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

Average Accuracy: 76.1% → 94.9%

Time: 16.1s

Precision: binary64

Cost: 1232

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

Math

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

↓

\[\begin{array}{l} t_0 := \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{if}\;z \leq -3 \cdot 10^{+65}:\\ \;\;\;\;\frac{y \cdot \frac{\frac{x}{z}}{z}}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\frac{y}{z}}{z}\\ \end{array} \]

FPCore

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

↓

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (/ (* x y) (* (* z z) (+ z 1.0)))))
   (if (<= z -3e+65)
     (/ (* y (/ (/ x z) z)) z)
     (if (<= z -1.25e-89)
       t_0
       (if (<= z 1.6e-95)
         (/ (* x (/ y z)) z)
         (if (<= z 4.5e+64) t_0 (* (/ x z) (/ (/ y z) 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 = (x * y) / ((z * z) * (z + 1.0));
	double tmp;
	if (z <= -3e+65) {
		tmp = (y * ((x / z) / z)) / z;
	} else if (z <= -1.25e-89) {
		tmp = t_0;
	} else if (z <= 1.6e-95) {
		tmp = (x * (y / z)) / z;
	} else if (z <= 4.5e+64) {
		tmp = t_0;
	} else {
		tmp = (x / z) * ((y / z) / 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 = (x * y) / ((z * z) * (z + 1.0d0))
    if (z <= (-3d+65)) then
        tmp = (y * ((x / z) / z)) / z
    else if (z <= (-1.25d-89)) then
        tmp = t_0
    else if (z <= 1.6d-95) then
        tmp = (x * (y / z)) / z
    else if (z <= 4.5d+64) then
        tmp = t_0
    else
        tmp = (x / z) * ((y / z) / 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 = (x * y) / ((z * z) * (z + 1.0));
	double tmp;
	if (z <= -3e+65) {
		tmp = (y * ((x / z) / z)) / z;
	} else if (z <= -1.25e-89) {
		tmp = t_0;
	} else if (z <= 1.6e-95) {
		tmp = (x * (y / z)) / z;
	} else if (z <= 4.5e+64) {
		tmp = t_0;
	} else {
		tmp = (x / z) * ((y / z) / z);
	}
	return tmp;
}

Python

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

↓

def code(x, y, z):
	t_0 = (x * y) / ((z * z) * (z + 1.0))
	tmp = 0
	if z <= -3e+65:
		tmp = (y * ((x / z) / z)) / z
	elif z <= -1.25e-89:
		tmp = t_0
	elif z <= 1.6e-95:
		tmp = (x * (y / z)) / z
	elif z <= 4.5e+64:
		tmp = t_0
	else:
		tmp = (x / z) * ((y / z) / 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(x * y) / Float64(Float64(z * z) * Float64(z + 1.0)))
	tmp = 0.0
	if (z <= -3e+65)
		tmp = Float64(Float64(y * Float64(Float64(x / z) / z)) / z);
	elseif (z <= -1.25e-89)
		tmp = t_0;
	elseif (z <= 1.6e-95)
		tmp = Float64(Float64(x * Float64(y / z)) / z);
	elseif (z <= 4.5e+64)
		tmp = t_0;
	else
		tmp = Float64(Float64(x / z) * Float64(Float64(y / z) / 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 = (x * y) / ((z * z) * (z + 1.0));
	tmp = 0.0;
	if (z <= -3e+65)
		tmp = (y * ((x / z) / z)) / z;
	elseif (z <= -1.25e-89)
		tmp = t_0;
	elseif (z <= 1.6e-95)
		tmp = (x * (y / z)) / z;
	elseif (z <= 4.5e+64)
		tmp = t_0;
	else
		tmp = (x / z) * ((y / z) / 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[(x * y), $MachinePrecision] / N[(N[(z * z), $MachinePrecision] * N[(z + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+65], N[(N[(y * N[(N[(x / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, -1.25e-89], t$95$0, If[LessEqual[z, 1.6e-95], N[(N[(x * N[(y / z), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision], If[LessEqual[z, 4.5e+64], t$95$0, N[(N[(x / z), $MachinePrecision] * N[(N[(y / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision]]]]]]

Target

Original	76.1%
Target	93.6%
Herbie	94.9%

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

Derivation

1. Split input into 4 regimes

2. if z < -3.0000000000000002e65

   1. Initial program 79.0%

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

   2. Simplified 91.0%

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

      [Start] 79.0	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      times-frac [=>] 91.0	\[ \color{blue}{\frac{x}{z \cdot z} \cdot \frac{y}{z + 1}} \]

   3. Taylor expanded in z around inf 91.0%

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

   4. Applied egg-rr 96.9%

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

      [Start] 91.0	\[ \frac{x}{z \cdot z} \cdot \frac{y}{z} \]
      associate-*r/ [=>] 91.0	\[ \color{blue}{\frac{\frac{x}{z \cdot z} \cdot y}{z}} \]
      associate-/r* [=>] 96.9	\[ \frac{\color{blue}{\frac{\frac{x}{z}}{z}} \cdot y}{z} \]

   if -3.0000000000000002e65 < z < -1.24999999999999992e-89 or 1.5999999999999999e-95 < z < 4.49999999999999973e64

   1. Initial program 92.6%

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

   if -1.24999999999999992e-89 < z < 1.5999999999999999e-95

   1. Initial program 37.5%

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

   2. Simplified 36.8%

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

      [Start] 37.5	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      times-frac [=>] 36.8	\[ \color{blue}{\frac{x}{z \cdot z} \cdot \frac{y}{z + 1}} \]

   3. Applied egg-rr 90.4%

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

      [Start] 36.8	\[ \frac{x}{z \cdot z} \cdot \frac{y}{z + 1} \]
      *-commutative [=>] 36.8	\[ \color{blue}{\frac{y}{z + 1} \cdot \frac{x}{z \cdot z}} \]
      associate-/r* [=>] 66.7	\[ \frac{y}{z + 1} \cdot \color{blue}{\frac{\frac{x}{z}}{z}} \]
      associate-*r/ [=>] 90.4	\[ \color{blue}{\frac{\frac{y}{z + 1} \cdot \frac{x}{z}}{z}} \]

   4. Taylor expanded in z around 0 70.5%

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

   5. Simplified 91.6%

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

      [Start] 70.5	\[ \frac{\frac{y \cdot x}{z}}{z} \]
      associate-/l* [=>] 91.4	\[ \frac{\color{blue}{\frac{y}{\frac{z}{x}}}}{z} \]
      associate-/r/ [=>] 91.6	\[ \frac{\color{blue}{\frac{y}{z} \cdot x}}{z} \]

   if 4.49999999999999973e64 < z

   1. Initial program 80.5%

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

   2. Simplified 92.1%

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

      [Start] 80.5	\[ \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)} \]
      times-frac [=>] 92.1	\[ \color{blue}{\frac{x}{z \cdot z} \cdot \frac{y}{z + 1}} \]

   3. Applied egg-rr 97.2%

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

      [Start] 92.1	\[ \frac{x}{z \cdot z} \cdot \frac{y}{z + 1} \]
      associate-*l/ [=>] 91.2	\[ \color{blue}{\frac{x \cdot \frac{y}{z + 1}}{z \cdot z}} \]
      associate-/r* [=>] 96.1	\[ \color{blue}{\frac{\frac{x \cdot \frac{y}{z + 1}}{z}}{z}} \]
      clear-num [=>] 95.9	\[ \frac{\frac{x \cdot \color{blue}{\frac{1}{\frac{z + 1}{y}}}}{z}}{z} \]
      un-div-inv [=>] 95.9	\[ \frac{\frac{\color{blue}{\frac{x}{\frac{z + 1}{y}}}}{z}}{z} \]
      associate-/l/ [=>] 97.2	\[ \frac{\color{blue}{\frac{x}{z \cdot \frac{z + 1}{y}}}}{z} \]

   4. Taylor expanded in z around inf 92.2%

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

   5. Simplified 97.2%

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

      [Start] 92.2	\[ \frac{\frac{x}{\frac{{z}^{2}}{y}}}{z} \]
      unpow2 [=>] 92.2	\[ \frac{\frac{x}{\frac{\color{blue}{z \cdot z}}{y}}}{z} \]
      associate-/l* [=>] 97.2	\[ \frac{\frac{x}{\color{blue}{\frac{z}{\frac{y}{z}}}}}{z} \]

   6. Applied egg-rr 97.5%

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

      [Start] 97.2	\[ \frac{\frac{x}{\frac{z}{\frac{y}{z}}}}{z} \]
      div-inv [=>] 97.2	\[ \color{blue}{\frac{x}{\frac{z}{\frac{y}{z}}} \cdot \frac{1}{z}} \]
      associate-/r/ [=>] 98.6	\[ \color{blue}{\left(\frac{x}{z} \cdot \frac{y}{z}\right)} \cdot \frac{1}{z} \]
      associate-*l* [=>] 97.5	\[ \color{blue}{\frac{x}{z} \cdot \left(\frac{y}{z} \cdot \frac{1}{z}\right)} \]
      div-inv [<=] 97.5	\[ \frac{x}{z} \cdot \color{blue}{\frac{\frac{y}{z}}{z}} \]

3. Recombined 4 regimes into one program.

4. Final simplification 94.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+65}:\\ \;\;\;\;\frac{y \cdot \frac{\frac{x}{z}}{z}}{z}\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-89}:\\ \;\;\;\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-95}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+64}:\\ \;\;\;\;\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\frac{y}{z}}{z}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	96.3%
Cost	2249

\[\begin{array}{l} t_0 := \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{if}\;t_0 \leq 0 \lor \neg \left(t_0 \leq 4 \cdot 10^{+200}\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z + 1}}{z}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 2
Accuracy	96.3%
Cost	2248

\[\begin{array}{l} t_0 := \frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z + 1}}{z}\\ \mathbf{elif}\;t_0 \leq 2 \cdot 10^{+272}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z \cdot \frac{z + 1}{y}}}{z}\\ \end{array} \]

Alternative 3
Accuracy	96.0%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\frac{y}{z}}{z}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-51}:\\ \;\;\;\;\frac{\left(x \cdot y\right) \cdot \frac{1}{z + z \cdot z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x} \cdot \left(z + 1\right)}}{z}\\ \end{array} \]

Alternative 4
Accuracy	96.1%
Cost	1352

\[\begin{array}{l} \mathbf{if}\;x \cdot y \leq -2 \cdot 10^{+239}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\frac{y}{z}}{z}\\ \mathbf{elif}\;x \cdot y \leq -2 \cdot 10^{-51}:\\ \;\;\;\;\frac{1}{z} \cdot \frac{x \cdot y}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{y}{\frac{z}{x} \cdot \left(z + 1\right)}}{z}\\ \end{array} \]

Alternative 5
Accuracy	93.4%
Cost	841

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

Alternative 6
Accuracy	93.5%
Cost	840

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

Alternative 7
Accuracy	93.9%
Cost	840

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

Alternative 8
Accuracy	93.4%
Cost	840

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

Alternative 9
Accuracy	93.8%
Cost	840

\[\begin{array}{l} \mathbf{if}\;z \leq -1:\\ \;\;\;\;\frac{y \cdot \frac{\frac{x}{z}}{z}}{z}\\ \mathbf{elif}\;z \leq 0.75:\\ \;\;\;\;\frac{y \cdot \left(\frac{x}{z} - x\right)}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{\frac{y}{z}}{z}\\ \end{array} \]

Alternative 10
Accuracy	72.1%
Cost	713

\[\begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+60} \lor \neg \left(z \leq 1.1 \cdot 10^{-131}\right):\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \end{array} \]

Alternative 11
Accuracy	72.0%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{-83}:\\ \;\;\;\;x \cdot \frac{y}{z \cdot z}\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-120}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 12
Accuracy	72.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -1.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{\frac{z \cdot z}{y}}\\ \mathbf{elif}\;z \leq 1.82 \cdot 10^{-121}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 13
Accuracy	73.2%
Cost	712

\[\begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{-27}:\\ \;\;\;\;\frac{x}{\frac{z \cdot z}{y}}\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-214}:\\ \;\;\;\;\frac{x}{z} \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z \cdot \frac{z}{x}}\\ \end{array} \]

Alternative 14
Accuracy	72.7%
Cost	712

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{\frac{z \cdot z}{y}}\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-43}:\\ \;\;\;\;\frac{x \cdot \frac{y}{z}}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z \cdot z}{x}}\\ \end{array} \]

Alternative 15
Accuracy	95.1%
Cost	704

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

Alternative 16
Accuracy	72.3%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 4.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{x}{z \cdot \frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 17
Accuracy	72.4%
Cost	580

\[\begin{array}{l} \mathbf{if}\;y \leq 4 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{\frac{z}{\frac{y}{z}}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z \cdot z}\\ \end{array} \]

Alternative 18
Accuracy	33.3%
Cost	516

\[\begin{array}{l} \mathbf{if}\;y \leq 2 \cdot 10^{-84}:\\ \;\;\;\;\frac{y}{z} \cdot \left(-x\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{-y}{\frac{z}{x}}\\ \end{array} \]

Alternative 19
Accuracy	66.7%
Cost	448

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

Alternative 20
Accuracy	28.9%
Cost	384

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

Reproduce

herbie shell --seed 2023133 
(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))))