5

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

   5. Applied rewrites 60.5%

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

   if -1.9999999999999999e-269 < y < 1.7999999999999999e36

   1. Initial program 71.9%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 57.5

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

   5. Applied rewrites 57.5%

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

   if 1.7999999999999999e36 < y

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 46.4%

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

4. Final simplification 53.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-269}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;\sqrt{z \cdot x + z \cdot y} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{z}{y}} \cdot 2\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;\sqrt{z \cdot y + \left(z \cdot x + x \cdot y\right)} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{z}{y}} \cdot 2\right) \cdot y\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+42)
   (* (* (sqrt (/ x y)) -2.0) y)
   (if (<= y 1.8e+36)
     (* (sqrt (+ (* z y) (+ (* z x) (* x y)))) 2.0)
     (* (* (sqrt (/ z y)) 2.0) y))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (sqrt((x / y)) * -2.0) * y;
	} else if (y <= 1.8e+36) {
		tmp = sqrt(((z * y) + ((z * x) + (x * y)))) * 2.0;
	} else {
		tmp = (sqrt((z / y)) * 2.0) * y;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.4d+42)) then
        tmp = (sqrt((x / y)) * (-2.0d0)) * y
    else if (y <= 1.8d+36) then
        tmp = sqrt(((z * y) + ((z * x) + (x * y)))) * 2.0d0
    else
        tmp = (sqrt((z / y)) * 2.0d0) * y
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (Math.sqrt((x / y)) * -2.0) * y;
	} else if (y <= 1.8e+36) {
		tmp = Math.sqrt(((z * y) + ((z * x) + (x * y)))) * 2.0;
	} else {
		tmp = (Math.sqrt((z / y)) * 2.0) * y;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.4e+42:
		tmp = (math.sqrt((x / y)) * -2.0) * y
	elif y <= 1.8e+36:
		tmp = math.sqrt(((z * y) + ((z * x) + (x * y)))) * 2.0
	else:
		tmp = (math.sqrt((z / y)) * 2.0) * y
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+42)
		tmp = Float64(Float64(sqrt(Float64(x / y)) * -2.0) * y);
	elseif (y <= 1.8e+36)
		tmp = Float64(sqrt(Float64(Float64(z * y) + Float64(Float64(z * x) + Float64(x * y)))) * 2.0);
	else
		tmp = Float64(Float64(sqrt(Float64(z / y)) * 2.0) * y);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+42)
		tmp = (sqrt((x / y)) * -2.0) * y;
	elseif (y <= 1.8e+36)
		tmp = sqrt(((z * y) + ((z * x) + (x * y)))) * 2.0;
	else
		tmp = (sqrt((z / y)) * 2.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.4e+42], N[(N[(N[Sqrt[N[(x / y), $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, 1.8e+36], N[(N[Sqrt[N[(N[(z * y), $MachinePrecision] + N[(N[(z * x), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[(N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision] * y), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999975e42

   1. Initial program 55.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 1.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 46.9%

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

   if -3.39999999999999975e42 < y < 1.7999999999999999e36

   1. Initial program 75.9%

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

   if 1.7999999999999999e36 < y

   1. Initial program 52.7%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 74.2%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 46.4%

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

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+36}:\\ \;\;\;\;\sqrt{z \cdot y + \left(z \cdot x + x \cdot y\right)} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\left(\sqrt{\frac{z}{y}} \cdot 2\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 82.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-269}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x + y\right) \cdot z} \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.4e+42)
   (* (* (sqrt (/ x y)) -2.0) y)
   (if (<= y -2e-269)
     (* (sqrt (* (+ z y) x)) 2.0)
     (* (sqrt (* (+ x y) z)) 2.0))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (sqrt((x / y)) * -2.0) * y;
	} else if (y <= -2e-269) {
		tmp = sqrt(((z + y) * x)) * 2.0;
	} else {
		tmp = sqrt(((x + y) * z)) * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.4d+42)) then
        tmp = (sqrt((x / y)) * (-2.0d0)) * y
    else if (y <= (-2d-269)) then
        tmp = sqrt(((z + y) * x)) * 2.0d0
    else
        tmp = sqrt(((x + y) * z)) * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.4e+42) {
		tmp = (Math.sqrt((x / y)) * -2.0) * y;
	} else if (y <= -2e-269) {
		tmp = Math.sqrt(((z + y) * x)) * 2.0;
	} else {
		tmp = Math.sqrt(((x + y) * z)) * 2.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.4e+42:
		tmp = (math.sqrt((x / y)) * -2.0) * y
	elif y <= -2e-269:
		tmp = math.sqrt(((z + y) * x)) * 2.0
	else:
		tmp = math.sqrt(((x + y) * z)) * 2.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.4e+42)
		tmp = Float64(Float64(sqrt(Float64(x / y)) * -2.0) * y);
	elseif (y <= -2e-269)
		tmp = Float64(sqrt(Float64(Float64(z + y) * x)) * 2.0);
	else
		tmp = Float64(sqrt(Float64(Float64(x + y) * z)) * 2.0);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.4e+42)
		tmp = (sqrt((x / y)) * -2.0) * y;
	elseif (y <= -2e-269)
		tmp = sqrt(((z + y) * x)) * 2.0;
	else
		tmp = sqrt(((x + y) * z)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.4e+42], N[(N[(N[Sqrt[N[(x / y), $MachinePrecision]], $MachinePrecision] * -2.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[y, -2e-269], N[(N[Sqrt[N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[Sqrt[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.39999999999999975e42

   1. Initial program 55.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{y \cdot \left(2 \cdot \sqrt{\frac{x + z}{y}} + \left(x \cdot z\right) \cdot \sqrt{\frac{1}{{y}^{3} \cdot \left(x + z\right)}}\right)} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

   5. Applied rewrites 1.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\frac{\frac{1}{z + x}}{{y}^{3}}}, z \cdot x, \sqrt{\frac{z + x}{y}} \cdot 2\right) \cdot y} \]

   6. Taylor expanded in y around -inf

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

   8. Applied rewrites 79.8%

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

   9. Taylor expanded in z around 0

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

   11. Applied rewrites 46.9%

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

   if -3.39999999999999975e42 < y < -1.9999999999999999e-269

   1. Initial program 81.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 60.5

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

   5. Applied rewrites 60.5%

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

   if -1.9999999999999999e-269 < y

   1. Initial program 63.5%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 44.4

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

   5. Applied rewrites 44.4%

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

4. Final simplification 48.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.4 \cdot 10^{+42}:\\ \;\;\;\;\left(\sqrt{\frac{x}{y}} \cdot -2\right) \cdot y\\ \mathbf{elif}\;y \leq -2 \cdot 10^{-269}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x + y\right) \cdot z} \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-250}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x + y\right) \cdot z} \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e-250)
   (* (sqrt (* (+ z y) x)) 2.0)
   (* (sqrt (* (+ x y) z)) 2.0)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e-250) {
		tmp = sqrt(((z + y) * x)) * 2.0;
	} else {
		tmp = sqrt(((x + y) * z)) * 2.0;
	}
	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 <= (-9.8d-250)) then
        tmp = sqrt(((z + y) * x)) * 2.0d0
    else
        tmp = sqrt(((x + y) * z)) * 2.0d0
    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 <= -9.8e-250) {
		tmp = Math.sqrt(((z + y) * x)) * 2.0;
	} else {
		tmp = Math.sqrt(((x + y) * z)) * 2.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -9.8e-250:
		tmp = math.sqrt(((z + y) * x)) * 2.0
	else:
		tmp = math.sqrt(((x + y) * z)) * 2.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e-250)
		tmp = Float64(sqrt(Float64(Float64(z + y) * x)) * 2.0);
	else
		tmp = Float64(sqrt(Float64(Float64(x + y) * z)) * 2.0);
	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 <= -9.8e-250)
		tmp = sqrt(((z + y) * x)) * 2.0;
	else
		tmp = sqrt(((x + y) * z)) * 2.0;
	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, -9.8e-250], N[(N[Sqrt[N[(N[(z + y), $MachinePrecision] * x), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[Sqrt[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999941e-250

   1. Initial program 69.2%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 49.0

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

   5. Applied rewrites 49.0%

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

   if -9.79999999999999941e-250 < y

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 44.9

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

   5. Applied rewrites 44.9%

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

4. Final simplification 46.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-250}:\\ \;\;\;\;\sqrt{\left(z + y\right) \cdot x} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x + y\right) \cdot z} \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-249}:\\ \;\;\;\;\sqrt{x \cdot y} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x + y\right) \cdot z} \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -8.6e-249) (* (sqrt (* x y)) 2.0) (* (sqrt (* (+ x y) z)) 2.0)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.6e-249) {
		tmp = sqrt((x * y)) * 2.0;
	} else {
		tmp = sqrt(((x + y) * z)) * 2.0;
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-8.6d-249)) then
        tmp = sqrt((x * y)) * 2.0d0
    else
        tmp = sqrt(((x + y) * z)) * 2.0d0
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -8.6e-249) {
		tmp = Math.sqrt((x * y)) * 2.0;
	} else {
		tmp = Math.sqrt(((x + y) * z)) * 2.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -8.6e-249:
		tmp = math.sqrt((x * y)) * 2.0
	else:
		tmp = math.sqrt(((x + y) * z)) * 2.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -8.6e-249)
		tmp = Float64(sqrt(Float64(x * y)) * 2.0);
	else
		tmp = Float64(sqrt(Float64(Float64(x + y) * z)) * 2.0);
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -8.6e-249)
		tmp = sqrt((x * y)) * 2.0;
	else
		tmp = sqrt(((x + y) * z)) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -8.6e-249], N[(N[Sqrt[N[(x * y), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[Sqrt[N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.6000000000000003e-249

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 29.6

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

   5. Applied rewrites 29.6%

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

   if -8.6000000000000003e-249 < y

   1. Initial program 63.6%

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

   3. Taylor expanded in z around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 N/A

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

      3. +-commutative N/A

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

      4. lower-+.f64 44.9

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

   5. Applied rewrites 44.9%

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

4. Final simplification 38.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.6 \cdot 10^{-249}:\\ \;\;\;\;\sqrt{x \cdot y} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{\left(x + y\right) \cdot z} \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-250}:\\ \;\;\;\;\sqrt{x \cdot y} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot y} \cdot 2\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -9.8e-250) (* (sqrt (* x y)) 2.0) (* (sqrt (* z y)) 2.0)))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -9.8e-250) {
		tmp = sqrt((x * y)) * 2.0;
	} else {
		tmp = sqrt((z * y)) * 2.0;
	}
	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 <= (-9.8d-250)) then
        tmp = sqrt((x * y)) * 2.0d0
    else
        tmp = sqrt((z * y)) * 2.0d0
    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 <= -9.8e-250) {
		tmp = Math.sqrt((x * y)) * 2.0;
	} else {
		tmp = Math.sqrt((z * y)) * 2.0;
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -9.8e-250:
		tmp = math.sqrt((x * y)) * 2.0
	else:
		tmp = math.sqrt((z * y)) * 2.0
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -9.8e-250)
		tmp = Float64(sqrt(Float64(x * y)) * 2.0);
	else
		tmp = Float64(sqrt(Float64(z * y)) * 2.0);
	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 <= -9.8e-250)
		tmp = sqrt((x * y)) * 2.0;
	else
		tmp = sqrt((z * y)) * 2.0;
	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, -9.8e-250], N[(N[Sqrt[N[(x * y), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision], N[(N[Sqrt[N[(z * y), $MachinePrecision]], $MachinePrecision] * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.79999999999999941e-250

   1. Initial program 69.2%

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

   3. Taylor expanded in z around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 29.6

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

   5. Applied rewrites 29.6%

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

   if -9.79999999999999941e-250 < y

   1. Initial program 63.6%

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

   3. Taylor expanded in x around 0

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

      1. *-commutative N/A

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

      2. lower-*.f64 19.6

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

   5. Applied rewrites 19.6%

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

4. Final simplification 23.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.8 \cdot 10^{-250}:\\ \;\;\;\;\sqrt{x \cdot y} \cdot 2\\ \mathbf{else}:\\ \;\;\;\;\sqrt{z \cdot y} \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 35.0% accurate, 1.8× speedup

Math

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

FPCore

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

C

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

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 = sqrt((x * y)) * 2.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.0%

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

3. Taylor expanded in z around 0

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

   1. *-commutative N/A

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

   2. lower-*.f64 24.1

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

5. Applied rewrites 24.1%

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

6. Final simplification 24.1%

   \[\leadsto \sqrt{x \cdot y} \cdot 2 \]
7. Add Preprocessing

Developer Target 1: 82.6% accurate, 0.0× 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 2024276 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< z 763695009057367500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (* 2 (sqrt (+ (* (+ x y) z) (* x y)))) (* (* (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4))) (+ (* 1/4 (* (* (pow y -3/4) (* (pow z -3/4) x)) (+ y z))) (* (pow z 1/4) (pow y 1/4)))) 2)))

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