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

Percentage Accurate: 70.4% → 95.0%

Time: 14.0s

Alternatives: 13

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: 70.4% 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: 95.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.1 \cdot 10^{-303}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(\left(0 - z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot {\left(y + x\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.1e-303)
   (* 2.0 (pow (exp (* 0.25 (- (log (- (- 0.0 z) y)) (log (/ -1.0 x))))) 2.0))
   (* (* 2.0 (sqrt z)) (pow (+ y x) 0.5))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e-303) {
		tmp = 2.0 * pow(exp((0.25 * (log(((0.0 - z) - y)) - log((-1.0 / x))))), 2.0);
	} else {
		tmp = (2.0 * sqrt(z)) * pow((y + x), 0.5);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.1d-303)) then
        tmp = 2.0d0 * (exp((0.25d0 * (log(((0.0d0 - z) - y)) - log(((-1.0d0) / x))))) ** 2.0d0)
    else
        tmp = (2.0d0 * sqrt(z)) * ((y + x) ** 0.5d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.1e-303) {
		tmp = 2.0 * Math.pow(Math.exp((0.25 * (Math.log(((0.0 - z) - y)) - Math.log((-1.0 / x))))), 2.0);
	} else {
		tmp = (2.0 * Math.sqrt(z)) * Math.pow((y + x), 0.5);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.1e-303:
		tmp = 2.0 * math.pow(math.exp((0.25 * (math.log(((0.0 - z) - y)) - math.log((-1.0 / x))))), 2.0)
	else:
		tmp = (2.0 * math.sqrt(z)) * math.pow((y + x), 0.5)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.1e-303)
		tmp = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(Float64(0.0 - z) - y)) - log(Float64(-1.0 / x))))) ^ 2.0));
	else
		tmp = Float64(Float64(2.0 * sqrt(z)) * (Float64(y + x) ^ 0.5));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.1e-303)
		tmp = 2.0 * (exp((0.25 * (log(((0.0 - z) - y)) - log((-1.0 / x))))) ^ 2.0);
	else
		tmp = (2.0 * sqrt(z)) * ((y + x) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -1.1e-303], N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[(N[(0.0 - z), $MachinePrecision] - y), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Power[N[(y + x), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.10000000000000007e-303

   1. Initial program 74.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 74.9%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(x \cdot y + z \cdot \left(x + y\right)\right)}^{\color{blue}{\frac{1}{2}}}\right)\right) \]

      2. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)}^{\frac{1}{2}}\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)}^{\frac{1}{2}}\right)\right) \]

      4. sqr-pow N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)}^{\left(\frac{\frac{1}{2}}{2}\right)} \cdot \color{blue}{{\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}}\right)\right) \]

      5. pow2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left({\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right)}^{\color{blue}{2}}\right)\right) \]

      6. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), \color{blue}{2}\right)\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      8. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      9. distribute-rgt-in N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(x \cdot y + z \cdot \left(x + y\right)\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(z \cdot \left(x + y\right)\right)\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      11. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      12. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right), \left(\frac{\frac{1}{2}}{2}\right)\right), 2\right)\right) \]

      14. metadata-eval 74.3%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right), \frac{1}{4}\right), 2\right)\right) \]

   6. Applied egg-rr 74.3%

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

   7. Taylor expanded in x around -inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\color{blue}{\left(e^{\frac{1}{4} \cdot \left(\log \left(-1 \cdot y + -1 \cdot z\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}, 2\right)\right) \]
   8. Step-by-step derivation

      1. exp-lowering-exp.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\left(\frac{1}{4} \cdot \left(\log \left(-1 \cdot y + -1 \cdot z\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \left(\log \left(-1 \cdot y + -1 \cdot z\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      3. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \left(\log \left(-1 \cdot y + -1 \cdot z\right) + \left(\mathsf{neg}\left(\log \left(\frac{-1}{x}\right)\right)\right)\right)\right)\right), 2\right)\right) \]

      4. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \left(\log \left(-1 \cdot y + -1 \cdot z\right) - \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      5. --lowering--.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\log \left(-1 \cdot y + -1 \cdot z\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      6. log-lowering-log.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(-1 \cdot y + -1 \cdot z\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      7. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(-1 \cdot z + -1 \cdot y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      8. mul-1-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(-1 \cdot z + \left(\mathsf{neg}\left(y\right)\right)\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      9. unsub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(-1 \cdot z - y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      10. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\left(-1 \cdot z\right), y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      11. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\left(\mathsf{neg}\left(z\right)\right), y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      12. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\left(0 - z\right), y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      13. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

      14. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right)\right), \mathsf{log.f64}\left(\left(\frac{-1}{x}\right)\right)\right)\right)\right), 2\right)\right) \]

      15. /-lowering-/.f64 48.1%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(\mathsf{\_.f64}\left(0, z\right), y\right)\right), \mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, x\right)\right)\right)\right)\right), 2\right)\right) \]

   9. Simplified 48.1%

      \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(\left(0 - z\right) - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

   if -1.10000000000000007e-303 < y

   1. Initial program 67.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 67.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 67.8%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 45.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 45.4%

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

      1. pow1/2 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

         \[\leadsto 2 \cdot {\left(z \cdot \left(x + y\right)\right)}^{\left(\frac{1}{4} \cdot \color{blue}{2}\right)} \]

      4. unpow-prod-down N/A

         \[\leadsto 2 \cdot \left({z}^{\left(\frac{1}{4} \cdot 2\right)} \cdot \color{blue}{{\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(2 \cdot {z}^{\left(\frac{1}{4} \cdot 2\right)}\right) \cdot \color{blue}{{\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot {z}^{\left(\frac{1}{4} \cdot 2\right)}\right), \color{blue}{\left({\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right), \left({\color{blue}{\left(x + y\right)}}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\frac{1}{2}}\right)\right), \left({\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      9. pow1/2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{z}\right)\right), \left({\left(x + \color{blue}{y}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      10. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \left({\left(x + \color{blue}{y}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      11. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\left(x + y\right), \color{blue}{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\left(y + x\right), \left(\color{blue}{\frac{1}{4}} \cdot 2\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{\frac{1}{4}} \cdot 2\right)\right)\right) \]

      14. metadata-eval 44.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\mathsf{+.f64}\left(y, x\right), \frac{1}{2}\right)\right) \]

   9. Applied egg-rr 44.6%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{z}\right) \cdot {\left(y + x\right)}^{0.5}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 93.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot {\left(e^{0.25 \cdot \left(\log \left(0 - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}^{2}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot {\left(y + x\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1.3e-292)
   (* 2.0 (pow (exp (* 0.25 (- (log (- 0.0 y)) (log (/ -1.0 x))))) 2.0))
   (* (* 2.0 (sqrt z)) (pow (+ y x) 0.5))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e-292) {
		tmp = 2.0 * pow(exp((0.25 * (log((0.0 - y)) - log((-1.0 / x))))), 2.0);
	} else {
		tmp = (2.0 * sqrt(z)) * pow((y + x), 0.5);
	}
	return tmp;
}

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-1.3d-292)) then
        tmp = 2.0d0 * (exp((0.25d0 * (log((0.0d0 - y)) - log(((-1.0d0) / x))))) ** 2.0d0)
    else
        tmp = (2.0d0 * sqrt(z)) * ((y + x) ** 0.5d0)
    end if
    code = tmp
end function

Java

assert x < y && y < z;
public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.3e-292) {
		tmp = 2.0 * Math.pow(Math.exp((0.25 * (Math.log((0.0 - y)) - Math.log((-1.0 / x))))), 2.0);
	} else {
		tmp = (2.0 * Math.sqrt(z)) * Math.pow((y + x), 0.5);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1.3e-292:
		tmp = 2.0 * math.pow(math.exp((0.25 * (math.log((0.0 - y)) - math.log((-1.0 / x))))), 2.0)
	else:
		tmp = (2.0 * math.sqrt(z)) * math.pow((y + x), 0.5)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1.3e-292)
		tmp = Float64(2.0 * (exp(Float64(0.25 * Float64(log(Float64(0.0 - y)) - log(Float64(-1.0 / x))))) ^ 2.0));
	else
		tmp = Float64(Float64(2.0 * sqrt(z)) * (Float64(y + x) ^ 0.5));
	end
	return tmp
end

MATLAB

x, y, z = num2cell(sort([x, y, z])){:}
function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -1.3e-292)
		tmp = 2.0 * (exp((0.25 * (log((0.0 - y)) - log((-1.0 / x))))) ^ 2.0);
	else
		tmp = (2.0 * sqrt(z)) * ((y + x) ^ 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x, y, and z should be sorted in increasing order before calling this function.
code[x_, y_, z_] := If[LessEqual[y, -1.3e-292], N[(2.0 * N[Power[N[Exp[N[(0.25 * N[(N[Log[N[(0.0 - y), $MachinePrecision]], $MachinePrecision] - N[Log[N[(-1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Power[N[(y + x), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.30000000000000007e-292

   1. Initial program 74.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 74.9%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot y}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(y \cdot x\right)\right)\right) \]

      4. *-lowering-*.f64 27.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, x\right)\right)\right) \]

   7. Simplified 27.5%

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

      1. pow1/2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(y \cdot x\right)}^{\color{blue}{\frac{1}{2}}}\right)\right) \]

      2. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(x \cdot y\right)}^{\frac{1}{2}}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(x \cdot y\right)}^{\left(\frac{1}{4} \cdot \color{blue}{2}\right)}\right)\right) \]

      4. sqr-pow N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(x \cdot y\right)}^{\left(\frac{\frac{1}{4} \cdot 2}{2}\right)} \cdot \color{blue}{{\left(x \cdot y\right)}^{\left(\frac{\frac{1}{4} \cdot 2}{2}\right)}}\right)\right) \]

      5. pow2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left({\left(x \cdot y\right)}^{\left(\frac{\frac{1}{4} \cdot 2}{2}\right)}\right)}^{\color{blue}{2}}\right)\right) \]

      6. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(x \cdot y\right)}^{\left(\frac{\frac{1}{4} \cdot 2}{2}\right)}\right), \color{blue}{2}\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(x \cdot y\right)}^{\left(\frac{\frac{1}{2}}{2}\right)}\right), 2\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left({\left(x \cdot y\right)}^{\frac{1}{4}}\right), 2\right)\right) \]

      9. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(x \cdot y\right), \frac{1}{4}\right), 2\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\left(y \cdot x\right), \frac{1}{4}\right), 2\right)\right) \]

      11. *-lowering-*.f64 27.4%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{pow.f64}\left(\mathsf{*.f64}\left(y, x\right), \frac{1}{4}\right), 2\right)\right) \]

   9. Applied egg-rr 27.4%

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

   10. Taylor expanded in x around -inf

       \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\color{blue}{\left(e^{\frac{1}{4} \cdot \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)}\right)}, 2\right)\right) \]
   11. Step-by-step derivation

       1. exp-lowering-exp.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\left(\frac{1}{4} \cdot \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       2. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \left(\log \left(-1 \cdot y\right) + -1 \cdot \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       3. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \left(\log \left(-1 \cdot y\right) + \left(\mathsf{neg}\left(\log \left(\frac{-1}{x}\right)\right)\right)\right)\right)\right), 2\right)\right) \]

       4. unsub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \left(\log \left(-1 \cdot y\right) - \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       5. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\log \left(-1 \cdot y\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       6. log-lowering-log.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(-1 \cdot y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       7. mul-1-neg N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(\mathsf{neg}\left(y\right)\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       8. neg-sub0 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\left(0 - y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       9. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right), \log \left(\frac{-1}{x}\right)\right)\right)\right), 2\right)\right) \]

       10. log-lowering-log.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right), \mathsf{log.f64}\left(\left(\frac{-1}{x}\right)\right)\right)\right)\right), 2\right)\right) \]

       11. /-lowering-/.f64 34.0%

           \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{exp.f64}\left(\mathsf{*.f64}\left(\frac{1}{4}, \mathsf{\_.f64}\left(\mathsf{log.f64}\left(\mathsf{\_.f64}\left(0, y\right)\right), \mathsf{log.f64}\left(\mathsf{/.f64}\left(-1, x\right)\right)\right)\right)\right), 2\right)\right) \]

   12. Simplified 34.0%

       \[\leadsto 2 \cdot {\color{blue}{\left(e^{0.25 \cdot \left(\log \left(0 - y\right) - \log \left(\frac{-1}{x}\right)\right)}\right)}}^{2} \]

   if -1.30000000000000007e-292 < y

   1. Initial program 68.0%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 68.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 68.0%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 45.7%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 45.7%

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

      1. pow1/2 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

         \[\leadsto 2 \cdot {\left(z \cdot \left(x + y\right)\right)}^{\left(\frac{1}{4} \cdot \color{blue}{2}\right)} \]

      4. unpow-prod-down N/A

         \[\leadsto 2 \cdot \left({z}^{\left(\frac{1}{4} \cdot 2\right)} \cdot \color{blue}{{\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(2 \cdot {z}^{\left(\frac{1}{4} \cdot 2\right)}\right) \cdot \color{blue}{{\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot {z}^{\left(\frac{1}{4} \cdot 2\right)}\right), \color{blue}{\left({\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right), \left({\color{blue}{\left(x + y\right)}}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\frac{1}{2}}\right)\right), \left({\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      9. pow1/2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{z}\right)\right), \left({\left(x + \color{blue}{y}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      10. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \left({\left(x + \color{blue}{y}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      11. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\left(x + y\right), \color{blue}{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\left(y + x\right), \left(\color{blue}{\frac{1}{4}} \cdot 2\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{\frac{1}{4}} \cdot 2\right)\right)\right) \]

      14. metadata-eval 44.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\mathsf{+.f64}\left(y, x\right), \frac{1}{2}\right)\right) \]

   9. Applied egg-rr 44.8%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{z}\right) \cdot {\left(y + x\right)}^{0.5}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 84.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.3 \cdot 10^{-251}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + \left(z + \frac{y \cdot z}{x}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot {\left(y + x\right)}^{0.5}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.3e-251)
   (* 2.0 (sqrt (* x (+ y (+ z (/ (* y z) x))))))
   (* (* 2.0 (sqrt z)) (pow (+ y x) 0.5))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 2.3e-251) {
		tmp = 2.0 * sqrt((x * (y + (z + ((y * z) / x)))));
	} else {
		tmp = (2.0 * sqrt(z)) * pow((y + x), 0.5);
	}
	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 <= 2.3d-251) then
        tmp = 2.0d0 * sqrt((x * (y + (z + ((y * z) / x)))))
    else
        tmp = (2.0d0 * sqrt(z)) * ((y + x) ** 0.5d0)
    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 <= 2.3e-251) {
		tmp = 2.0 * Math.sqrt((x * (y + (z + ((y * z) / x)))));
	} else {
		tmp = (2.0 * Math.sqrt(z)) * Math.pow((y + x), 0.5);
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 2.3e-251:
		tmp = 2.0 * math.sqrt((x * (y + (z + ((y * z) / x)))))
	else:
		tmp = (2.0 * math.sqrt(z)) * math.pow((y + x), 0.5)
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 2.3e-251)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + Float64(z + Float64(Float64(y * z) / x))))));
	else
		tmp = Float64(Float64(2.0 * sqrt(z)) * (Float64(y + x) ^ 0.5));
	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 <= 2.3e-251)
		tmp = 2.0 * sqrt((x * (y + (z + ((y * z) / x)))));
	else
		tmp = (2.0 * sqrt(z)) * ((y + x) ^ 0.5);
	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, 2.3e-251], N[(2.0 * N[Sqrt[N[(x * N[(y + N[(z + N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Power[N[(y + x), $MachinePrecision], 0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.30000000000000017e-251

   1. Initial program 73.3%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 73.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(y + \left(z + \frac{y \cdot z}{x}\right)\right)\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 69.2%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right)\right)\right)\right)\right)\right) \]

   7. Simplified 69.2%

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

   if 2.30000000000000017e-251 < y

   1. Initial program 68.4%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 68.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 68.4%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 42.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 42.8%

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

      1. pow1/2 N/A

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

      2. +-commutative N/A

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

      3. metadata-eval N/A

         \[\leadsto 2 \cdot {\left(z \cdot \left(x + y\right)\right)}^{\left(\frac{1}{4} \cdot \color{blue}{2}\right)} \]

      4. unpow-prod-down N/A

         \[\leadsto 2 \cdot \left({z}^{\left(\frac{1}{4} \cdot 2\right)} \cdot \color{blue}{{\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}}\right) \]

      5. associate-*r* N/A

         \[\leadsto \left(2 \cdot {z}^{\left(\frac{1}{4} \cdot 2\right)}\right) \cdot \color{blue}{{\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}} \]

      6. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot {z}^{\left(\frac{1}{4} \cdot 2\right)}\right), \color{blue}{\left({\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)}\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right), \left({\color{blue}{\left(x + y\right)}}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      8. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\frac{1}{2}}\right)\right), \left({\left(x + y\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      9. pow1/2 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{z}\right)\right), \left({\left(x + \color{blue}{y}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      10. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \left({\left(x + \color{blue}{y}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      11. pow-lowering-pow.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\left(x + y\right), \color{blue}{\left(\frac{1}{4} \cdot 2\right)}\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\left(y + x\right), \left(\color{blue}{\frac{1}{4}} \cdot 2\right)\right)\right) \]

      13. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\mathsf{+.f64}\left(y, x\right), \left(\color{blue}{\frac{1}{4}} \cdot 2\right)\right)\right) \]

      14. metadata-eval 45.8%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{pow.f64}\left(\mathsf{+.f64}\left(y, x\right), \frac{1}{2}\right)\right) \]

   9. Applied egg-rr 45.8%

      \[\leadsto \color{blue}{\left(2 \cdot \sqrt{z}\right) \cdot {\left(y + x\right)}^{0.5}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 82.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-251}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + \left(z + \frac{y \cdot z}{x}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(2 \cdot \sqrt{z}\right) \cdot \sqrt{y}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 2.5e-251)
   (* 2.0 (sqrt (* x (+ y (+ z (/ (* y z) 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 <= 2.5e-251) {
		tmp = 2.0 * sqrt((x * (y + (z + ((y * z) / 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 <= 2.5d-251) then
        tmp = 2.0d0 * sqrt((x * (y + (z + ((y * z) / 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 <= 2.5e-251) {
		tmp = 2.0 * Math.sqrt((x * (y + (z + ((y * z) / 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 <= 2.5e-251:
		tmp = 2.0 * math.sqrt((x * (y + (z + ((y * z) / 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 <= 2.5e-251)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + Float64(z + Float64(Float64(y * z) / x))))));
	else
		tmp = Float64(Float64(2.0 * 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 <= 2.5e-251)
		tmp = 2.0 * sqrt((x * (y + (z + ((y * z) / 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, 2.5e-251], N[(2.0 * N[Sqrt[N[(x * N[(y + N[(z + N[(N[(y * z), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(2.0 * N[Sqrt[z], $MachinePrecision]), $MachinePrecision] * N[Sqrt[y], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.5000000000000001e-251

   1. Initial program 73.3%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 73.3%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 73.3%

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

   5. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(y + \left(z + \frac{y \cdot z}{x}\right)\right)\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(y + \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 69.2%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(y, z\right), x\right)\right)\right)\right)\right)\right) \]

   7. Simplified 69.2%

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

   if 2.5000000000000001e-251 < y

   1. Initial program 68.4%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 68.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 68.4%

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

   5. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(y \cdot \left(x + \left(z + \frac{x \cdot z}{y}\right)\right)\right)}\right)\right) \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, \left(x + \left(z + \frac{x \cdot z}{y}\right)\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \left(z + \frac{x \cdot z}{y}\right)\right)\right)\right)\right) \]

      3. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(z, \left(\frac{x \cdot z}{y}\right)\right)\right)\right)\right)\right) \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(x \cdot z\right), y\right)\right)\right)\right)\right)\right) \]

      5. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(z \cdot x\right), y\right)\right)\right)\right)\right)\right) \]

      6. *-lowering-*.f64 63.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, x\right), y\right)\right)\right)\right)\right)\right) \]

   7. Simplified 63.5%

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

   8. Taylor expanded in x around 0

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(y \cdot z\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot y\right)\right)\right) \]

      2. *-lowering-*.f64 23.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, y\right)\right)\right) \]

   10. Simplified 23.4%

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

       1. sqrt-prod N/A

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

       2. pow1/2 N/A

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

       3. associate-*r* N/A

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

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\left(2 \cdot {z}^{\frac{1}{2}}\right), \color{blue}{\left(\sqrt{y}\right)}\right) \]

       5. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left({z}^{\frac{1}{2}}\right)\right), \left(\sqrt{\color{blue}{y}}\right)\right) \]

       6. pow1/2 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \left(\sqrt{z}\right)\right), \left(\sqrt{y}\right)\right) \]

       7. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \left(\sqrt{y}\right)\right) \]

       8. sqrt-lowering-sqrt.f64 32.9%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(z\right)\right), \mathsf{sqrt.f64}\left(y\right)\right) \]

   12. Applied egg-rr 32.9%

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

Alternative 5: 82.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-292)
   (* 2.0 (sqrt (* x (+ y z))))
   (if (<= y 9e+39)
     (* 2.0 (sqrt (+ (* y z) (* z x))))
     (* y (* 2.0 (sqrt (/ z y)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-292) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= 9e+39) {
		tmp = 2.0 * sqrt(((y * z) + (z * x)));
	} else {
		tmp = y * (2.0 * sqrt((z / 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 <= (-1d-292)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= 9d+39) then
        tmp = 2.0d0 * sqrt(((y * z) + (z * x)))
    else
        tmp = y * (2.0d0 * sqrt((z / 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 <= -1e-292) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= 9e+39) {
		tmp = 2.0 * Math.sqrt(((y * z) + (z * x)));
	} else {
		tmp = y * (2.0 * Math.sqrt((z / y)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1e-292:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= 9e+39:
		tmp = 2.0 * math.sqrt(((y * z) + (z * x)))
	else:
		tmp = y * (2.0 * math.sqrt((z / y)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-292)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= 9e+39)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y * z) + Float64(z * x))));
	else
		tmp = Float64(y * Float64(2.0 * sqrt(Float64(z / 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 <= -1e-292)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= 9e+39)
		tmp = 2.0 * sqrt(((y * z) + (z * x)));
	else
		tmp = y * (2.0 * sqrt((z / 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, -1e-292], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+39], N[(2.0 * N[Sqrt[N[(N[(y * z), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0000000000000001e-292

   1. Initial program 74.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 74.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot \left(y + z\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot \left(y + z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(y + z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 54.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, z\right)\right)\right)\right) \]

   7. Simplified 54.0%

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

   if -1.0000000000000001e-292 < y < 8.99999999999999991e39

   1. Initial program 79.5%

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

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\color{blue}{\left(x \cdot z\right)}, \mathsf{*.f64}\left(y, z\right)\right)\right)\right) \]
   4. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(z \cdot x\right), \mathsf{*.f64}\left(y, z\right)\right)\right)\right) \]

      2. *-lowering-*.f64 59.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(z, x\right), \mathsf{*.f64}\left(y, z\right)\right)\right)\right) \]

   5. Simplified 59.4%

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

   if 8.99999999999999991e39 < y

   1. Initial program 51.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 51.9%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 26.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 26.5%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(z + \frac{y \cdot z}{x}\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(z \cdot y\right), x\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 11.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right)\right)\right)\right)\right) \]

   10. Simplified 11.8%

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

   11. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}} + x \cdot \sqrt{\frac{z}{{y}^{3}}}\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot \sqrt{\frac{z}{{y}^{3}}} + \color{blue}{2 \cdot \sqrt{\frac{z}{y}}}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \sqrt{\frac{z}{{y}^{3}}}\right), \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\sqrt{\frac{z}{{y}^{3}}}\right)\right), \left(\color{blue}{2} \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       5. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\left(\frac{z}{{y}^{3}}\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left({y}^{3}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot {y}^{2}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right)\right) \]

       13. sqrt-lowering-sqrt.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right)\right) \]

       14. /-lowering-/.f64 41.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right)\right) \]

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right) \]
   15. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right) \]

       2. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right) \]

       3. /-lowering-/.f64 41.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right) \]

   16. Simplified 41.7%

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

4. Final simplification 52.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + z \cdot x}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + \left(y \cdot x + z \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 9e+39)
   (* 2.0 (sqrt (+ (* y z) (+ (* y x) (* z x)))))
   (* y (* 2.0 (sqrt (/ z y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 9e+39) {
		tmp = 2.0 * sqrt(((y * z) + ((y * x) + (z * x))));
	} else {
		tmp = y * (2.0 * sqrt((z / 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 <= 9d+39) then
        tmp = 2.0d0 * sqrt(((y * z) + ((y * x) + (z * x))))
    else
        tmp = y * (2.0d0 * sqrt((z / 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 <= 9e+39) {
		tmp = 2.0 * Math.sqrt(((y * z) + ((y * x) + (z * x))));
	} else {
		tmp = y * (2.0 * Math.sqrt((z / y)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 9e+39:
		tmp = 2.0 * math.sqrt(((y * z) + ((y * x) + (z * x))))
	else:
		tmp = y * (2.0 * math.sqrt((z / y)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 9e+39)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y * z) + Float64(Float64(y * x) + Float64(z * x)))));
	else
		tmp = Float64(y * Float64(2.0 * sqrt(Float64(z / 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 <= 9e+39)
		tmp = 2.0 * sqrt(((y * z) + ((y * x) + (z * x))));
	else
		tmp = y * (2.0 * sqrt((z / 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, 9e+39], N[(2.0 * N[Sqrt[N[(N[(y * z), $MachinePrecision] + N[(N[(y * x), $MachinePrecision] + N[(z * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.99999999999999991e39

   1. Initial program 76.8%

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

   if 8.99999999999999991e39 < y

   1. Initial program 51.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 51.9%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 26.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 26.5%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(z + \frac{y \cdot z}{x}\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(z \cdot y\right), x\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 11.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right)\right)\right)\right)\right) \]

   10. Simplified 11.8%

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

   11. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}} + x \cdot \sqrt{\frac{z}{{y}^{3}}}\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot \sqrt{\frac{z}{{y}^{3}}} + \color{blue}{2 \cdot \sqrt{\frac{z}{y}}}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \sqrt{\frac{z}{{y}^{3}}}\right), \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\sqrt{\frac{z}{{y}^{3}}}\right)\right), \left(\color{blue}{2} \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       5. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\left(\frac{z}{{y}^{3}}\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left({y}^{3}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot {y}^{2}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right)\right) \]

       13. sqrt-lowering-sqrt.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right)\right) \]

       14. /-lowering-/.f64 41.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right)\right) \]

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right) \]
   15. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right) \]

       2. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right) \]

       3. /-lowering-/.f64 41.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right) \]

   16. Simplified 41.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z + \left(y \cdot x + z \cdot x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 82.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-292)
   (* 2.0 (sqrt (* x (+ y z))))
   (if (<= y 9e+39)
     (* 2.0 (sqrt (* z (+ y x))))
     (* y (* 2.0 (sqrt (/ z y)))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= -1e-292) {
		tmp = 2.0 * sqrt((x * (y + z)));
	} else if (y <= 9e+39) {
		tmp = 2.0 * sqrt((z * (y + x)));
	} else {
		tmp = y * (2.0 * sqrt((z / 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 <= (-1d-292)) then
        tmp = 2.0d0 * sqrt((x * (y + z)))
    else if (y <= 9d+39) then
        tmp = 2.0d0 * sqrt((z * (y + x)))
    else
        tmp = y * (2.0d0 * sqrt((z / 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 <= -1e-292) {
		tmp = 2.0 * Math.sqrt((x * (y + z)));
	} else if (y <= 9e+39) {
		tmp = 2.0 * Math.sqrt((z * (y + x)));
	} else {
		tmp = y * (2.0 * Math.sqrt((z / y)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= -1e-292:
		tmp = 2.0 * math.sqrt((x * (y + z)))
	elif y <= 9e+39:
		tmp = 2.0 * math.sqrt((z * (y + x)))
	else:
		tmp = y * (2.0 * math.sqrt((z / y)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= -1e-292)
		tmp = Float64(2.0 * sqrt(Float64(x * Float64(y + z))));
	elseif (y <= 9e+39)
		tmp = Float64(2.0 * sqrt(Float64(z * Float64(y + x))));
	else
		tmp = Float64(y * Float64(2.0 * sqrt(Float64(z / 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 <= -1e-292)
		tmp = 2.0 * sqrt((x * (y + z)));
	elseif (y <= 9e+39)
		tmp = 2.0 * sqrt((z * (y + x)));
	else
		tmp = y * (2.0 * sqrt((z / 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, -1e-292], N[(2.0 * N[Sqrt[N[(x * N[(y + z), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+39], N[(2.0 * N[Sqrt[N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.0000000000000001e-292

   1. Initial program 74.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 74.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot \left(y + z\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot \left(y + z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(y + z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 54.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, z\right)\right)\right)\right) \]

   7. Simplified 54.0%

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

   if -1.0000000000000001e-292 < y < 8.99999999999999991e39

   1. Initial program 79.5%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 79.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 79.5%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 59.4%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 59.4%

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

   if 8.99999999999999991e39 < y

   1. Initial program 51.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 51.9%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 26.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 26.5%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(z + \frac{y \cdot z}{x}\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(z \cdot y\right), x\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 11.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right)\right)\right)\right)\right) \]

   10. Simplified 11.8%

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

   11. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}} + x \cdot \sqrt{\frac{z}{{y}^{3}}}\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot \sqrt{\frac{z}{{y}^{3}}} + \color{blue}{2 \cdot \sqrt{\frac{z}{y}}}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \sqrt{\frac{z}{{y}^{3}}}\right), \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\sqrt{\frac{z}{{y}^{3}}}\right)\right), \left(\color{blue}{2} \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       5. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\left(\frac{z}{{y}^{3}}\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left({y}^{3}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot {y}^{2}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right)\right) \]

       13. sqrt-lowering-sqrt.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right)\right) \]

       14. /-lowering-/.f64 41.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right)\right) \]

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right) \]
   15. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right) \]

       2. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right) \]

       3. /-lowering-/.f64 41.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right) \]

   16. Simplified 41.7%

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

Alternative 8: 82.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 9e+39)
   (* 2.0 (sqrt (+ (* y x) (* z (+ y x)))))
   (* y (* 2.0 (sqrt (/ z y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 9e+39) {
		tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
	} else {
		tmp = y * (2.0 * sqrt((z / 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 <= 9d+39) then
        tmp = 2.0d0 * sqrt(((y * x) + (z * (y + x))))
    else
        tmp = y * (2.0d0 * sqrt((z / 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 <= 9e+39) {
		tmp = 2.0 * Math.sqrt(((y * x) + (z * (y + x))));
	} else {
		tmp = y * (2.0 * Math.sqrt((z / y)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 9e+39:
		tmp = 2.0 * math.sqrt(((y * x) + (z * (y + x))))
	else:
		tmp = y * (2.0 * math.sqrt((z / y)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 9e+39)
		tmp = Float64(2.0 * sqrt(Float64(Float64(y * x) + Float64(z * Float64(y + x)))));
	else
		tmp = Float64(y * Float64(2.0 * sqrt(Float64(z / 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 <= 9e+39)
		tmp = 2.0 * sqrt(((y * x) + (z * (y + x))));
	else
		tmp = y * (2.0 * sqrt((z / 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, 9e+39], N[(2.0 * N[Sqrt[N[(N[(y * x), $MachinePrecision] + N[(z * N[(y + x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 8.99999999999999991e39

   1. Initial program 76.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 76.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 76.8%

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

   if 8.99999999999999991e39 < y

   1. Initial program 51.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 51.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 51.9%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 26.5%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 26.5%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(z + \frac{y \cdot z}{x}\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(z \cdot y\right), x\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 11.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right)\right)\right)\right)\right) \]

   10. Simplified 11.8%

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

   11. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}} + x \cdot \sqrt{\frac{z}{{y}^{3}}}\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot \sqrt{\frac{z}{{y}^{3}}} + \color{blue}{2 \cdot \sqrt{\frac{z}{y}}}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \sqrt{\frac{z}{{y}^{3}}}\right), \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\sqrt{\frac{z}{{y}^{3}}}\right)\right), \left(\color{blue}{2} \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       5. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\left(\frac{z}{{y}^{3}}\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left({y}^{3}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot {y}^{2}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right)\right) \]

       13. sqrt-lowering-sqrt.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right)\right) \]

       14. /-lowering-/.f64 41.8%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right)\right) \]

   13. Simplified 41.8%

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

   14. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right) \]
   15. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right) \]

       2. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right) \]

       3. /-lowering-/.f64 41.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right) \]

   16. Simplified 41.7%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 9 \cdot 10^{+39}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x + z \cdot \left(y + x\right)}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 81.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 0.4:\\ \;\;\;\;2 \cdot {\left(\frac{\frac{1}{y}}{z + x}\right)}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(2 \cdot \sqrt{\frac{z}{y}}\right)\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 0.4)
   (* 2.0 (pow (/ (/ 1.0 y) (+ z x)) -0.5))
   (* y (* 2.0 (sqrt (/ z y))))))

C

assert(x < y && y < z);
double code(double x, double y, double z) {
	double tmp;
	if (y <= 0.4) {
		tmp = 2.0 * pow(((1.0 / y) / (z + x)), -0.5);
	} else {
		tmp = y * (2.0 * sqrt((z / 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 <= 0.4d0) then
        tmp = 2.0d0 * (((1.0d0 / y) / (z + x)) ** (-0.5d0))
    else
        tmp = y * (2.0d0 * sqrt((z / 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 <= 0.4) {
		tmp = 2.0 * Math.pow(((1.0 / y) / (z + x)), -0.5);
	} else {
		tmp = y * (2.0 * Math.sqrt((z / y)));
	}
	return tmp;
}

Python

[x, y, z] = sort([x, y, z])
def code(x, y, z):
	tmp = 0
	if y <= 0.4:
		tmp = 2.0 * math.pow(((1.0 / y) / (z + x)), -0.5)
	else:
		tmp = y * (2.0 * math.sqrt((z / y)))
	return tmp

Julia

x, y, z = sort([x, y, z])
function code(x, y, z)
	tmp = 0.0
	if (y <= 0.4)
		tmp = Float64(2.0 * (Float64(Float64(1.0 / y) / Float64(z + x)) ^ -0.5));
	else
		tmp = Float64(y * Float64(2.0 * sqrt(Float64(z / 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 <= 0.4)
		tmp = 2.0 * (((1.0 / y) / (z + x)) ^ -0.5);
	else
		tmp = y * (2.0 * sqrt((z / 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, 0.4], N[(2.0 * N[Power[N[(N[(1.0 / y), $MachinePrecision] / N[(z + x), $MachinePrecision]), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision], N[(y * N[(2.0 * N[Sqrt[N[(z / y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 0.40000000000000002

   1. Initial program 76.8%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 76.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 76.8%

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

      1. flip-+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\sqrt{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}{x \cdot y - z \cdot \left(x + y\right)}}\right)\right) \]

      2. fmm-def N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\sqrt{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}{\mathsf{fma}\left(x, y, \mathsf{neg}\left(z \cdot \left(x + y\right)\right)\right)}}\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\sqrt{\frac{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}{\mathsf{fma}\left(x, y, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right)}}\right)\right) \]

      4. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\sqrt{\frac{1}{\frac{\mathsf{fma}\left(x, y, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right)}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}}}\right)\right) \]

      5. sqrt-div N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\frac{\sqrt{1}}{\color{blue}{\sqrt{\frac{\mathsf{fma}\left(x, y, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right)}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}}}}\right)\right) \]

      6. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left(\frac{1}{\sqrt{\color{blue}{\frac{\mathsf{fma}\left(x, y, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right)}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}}}}\right)\right) \]

      7. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{/.f64}\left(1, \color{blue}{\left(\sqrt{\frac{\mathsf{fma}\left(x, y, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right)}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}}\right)}\right)\right) \]

      8. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{/.f64}\left(1, \mathsf{sqrt.f64}\left(\left(\frac{\mathsf{fma}\left(x, y, \mathsf{neg}\left(\left(x + y\right) \cdot z\right)\right)}{\left(x \cdot y\right) \cdot \left(x \cdot y\right) - \left(z \cdot \left(x + y\right)\right) \cdot \left(z \cdot \left(x + y\right)\right)}\right)\right)\right)\right) \]

   6. Applied egg-rr 76.6%

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

      1. inv-pow N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(\sqrt{\frac{1}{x \cdot y + z \cdot \left(x + y\right)}}\right)}^{\color{blue}{-1}}\right)\right) \]

      2. pow1/2 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left({\left(\frac{1}{x \cdot y + z \cdot \left(x + y\right)}\right)}^{\frac{1}{2}}\right)}^{-1}\right)\right) \]

      3. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left({\left(\frac{1}{x \cdot y + z \cdot \left(x + y\right)}\right)}^{\left(\frac{1}{4} \cdot 2\right)}\right)}^{-1}\right)\right) \]

      4. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(2, \left({\left(\frac{1}{x \cdot y + z \cdot \left(x + y\right)}\right)}^{\color{blue}{\left(\left(\frac{1}{4} \cdot 2\right) \cdot -1\right)}}\right)\right) \]

      5. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left(\frac{1}{x \cdot y + z \cdot \left(x + y\right)}\right), \color{blue}{\left(\left(\frac{1}{4} \cdot 2\right) \cdot -1\right)}\right)\right) \]

      6. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \left(x \cdot y + z \cdot \left(x + y\right)\right)\right), \left(\color{blue}{\left(\frac{1}{4} \cdot 2\right)} \cdot -1\right)\right)\right) \]

      7. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\left(x \cdot y\right), \left(z \cdot \left(x + y\right)\right)\right)\right), \left(\left(\frac{1}{4} \cdot \color{blue}{2}\right) \cdot -1\right)\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right), \left(\left(\frac{1}{4} \cdot 2\right) \cdot -1\right)\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right), \left(\left(\frac{1}{4} \cdot 2\right) \cdot -1\right)\right)\right) \]

      10. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right), \left(\left(\frac{1}{4} \cdot 2\right) \cdot -1\right)\right)\right) \]

      11. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right), \left(\frac{1}{2} \cdot -1\right)\right)\right) \]

      12. metadata-eval 76.7%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(1, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right), \frac{-1}{2}\right)\right) \]

   8. Applied egg-rr 76.7%

      \[\leadsto 2 \cdot \color{blue}{{\left(\frac{1}{x \cdot y + z \cdot \left(x + y\right)}\right)}^{-0.5}} \]

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\color{blue}{\left(\frac{1}{y \cdot \left(x + z\right)}\right)}, \frac{-1}{2}\right)\right) \]
   10. Step-by-step derivation

       1. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\left(\frac{\frac{1}{y}}{x + z}\right), \frac{-1}{2}\right)\right) \]

       2. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(\left(\frac{1}{y}\right), \left(x + z\right)\right), \frac{-1}{2}\right)\right) \]

       3. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(x + z\right)\right), \frac{-1}{2}\right)\right) \]

       4. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \left(z + x\right)\right), \frac{-1}{2}\right)\right) \]

       5. +-lowering-+.f64 42.4%

          \[\leadsto \mathsf{*.f64}\left(2, \mathsf{pow.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, y\right), \mathsf{+.f64}\left(z, x\right)\right), \frac{-1}{2}\right)\right) \]

   11. Simplified 42.4%

       \[\leadsto 2 \cdot {\color{blue}{\left(\frac{\frac{1}{y}}{z + x}\right)}}^{-0.5} \]

   if 0.40000000000000002 < y

   1. Initial program 54.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 54.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 54.8%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 28.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 28.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\color{blue}{\left(x \cdot \left(z + \frac{y \cdot z}{x}\right)\right)}\right)\right) \]
   9. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(z + \frac{y \cdot z}{x}\right)\right)\right)\right) \]

      2. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \left(\frac{y \cdot z}{x}\right)\right)\right)\right)\right) \]

      3. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(y \cdot z\right), x\right)\right)\right)\right)\right) \]

      4. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\left(z \cdot y\right), x\right)\right)\right)\right)\right) \]

      5. *-lowering-*.f64 15.1%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(z, \mathsf{/.f64}\left(\mathsf{*.f64}\left(z, y\right), x\right)\right)\right)\right)\right) \]

   10. Simplified 15.1%

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

   11. Taylor expanded in y around inf

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

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}} + x \cdot \sqrt{\frac{z}{{y}^{3}}}\right)}\right) \]

       2. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(y, \left(x \cdot \sqrt{\frac{z}{{y}^{3}}} + \color{blue}{2 \cdot \sqrt{\frac{z}{y}}}\right)\right) \]

       3. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\left(x \cdot \sqrt{\frac{z}{{y}^{3}}}\right), \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \left(\sqrt{\frac{z}{{y}^{3}}}\right)\right), \left(\color{blue}{2} \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       5. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\left(\frac{z}{{y}^{3}}\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left({y}^{3}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       7. cube-mult N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       8. unpow2 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \left(y \cdot {y}^{2}\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       9. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left({y}^{2}\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       10. unpow2 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \left(y \cdot y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       11. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \left(2 \cdot \sqrt{\frac{z}{y}}\right)\right)\right) \]

       12. *-lowering-*.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right)\right) \]

       13. sqrt-lowering-sqrt.f64 N/A

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right)\right) \]

       14. /-lowering-/.f64 40.0%

           \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(y, y\right)\right)\right)\right)\right), \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right)\right) \]

   13. Simplified 40.0%

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

   14. Taylor expanded in x around 0

       \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(2 \cdot \sqrt{\frac{z}{y}}\right)}\right) \]
   15. Step-by-step derivation

       1. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\frac{z}{y}}\right)}\right)\right) \]

       2. sqrt-lowering-sqrt.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\frac{z}{y}\right)\right)\right)\right) \]

       3. /-lowering-/.f64 39.7%

          \[\leadsto \mathsf{*.f64}\left(y, \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(z, y\right)\right)\right)\right) \]

   16. Simplified 39.7%

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

Alternative 10: 70.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-292}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{z \cdot \left(y + x\right)}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -1e-292) (* 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 <= -1e-292) {
		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 <= (-1d-292)) 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 <= -1e-292) {
		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 <= -1e-292:
		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 <= -1e-292)
		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 <= -1e-292)
		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, -1e-292], 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 < -1.0000000000000001e-292

   1. Initial program 74.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 74.9%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot \left(y + z\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot \left(y + z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(y + z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 54.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, z\right)\right)\right)\right) \]

   7. Simplified 54.0%

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

   if -1.0000000000000001e-292 < y

   1. Initial program 68.0%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 68.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 68.0%

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

   5. Taylor expanded in z around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{z \cdot \left(x + y\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(z \cdot \left(x + y\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right) \]

      4. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \left(y + x\right)\right)\right)\right) \]

      5. +-lowering-+.f64 45.7%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(z, \mathsf{+.f64}\left(y, x\right)\right)\right)\right) \]

   7. Simplified 45.7%

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

Alternative 11: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.7 \cdot 10^{-255}:\\ \;\;\;\;2 \cdot \sqrt{x \cdot \left(y + z\right)}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y 1.7e-255) (* 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 <= 1.7e-255) {
		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 <= 1.7d-255) 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 <= 1.7e-255) {
		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 <= 1.7e-255:
		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 <= 1.7e-255)
		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 <= 1.7e-255)
		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, 1.7e-255], 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 < 1.69999999999999992e-255

   1. Initial program 73.6%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 73.6%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 73.6%

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

   5. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot \left(y + z\right)}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot \left(y + z\right)\right)\right)\right) \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \left(y + z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 56.2%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, z\right)\right)\right)\right) \]

   7. Simplified 56.2%

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

   if 1.69999999999999992e-255 < y

   1. Initial program 68.1%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 68.1%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 68.1%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(y \cdot z\right)\right)\right) \]

      3. *-lowering-*.f64 23.0%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, z\right)\right)\right) \]

   7. Simplified 23.0%

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

Alternative 12: 68.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} [x, y, z] = \mathsf{sort}([x, y, z])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{-311}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \sqrt{y \cdot z}\\ \end{array} \end{array} \]

FPCore

NOTE: x, y, and z should be sorted in increasing order before calling this function.
(FPCore (x y z)
 :precision binary64
 (if (<= y -5e-311) (* 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 <= -5e-311) {
		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 <= (-5d-311)) 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 <= -5e-311) {
		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 <= -5e-311:
		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 <= -5e-311)
		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 <= -5e-311)
		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, -5e-311], 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 < -5.00000000000023e-311

   1. Initial program 74.9%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 74.9%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 74.9%

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

   5. Taylor expanded in z around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot y}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y\right)\right)\right) \]

      3. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(y \cdot x\right)\right)\right) \]

      4. *-lowering-*.f64 26.7%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, x\right)\right)\right) \]

   7. Simplified 26.7%

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

   if -5.00000000000023e-311 < y

   1. Initial program 67.7%

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

      3. associate-+l+ N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      4. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

      6. distribute-rgt-out N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

      7. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

      8. +-lowering-+.f64 67.8%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

   3. Simplified 67.8%

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

   5. Taylor expanded in x around 0

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{y \cdot z}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(y \cdot z\right)\right)\right) \]

      3. *-lowering-*.f64 20.3%

         \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, z\right)\right)\right) \]

   7. Simplified 20.3%

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

Alternative 13: 35.2% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

NOTE: x, y, and z should be sorted in increasing order before calling this function.
real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = 2.0d0 * sqrt((y * x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 71.0%

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{\left(x \cdot y + x \cdot z\right) + y \cdot z}\right)}\right) \]

   2. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(\left(x \cdot y + x \cdot z\right) + y \cdot z\right)\right)\right) \]

   3. associate-+l+ N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y + \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

   4. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\left(x \cdot y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

   5. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(x \cdot z + y \cdot z\right)\right)\right)\right) \]

   6. distribute-rgt-out N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \left(x + y\right)\right)\right)\right)\right) \]

   7. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \left(x + y\right)\right)\right)\right)\right) \]

   8. +-lowering-+.f64 71.1%

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(z, \mathsf{+.f64}\left(x, y\right)\right)\right)\right)\right) \]

3. Simplified 71.1%

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

5. Taylor expanded in z around 0

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

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \color{blue}{\left(\sqrt{x \cdot y}\right)}\right) \]

   2. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(x \cdot y\right)\right)\right) \]

   3. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\left(y \cdot x\right)\right)\right) \]

   4. *-lowering-*.f64 25.8%

      \[\leadsto \mathsf{*.f64}\left(2, \mathsf{sqrt.f64}\left(\mathsf{*.f64}\left(y, x\right)\right)\right) \]

7. Simplified 25.8%

   \[\leadsto \color{blue}{2 \cdot \sqrt{y \cdot x}} \]
8. Add Preprocessing

Developer Target 1: 82.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.25 \cdot \left(\left({y}^{-0.75} \cdot \left({z}^{-0.75} \cdot x\right)\right) \cdot \left(y + z\right)\right) + {z}^{0.25} \cdot {y}^{0.25}\\ \mathbf{if}\;z < 7.636950090573675 \cdot 10^{+176}:\\ \;\;\;\;2 \cdot \sqrt{\left(x + y\right) \cdot z + x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\left(t\_0 \cdot t\_0\right) \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0
         (+
          (* 0.25 (* (* (pow y -0.75) (* (pow z -0.75) x)) (+ y z)))
          (* (pow z 0.25) (pow y 0.25)))))
   (if (< z 7.636950090573675e+176)
     (* 2.0 (sqrt (+ (* (+ x y) z) (* x y))))
     (* (* t_0 t_0) 2.0))))

C

double code(double x, double y, double z) {
	double t_0 = (0.25 * ((pow(y, -0.75) * (pow(z, -0.75) * x)) * (y + z))) + (pow(z, 0.25) * pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (0.25d0 * (((y ** (-0.75d0)) * ((z ** (-0.75d0)) * x)) * (y + z))) + ((z ** 0.25d0) * (y ** 0.25d0))
    if (z < 7.636950090573675d+176) then
        tmp = 2.0d0 * sqrt((((x + y) * z) + (x * y)))
    else
        tmp = (t_0 * t_0) * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = (0.25 * ((Math.pow(y, -0.75) * (Math.pow(z, -0.75) * x)) * (y + z))) + (Math.pow(z, 0.25) * Math.pow(y, 0.25));
	double tmp;
	if (z < 7.636950090573675e+176) {
		tmp = 2.0 * Math.sqrt((((x + y) * z) + (x * y)));
	} else {
		tmp = (t_0 * t_0) * 2.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = (0.25 * ((math.pow(y, -0.75) * (math.pow(z, -0.75) * x)) * (y + z))) + (math.pow(z, 0.25) * math.pow(y, 0.25))
	tmp = 0
	if z < 7.636950090573675e+176:
		tmp = 2.0 * math.sqrt((((x + y) * z) + (x * y)))
	else:
		tmp = (t_0 * t_0) * 2.0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(Float64(0.25 * Float64(Float64((y ^ -0.75) * Float64((z ^ -0.75) * x)) * Float64(y + z))) + Float64((z ^ 0.25) * (y ^ 0.25)))
	tmp = 0.0
	if (z < 7.636950090573675e+176)
		tmp = Float64(2.0 * sqrt(Float64(Float64(Float64(x + y) * z) + Float64(x * y))));
	else
		tmp = Float64(Float64(t_0 * t_0) * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = (0.25 * (((y ^ -0.75) * ((z ^ -0.75) * x)) * (y + z))) + ((z ^ 0.25) * (y ^ 0.25));
	tmp = 0.0;
	if (z < 7.636950090573675e+176)
		tmp = 2.0 * sqrt((((x + y) * z) + (x * y)));
	else
		tmp = (t_0 * t_0) * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(0.25 * N[(N[(N[Power[y, -0.75], $MachinePrecision] * N[(N[Power[z, -0.75], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] * N[(y + z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[z, 0.25], $MachinePrecision] * N[Power[y, 0.25], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[z, 7.636950090573675e+176], N[(2.0 * N[Sqrt[N[(N[(N[(x + y), $MachinePrecision] * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[(t$95$0 * t$95$0), $MachinePrecision] * 2.0), $MachinePrecision]]]

Reproduce

herbie shell --seed 2024161 
(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)))))