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

Percentage Accurate: 70.9% → 85.7%

Time: 18.1s

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: 70.9% 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: 85.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(\left(z + x\right) + x \cdot \frac{z}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(x, \frac{y}{z}, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -6.8e-277)
   (* 2.0 (sqrt (* y (+ (+ z x) (* x (/ z y))))))
   (* 2.0 (* (sqrt (fma x (/ y z) (+ y x))) (sqrt z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -6.8e-277) {
		tmp = 2.0 * sqrt((y * ((z + x) + (x * (z / y)))));
	} else {
		tmp = 2.0 * (sqrt(fma(x, (y / z), (y + x))) * sqrt(z));
	}
	return tmp;
}

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -6.8e-277)
		tmp = Float64(2.0 * sqrt(Float64(y * Float64(Float64(z + x) + Float64(x * Float64(z / y))))));
	else
		tmp = Float64(2.0 * Float64(sqrt(fma(x, Float64(y / z), Float64(y + x))) * sqrt(z)));
	end
	return tmp
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -6.8e-277], N[(2.0 * N[Sqrt[N[(y * N[(N[(z + x), $MachinePrecision] + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[N[(x * N[(y / z), $MachinePrecision] + N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] * N[Sqrt[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.79999999999999964e-277

   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. associate-+l+ 71.1%

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

      2. +-commutative 71.1%

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

      3. distribute-rgt-in 71.2%

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

   3. Simplified 71.2%

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

   5. Taylor expanded in y around inf 64.4%

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

      1. associate-+r+ 64.4%

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

      2. +-commutative 64.4%

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

      3. associate-/l* 59.8%

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

   7. Simplified 59.8%

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

   if -6.79999999999999964e-277 < y

   1. Initial program 70.1%

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

      1. associate-+l+ 70.1%

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

      2. +-commutative 70.1%

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

      3. distribute-rgt-in 70.2%

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

   3. Simplified 70.2%

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

   5. Taylor expanded in z around inf 57.9%

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

      1. associate-+r+ 57.9%

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

      2. +-commutative 57.9%

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

      3. associate-/l* 56.4%

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

   7. Simplified 56.4%

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

      1. *-commutative 56.4%

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

      2. sqrt-prod 51.4%

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

      3. +-commutative 51.4%

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

      4. fma-define 51.4%

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

   9. Applied egg-rr 51.4%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.8 \cdot 10^{-277}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(\left(z + x\right) + x \cdot \frac{z}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{\mathsf{fma}\left(x, \frac{y}{z}, y + x\right)} \cdot \sqrt{z}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 85.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{-308}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(\left(z + x\right) + x \cdot \frac{z}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y + x}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 3.9e-308)
   (* 2.0 (sqrt (* y (+ (+ z x) (* x (/ z y))))))
   (* 2.0 (* (sqrt z) (sqrt (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 3.9e-308) {
		tmp = 2.0 * sqrt((y * ((z + x) + (x * (z / y)))));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt((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 <= 3.9d-308) then
        tmp = 2.0d0 * sqrt((y * ((z + x) + (x * (z / y)))))
    else
        tmp = 2.0d0 * (sqrt(z) * sqrt((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 <= 3.9e-308) {
		tmp = 2.0 * Math.sqrt((y * ((z + x) + (x * (z / y)))));
	} else {
		tmp = 2.0 * (Math.sqrt(z) * Math.sqrt((y + x)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 3.9e-308:
		tmp = 2.0 * math.sqrt((y * ((z + x) + (x * (z / y)))))
	else:
		tmp = 2.0 * (math.sqrt(z) * math.sqrt((y + x)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 3.9e-308)
		tmp = Float64(2.0 * sqrt(Float64(y * Float64(Float64(z + x) + Float64(x * Float64(z / y))))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(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 <= 3.9e-308)
		tmp = 2.0 * sqrt((y * ((z + x) + (x * (z / y)))));
	else
		tmp = 2.0 * (sqrt(z) * sqrt((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, 3.9e-308], N[(2.0 * N[Sqrt[N[(y * N[(N[(z + x), $MachinePrecision] + N[(x * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[N[(y + x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.8999999999999999e-308

   1. Initial program 70.5%

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

      1. associate-+l+ 70.5%

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

      2. +-commutative 70.5%

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

      3. distribute-rgt-in 70.6%

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

   3. Simplified 70.6%

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

   5. Taylor expanded in y around inf 63.3%

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

      1. associate-+r+ 63.3%

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

      2. +-commutative 63.3%

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

      3. associate-/l* 58.1%

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

   7. Simplified 58.1%

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

   if 3.8999999999999999e-308 < y

   1. Initial program 70.7%

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

      1. associate-+l+ 70.7%

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

      2. +-commutative 70.7%

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

      3. distribute-rgt-in 70.7%

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

   3. Simplified 70.7%

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

   5. Taylor expanded in z around inf 41.5%

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

      1. +-commutative 41.5%

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

   7. Simplified 41.5%

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

      1. sqrt-prod 45.5%

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

      2. *-commutative 45.5%

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

      3. +-commutative 45.5%

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

   9. Applied egg-rr 45.5%

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

4. Final simplification 51.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3.9 \cdot 10^{-308}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(\left(z + x\right) + x \cdot \frac{z}{y}\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y + x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.8e-241)
   (* 2.0 (sqrt (+ (* y x) (* z (+ y x)))))
   (* 2.0 (* (sqrt z) (sqrt y)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.8e-241) {
		tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
	} else {
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 2.8d-241) then
        tmp = 2.0d0 * sqrt(((y * x) + (z * (y + x))))
    else
        tmp = 2.0d0 * (sqrt(z) * sqrt(y))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.8e-241) {
		tmp = 2.0 * Math.sqrt(((y * x) + (z * (y + x))));
	} else {
		tmp = 2.0 * (Math.sqrt(z) * Math.sqrt(y));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 2.8e-241:
		tmp = 2.0 * math.sqrt(((y * x) + (z * (y + x))))
	else:
		tmp = 2.0 * (math.sqrt(z) * math.sqrt(y))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2.8e-241)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y * x) + Float64(z * Float64(y + x)))));
	else
		tmp = Float64(2.0 * Float64(sqrt(z) * sqrt(y)));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 2.8e-241)
		tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
	else
		tmp = 2.0 * (sqrt(z) * sqrt(y));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, 2.8e-241], N[(2.0 * N[Sqrt[N[(N[(y * x), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[(N[Sqrt[z], $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.7999999999999999e-241

   1. Initial program 71.3%

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

      1. associate-+l+ 71.3%

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

      2. +-commutative 71.3%

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

      3. distribute-rgt-in 71.4%

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

   3. Simplified 71.4%

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

   if 2.7999999999999999e-241 < y

   1. Initial program 69.8%

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

      1. associate-+l+ 69.8%

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

      2. +-commutative 69.8%

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

      3. distribute-rgt-in 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in x around 0 24.2%

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

      1. *-commutative 24.2%

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

      2. sqrt-prod 33.2%

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

   7. Applied egg-rr 33.2%

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

4. Final simplification 53.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.8 \cdot 10^{-241}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(\sqrt{z} \cdot \sqrt{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(z \cdot \left(1 + \frac{x}{y}\right)\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-267)
   (* 2.0 (sqrt (* x (+ y z))))
   (* 2.0 (sqrt (* y (* z (+ 1.0 (/ x y))))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-267) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * sqrt((y * (z * (1.0 + (x / 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 <= (-3.8d-267)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * sqrt((y * (z * (1.0d0 + (x / 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 <= -3.8e-267) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * Math.sqrt((y * (z * (1.0 + (x / y)))));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.8e-267:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * math.sqrt((y * (z * (1.0 + (x / y)))))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-267)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * sqrt(Float64(y * Float64(z * Float64(1.0 + Float64(x / 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 <= -3.8e-267)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * sqrt((y * (z * (1.0 + (x / 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, -3.8e-267], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * N[(z * N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000003e-267

   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. associate-+l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. distribute-rgt-in 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in x around inf 49.8%

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

   if -3.80000000000000003e-267 < y

   1. Initial program 69.9%

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

      1. associate-+l+ 69.9%

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

      2. +-commutative 69.9%

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

      3. distribute-rgt-in 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in z around inf 42.0%

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

      1. +-commutative 42.0%

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

   7. Simplified 42.0%

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

   8. Taylor expanded in y around inf 31.2%

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

      1. associate-/l* 27.5%

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

   10. Simplified 27.5%

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

   11. Taylor expanded in z around 0 31.2%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot \left(z \cdot \left(1 + \frac{x}{y}\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-267) (* 2.0 (sqrt (* x (+ y z)))) (* 2.0 (sqrt (* y z)))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-267) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} 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 <= (-3.8d-267)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    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 <= -3.8e-267) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} 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 <= -3.8e-267:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	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 <= -3.8e-267)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	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 <= -3.8e-267)
		tmp = 2.0 * sqrt((x * (y + z)));
	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, -3.8e-267], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000003e-267

   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. associate-+l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. distribute-rgt-in 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in x around inf 49.8%

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

   if -3.80000000000000003e-267 < y

   1. Initial program 69.9%

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

      1. associate-+l+ 69.9%

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

      2. +-commutative 69.9%

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

      3. distribute-rgt-in 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in x around 0 21.6%

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

4. Final simplification 35.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 70.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-267)
   (* 2.0 (sqrt (* x (+ y z))))
   (* 2.0 (sqrt (* z (+ y x))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-267) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * sqrt((z * (y + x)));
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-3.8d-267)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else
        tmp = 2.0d0 * sqrt((z * (y + x)))
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.8e-267) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else {
		tmp = 2.0 * Math.sqrt((z * (y + x)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -3.8e-267:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	else:
		tmp = 2.0 * math.sqrt((z * (y + x)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -3.8e-267)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	else
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.8e-267)
		tmp = 2.0 * sqrt((x * (y + z)));
	else
		tmp = 2.0 * sqrt((z * (y + x)));
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -3.8e-267], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000003e-267

   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. associate-+l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. distribute-rgt-in 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in x around inf 49.8%

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

   if -3.80000000000000003e-267 < y

   1. Initial program 69.9%

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

      1. associate-+l+ 69.9%

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

      2. +-commutative 69.9%

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

      3. distribute-rgt-in 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in z around inf 42.0%

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

      1. +-commutative 42.0%

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

   7. Simplified 42.0%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 70.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

Derivation

1. Initial program 70.6%

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

   1. associate-+l+ 70.6%

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

   2. +-commutative 70.6%

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

   3. distribute-rgt-in 70.7%

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

3. Simplified 70.7%

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

5. Final simplification 70.7%

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

Alternative 8: 68.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -3.8e-267) (* 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 <= -3.8e-267) {
		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 <= (-3.8d-267)) 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 <= -3.8e-267) {
		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 <= -3.8e-267:
		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 <= -3.8e-267)
		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 <= -3.8e-267)
		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, -3.8e-267], N[(2.0 * N[Sqrt[N[(y * x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(2.0 * N[Sqrt[N[(y * z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.80000000000000003e-267

   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. associate-+l+ 71.4%

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

      2. +-commutative 71.4%

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

      3. distribute-rgt-in 71.5%

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

   3. Simplified 71.5%

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

   5. Taylor expanded in z around 0 24.0%

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

      1. *-commutative 24.0%

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

   7. Simplified 24.0%

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

   if -3.80000000000000003e-267 < y

   1. Initial program 69.9%

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

      1. associate-+l+ 69.9%

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

      2. +-commutative 69.9%

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

      3. distribute-rgt-in 69.9%

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

   3. Simplified 69.9%

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

   5. Taylor expanded in x around 0 21.6%

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

4. Final simplification 22.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{-267}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 36.3% 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 70.6%

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

   1. associate-+l+ 70.6%

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

   2. +-commutative 70.6%

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

   3. distribute-rgt-in 70.7%

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

3. Simplified 70.7%

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

5. Taylor expanded in z around 0 27.2%

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

   1. *-commutative 27.2%

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

7. Simplified 27.2%

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

8. Final simplification 27.2%

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

Developer target: 83.6% 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 2024055 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:descartes from diagrams-contrib-1.3.0.5"
  :precision binary64

  :alt
  (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)))))