Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2

Average Accuracy: 76.8% → 98.7%

Time: 12.9s

Precision: binary64

Cost: 1872

\[ \begin{array}{c}[x, y] = \mathsf{sort}([x, y])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} t_0 := \frac{1}{z} \cdot \frac{x \cdot y}{z + z \cdot z}\\ \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-230}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-286}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+77}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z + 1}}{z}\\ \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (/ (* x y) (* (* z z) (+ z 1.0))))

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* (/ 1.0 z) (/ (* x y) (+ z (* z z))))))
   (if (<= (* x y) -2e+171)
     (/ (/ x z) (* z (/ (+ z 1.0) y)))
     (if (<= (* x y) -1e-230)
       t_0
       (if (<= (* x y) 2e-286)
         (* (/ x z) (/ y z))
         (if (<= (* x y) 2e+77) t_0 (/ (* (/ x z) (/ y (+ z 1.0))) z)))))))

C

double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

↓

double code(double x, double y, double z) {
	double t_0 = (1.0 / z) * ((x * y) / (z + (z * z)));
	double tmp;
	if ((x * y) <= -2e+171) {
		tmp = (x / z) / (z * ((z + 1.0) / y));
	} else if ((x * y) <= -1e-230) {
		tmp = t_0;
	} else if ((x * y) <= 2e-286) {
		tmp = (x / z) * (y / z);
	} else if ((x * y) <= 2e+77) {
		tmp = t_0;
	} else {
		tmp = ((x / z) * (y / (z + 1.0))) / z;
	}
	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
    code = (x * y) / ((z * z) * (z + 1.0d0))
end function

↓

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 / z) * ((x * y) / (z + (z * z)))
    if ((x * y) <= (-2d+171)) then
        tmp = (x / z) / (z * ((z + 1.0d0) / y))
    else if ((x * y) <= (-1d-230)) then
        tmp = t_0
    else if ((x * y) <= 2d-286) then
        tmp = (x / z) * (y / z)
    else if ((x * y) <= 2d+77) then
        tmp = t_0
    else
        tmp = ((x / z) * (y / (z + 1.0d0))) / z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	return (x * y) / ((z * z) * (z + 1.0));
}

↓

public static double code(double x, double y, double z) {
	double t_0 = (1.0 / z) * ((x * y) / (z + (z * z)));
	double tmp;
	if ((x * y) <= -2e+171) {
		tmp = (x / z) / (z * ((z + 1.0) / y));
	} else if ((x * y) <= -1e-230) {
		tmp = t_0;
	} else if ((x * y) <= 2e-286) {
		tmp = (x / z) * (y / z);
	} else if ((x * y) <= 2e+77) {
		tmp = t_0;
	} else {
		tmp = ((x / z) * (y / (z + 1.0))) / z;
	}
	return tmp;
}

Python

def code(x, y, z):
	return (x * y) / ((z * z) * (z + 1.0))

↓

def code(x, y, z):
	t_0 = (1.0 / z) * ((x * y) / (z + (z * z)))
	tmp = 0
	if (x * y) <= -2e+171:
		tmp = (x / z) / (z * ((z + 1.0) / y))
	elif (x * y) <= -1e-230:
		tmp = t_0
	elif (x * y) <= 2e-286:
		tmp = (x / z) * (y / z)
	elif (x * y) <= 2e+77:
		tmp = t_0
	else:
		tmp = ((x / z) * (y / (z + 1.0))) / z
	return tmp

Julia

function code(x, y, z)
	return Float64(Float64(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
end

↓

function code(x, y, z)
	t_0 = Float64(Float64(1.0 / z) * Float64(Float64(x * y) / Float64(z + Float64(z * z))))
	tmp = 0.0
	if (Float64(x * y) <= -2e+171)
		tmp = Float64(Float64(x / z) / Float64(z * Float64(Float64(z + 1.0) / y)));
	elseif (Float64(x * y) <= -1e-230)
		tmp = t_0;
	elseif (Float64(x * y) <= 2e-286)
		tmp = Float64(Float64(x / z) * Float64(y / z));
	elseif (Float64(x * y) <= 2e+77)
		tmp = t_0;
	else
		tmp = Float64(Float64(Float64(x / z) * Float64(y / Float64(z + 1.0))) / z);
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z)
	tmp = (x * y) / ((z * z) * (z + 1.0));
end

↓

function tmp_2 = code(x, y, z)
	t_0 = (1.0 / z) * ((x * y) / (z + (z * z)));
	tmp = 0.0;
	if ((x * y) <= -2e+171)
		tmp = (x / z) / (z * ((z + 1.0) / y));
	elseif ((x * y) <= -1e-230)
		tmp = t_0;
	elseif ((x * y) <= 2e-286)
		tmp = (x / z) * (y / z);
	elseif ((x * y) <= 2e+77)
		tmp = t_0;
	else
		tmp = ((x / z) * (y / (z + 1.0))) / z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := N[(N[(x * y), $MachinePrecision] / N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_] := Block[{t$95$0 = N[(N[(1.0 / z), $MachinePrecision] * N[(N[(x * y), $MachinePrecision] / N[(z + N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(x * y), $MachinePrecision], -2e+171], N[(N[(x / z), $MachinePrecision] / N[(z * N[(N[(z + 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], -1e-230], t$95$0, If[LessEqual[N[(x * y), $MachinePrecision], 2e-286], N[(N[(x / z), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * y), $MachinePrecision], 2e+77], t$95$0, N[(N[(N[(x / z), $MachinePrecision] * N[(y / N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]]]]]]

Target

Original	76.8%
Target	93.6%
Herbie	98.7%

\[\begin{array}{l} \mathbf{if}\;z < 249.6182814532307:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array} \]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x y) < -1.99999999999999991e171

   1. Initial program 46.2%

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

   2. Simplified 82.4%

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

      [Start] 46.2	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      times-frac [=>] 82.4	\[ \color{blue}{\frac{x}{z \cdot z} \cdot \frac{y}{z + 1}} \]

   3. Applied egg-rr 96.5%

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

      [Start] 82.4	\[ \frac{x}{z \cdot z} \cdot \frac{y}{z + 1} \]
      clear-num [=>] 82.4	\[ \frac{x}{z \cdot z} \cdot \color{blue}{\frac{1}{\frac{z + 1}{y}}} \]
      un-div-inv [=>] 82.4	\[ \color{blue}{\frac{\frac{x}{z \cdot z}}{\frac{z + 1}{y}}} \]
      associate-/r* [=>] 96.2	\[ \frac{\color{blue}{\frac{\frac{x}{z}}{z}}}{\frac{z + 1}{y}} \]
      associate-/l/ [=>] 96.5	\[ \color{blue}{\frac{\frac{x}{z}}{\frac{z + 1}{y} \cdot z}} \]

   if -1.99999999999999991e171 < (*.f64 x y) < -1.00000000000000005e-230 or 2.0000000000000001e-286 < (*.f64 x y) < 1.99999999999999997e77

   1. Initial program 91.1%

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

   2. Applied egg-rr 99.6%

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

      [Start] 91.1	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      *-un-lft-identity [=>] 91.1	\[ \frac{\color{blue}{1 \cdot \left(x \cdot y\right)}}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      associate-*l* [=>] 91.2	\[ \frac{1 \cdot \left(x \cdot y\right)}{\color{blue}{z \cdot \left(z \cdot \left(z + 1\right)\right)}} \]
      times-frac [=>] 99.6	\[ \color{blue}{\frac{1}{z} \cdot \frac{x \cdot y}{z \cdot \left(z + 1\right)}} \]
      *-commutative [=>] 99.6	\[ \frac{1}{z} \cdot \frac{x \cdot y}{\color{blue}{\left(z + 1\right) \cdot z}} \]
      distribute-rgt1-in [<=] 99.6	\[ \frac{1}{z} \cdot \frac{x \cdot y}{\color{blue}{z + z \cdot z}} \]

   if -1.00000000000000005e-230 < (*.f64 x y) < 2.0000000000000001e-286

   1. Initial program 64.9%

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

   2. Simplified 89.7%

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

      [Start] 64.9	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      *-commutative [=>] 64.9	\[ \frac{\color{blue}{y \cdot x}}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      associate-*r/ [<=] 76.1	\[ \color{blue}{y \cdot \frac{x}{\left(z \cdot z\right) \cdot \left(z + 1\right)}} \]
      associate-*l* [=>] 76.1	\[ y \cdot \frac{x}{\color{blue}{z \cdot \left(z \cdot \left(z + 1\right)\right)}} \]
      associate-/r* [=>] 89.7	\[ y \cdot \color{blue}{\frac{\frac{x}{z}}{z \cdot \left(z + 1\right)}} \]
      distribute-rgt-in [=>] 89.7	\[ y \cdot \frac{\frac{x}{z}}{\color{blue}{z \cdot z + 1 \cdot z}} \]
      *-lft-identity [=>] 89.7	\[ y \cdot \frac{\frac{x}{z}}{z \cdot z + \color{blue}{z}} \]
      fma-def [=>] 89.7	\[ y \cdot \frac{\frac{x}{z}}{\color{blue}{\mathsf{fma}\left(z, z, z\right)}} \]

   3. Taylor expanded in z around 0 63.5%

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

   4. Simplified 98.2%

      \[\leadsto \color{blue}{\frac{x}{z} \cdot \frac{y}{z}} \]
      Proof

      [Start] 63.5	\[ \frac{y \cdot x}{{z}^{2}} \]
      *-commutative [=>] 63.5	\[ \frac{\color{blue}{x \cdot y}}{{z}^{2}} \]
      unpow2 [=>] 63.5	\[ \frac{x \cdot y}{\color{blue}{z \cdot z}} \]
      times-frac [=>] 98.2	\[ \color{blue}{\frac{x}{z} \cdot \frac{y}{z}} \]

   if 1.99999999999999997e77 < (*.f64 x y)

   1. Initial program 59.9%

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

   2. Simplified 85.5%

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

      [Start] 59.9	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      times-frac [=>] 85.5	\[ \color{blue}{\frac{x}{z \cdot z} \cdot \frac{y}{z + 1}} \]

   3. Applied egg-rr 97.6%

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

      [Start] 85.5	\[ \frac{x}{z \cdot z} \cdot \frac{y}{z + 1} \]
      *-commutative [=>] 85.5	\[ \color{blue}{\frac{y}{z + 1} \cdot \frac{x}{z \cdot z}} \]
      associate-/r* [=>] 94.8	\[ \frac{y}{z + 1} \cdot \color{blue}{\frac{\frac{x}{z}}{z}} \]
      associate-*r/ [=>] 97.6	\[ \color{blue}{\frac{\frac{y}{z + 1} \cdot \frac{x}{z}}{z}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+171}:\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z + 1}{y}}\\ \mathbf{elif}\;x \cdot y \leq -1 \cdot 10^{-230}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x \cdot y}{z + z \cdot z}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{-286}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{elif}\;x \cdot y \leq 2 \cdot 10^{+77}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x \cdot y}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z + 1}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	94.9%
Cost	1232

\[\begin{array}{l} t_0 := \frac{y}{z + 1} \cdot \frac{x}{z \cdot z}\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;\frac{\frac{y}{z \cdot \frac{z}{x}}}{z}\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-152}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{+35}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{\frac{z}{x}}}{z}\\ \end{array} \]

Alternative 2
Accuracy	94.5%
Cost	1100

\[\begin{array}{l} t_0 := \frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{if}\;y \leq -7.2 \cdot 10^{-222}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.48 \cdot 10^{-276}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\ \mathbf{elif}\;y \leq 2 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z + 1} \cdot \frac{\frac{x}{z}}{z}\\ \end{array} \]

Alternative 3
Accuracy	94.5%
Cost	969

\[\begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{-68} \lor \neg \left(z \leq 2.5 \cdot 10^{-152}\right):\\ \;\;\;\;\frac{y}{z + 1} \cdot \frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \end{array} \]

Alternative 4
Accuracy	96.4%
Cost	969

\[\begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-222} \lor \neg \left(y \leq 1.8 \cdot 10^{-277}\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z + 1}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\ \end{array} \]

Alternative 5
Accuracy	94.8%
Cost	968

\[\begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{\frac{x}{z \cdot \frac{z + 1}{y}}}{z}\\ \mathbf{elif}\;y \leq 6 \cdot 10^{+292}:\\ \;\;\;\;\frac{y}{z + 1} \cdot \frac{\frac{x}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 6
Accuracy	90.1%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{y}{z} \cdot \frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \end{array} \]

Alternative 7
Accuracy	93.6%
Cost	841

\[\begin{array}{l} \mathbf{if}\;z \leq -1 \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \end{array} \]

Alternative 8
Accuracy	93.0%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 9
Accuracy	92.4%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{\frac{y}{z \cdot \frac{z}{x}}}{z}\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{z \cdot \frac{z}{y}}\\ \end{array} \]

Alternative 10
Accuracy	71.0%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+119} \lor \neg \left(z \leq 5 \cdot 10^{-152}\right):\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \end{array} \]

Alternative 11
Accuracy	71.8%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -2.2 \cdot 10^{-58} \lor \neg \left(z \leq 5.6 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{\frac{z \cdot z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z}\\ \end{array} \]

Alternative 12
Accuracy	71.9%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -7.5 \cdot 10^{-66} \lor \neg \left(z \leq 5.6 \cdot 10^{-67}\right):\\ \;\;\;\;\frac{x}{\frac{z \cdot z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x}}}{z}\\ \end{array} \]

Alternative 13
Accuracy	71.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{-234}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot z}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 14
Accuracy	72.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq 10^{-142}:\\ \;\;\;\;\frac{x}{z \cdot \frac{z}{y}}\\ \mathbf{elif}\;y \leq 10^{+102}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 15
Accuracy	72.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;y \leq 2.5 \cdot 10^{-142}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+101}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 16
Accuracy	71.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-58}:\\ \;\;\;\;\frac{x}{\frac{z \cdot z}{y}}\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-152}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z \cdot z}{x}}\\ \end{array} \]

Alternative 17
Accuracy	72.3%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-106}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{\frac{x}{z}}}\\ \end{array} \]

Alternative 18
Accuracy	64.9%
Cost	448

\[\frac{x}{z} \cdot \frac{y}{z} \]

Reproduce

herbie shell --seed 2023135 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1.0))))