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

Average Error: 0.0 → 18.0

Time: 18.0s

Precision: binary64

Cost: 1360

Math

\[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

↓

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(y + -2\right)\right) + z \cdot \left(1 - y\right)\\ t_2 := \left(x - \left(t + -1\right) \cdot a\right) + t \cdot b\\ \mathbf{if}\;t \leq -1.5999351883990136 \cdot 10^{+40}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.0679795993739348 \cdot 10^{-225}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.410991055704619 \cdot 10^{-116}:\\ \;\;\;\;x + \left(a + z\right)\\ \mathbf{elif}\;t \leq 2916.315739342115:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

FPCore

(FPCore (x y z t a b)
 :precision binary64
 (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))

↓

(FPCore (x y z t a b)
 :precision binary64
 (let* ((t_1 (+ (+ x (* b (+ y -2.0))) (* z (- 1.0 y))))
        (t_2 (+ (- x (* (+ t -1.0) a)) (* t b))))
   (if (<= t -1.5999351883990136e+40)
     t_2
     (if (<= t 1.0679795993739348e-225)
       t_1
       (if (<= t 6.410991055704619e-116)
         (+ x (+ a z))
         (if (<= t 2916.315739342115) t_1 t_2))))))

C

double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

↓

double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (b * (y + -2.0))) + (z * (1.0 - y));
	double t_2 = (x - ((t + -1.0) * a)) + (t * b);
	double tmp;
	if (t <= -1.5999351883990136e+40) {
		tmp = t_2;
	} else if (t <= 1.0679795993739348e-225) {
		tmp = t_1;
	} else if (t <= 6.410991055704619e-116) {
		tmp = x + (a + z);
	} else if (t <= 2916.315739342115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    code = ((x - ((y - 1.0d0) * z)) - ((t - 1.0d0) * a)) + (((y + t) - 2.0d0) * b)
end function

↓

real(8) function code(x, y, z, t, a, b)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8), intent (in) :: b
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = (x + (b * (y + (-2.0d0)))) + (z * (1.0d0 - y))
    t_2 = (x - ((t + (-1.0d0)) * a)) + (t * b)
    if (t <= (-1.5999351883990136d+40)) then
        tmp = t_2
    else if (t <= 1.0679795993739348d-225) then
        tmp = t_1
    else if (t <= 6.410991055704619d-116) then
        tmp = x + (a + z)
    else if (t <= 2916.315739342115d0) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a, double b) {
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
}

↓

public static double code(double x, double y, double z, double t, double a, double b) {
	double t_1 = (x + (b * (y + -2.0))) + (z * (1.0 - y));
	double t_2 = (x - ((t + -1.0) * a)) + (t * b);
	double tmp;
	if (t <= -1.5999351883990136e+40) {
		tmp = t_2;
	} else if (t <= 1.0679795993739348e-225) {
		tmp = t_1;
	} else if (t <= 6.410991055704619e-116) {
		tmp = x + (a + z);
	} else if (t <= 2916.315739342115) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z, t, a, b):
	return ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b)

↓

def code(x, y, z, t, a, b):
	t_1 = (x + (b * (y + -2.0))) + (z * (1.0 - y))
	t_2 = (x - ((t + -1.0) * a)) + (t * b)
	tmp = 0
	if t <= -1.5999351883990136e+40:
		tmp = t_2
	elif t <= 1.0679795993739348e-225:
		tmp = t_1
	elif t <= 6.410991055704619e-116:
		tmp = x + (a + z)
	elif t <= 2916.315739342115:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z, t, a, b)
	return Float64(Float64(Float64(x - Float64(Float64(y - 1.0) * z)) - Float64(Float64(t - 1.0) * a)) + Float64(Float64(Float64(y + t) - 2.0) * b))
end

↓

function code(x, y, z, t, a, b)
	t_1 = Float64(Float64(x + Float64(b * Float64(y + -2.0))) + Float64(z * Float64(1.0 - y)))
	t_2 = Float64(Float64(x - Float64(Float64(t + -1.0) * a)) + Float64(t * b))
	tmp = 0.0
	if (t <= -1.5999351883990136e+40)
		tmp = t_2;
	elseif (t <= 1.0679795993739348e-225)
		tmp = t_1;
	elseif (t <= 6.410991055704619e-116)
		tmp = Float64(x + Float64(a + z));
	elseif (t <= 2916.315739342115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp = code(x, y, z, t, a, b)
	tmp = ((x - ((y - 1.0) * z)) - ((t - 1.0) * a)) + (((y + t) - 2.0) * b);
end

↓

function tmp_2 = code(x, y, z, t, a, b)
	t_1 = (x + (b * (y + -2.0))) + (z * (1.0 - y));
	t_2 = (x - ((t + -1.0) * a)) + (t * b);
	tmp = 0.0;
	if (t <= -1.5999351883990136e+40)
		tmp = t_2;
	elseif (t <= 1.0679795993739348e-225)
		tmp = t_1;
	elseif (t <= 6.410991055704619e-116)
		tmp = x + (a + z);
	elseif (t <= 2916.315739342115)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_, b_] := N[(N[(N[(x - N[(N[(y - 1.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision] - N[(N[(t - 1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(y + t), $MachinePrecision] - 2.0), $MachinePrecision] * b), $MachinePrecision]), $MachinePrecision]

↓

code[x_, y_, z_, t_, a_, b_] := Block[{t$95$1 = N[(N[(x + N[(b * N[(y + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(x - N[(N[(t + -1.0), $MachinePrecision] * a), $MachinePrecision]), $MachinePrecision] + N[(t * b), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -1.5999351883990136e+40], t$95$2, If[LessEqual[t, 1.0679795993739348e-225], t$95$1, If[LessEqual[t, 6.410991055704619e-116], N[(x + N[(a + z), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 2916.315739342115], t$95$1, t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -1.59993518839901359e40 or 2916.3157393421152 < t

   1. Initial program 0.0

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in z around 0 14.6

      \[\leadsto \color{blue}{\left(x - \left(t - 1\right) \cdot a\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]

   3. Taylor expanded in t around inf 18.1

      \[\leadsto \left(x - \left(t - 1\right) \cdot a\right) + \color{blue}{t \cdot b} \]

   if -1.59993518839901359e40 < t < 1.0679795993739348e-225 or 6.4109910557046191e-116 < t < 2916.3157393421152

   1. Initial program 0.0

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in a around 0 15.6

      \[\leadsto \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - z \cdot \left(y - 1\right)} \]

   3. Taylor expanded in t around 0 16.6

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

   4. Simplified 16.6

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

   if 1.0679795993739348e-225 < t < 6.4109910557046191e-116

   1. Initial program 0.0

      \[\left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   2. Taylor expanded in b around 0 16.4

      \[\leadsto \color{blue}{x - \left(\left(t - 1\right) \cdot a + z \cdot \left(y - 1\right)\right)} \]

   3. Taylor expanded in y around 0 24.2

      \[\leadsto x - \color{blue}{\left(-1 \cdot z + \left(t - 1\right) \cdot a\right)} \]

   4. Simplified 24.2

      \[\leadsto x - \color{blue}{\left(t \cdot a - \left(a + z\right)\right)} \]

   5. Taylor expanded in t around 0 24.2

      \[\leadsto x - \color{blue}{-1 \cdot \left(a + z\right)} \]

   6. Simplified 24.2

      \[\leadsto x - \color{blue}{\left(\left(-a\right) - z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 18.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -1.5999351883990136 \cdot 10^{+40}:\\ \;\;\;\;\left(x - \left(t + -1\right) \cdot a\right) + t \cdot b\\ \mathbf{elif}\;t \leq 1.0679795993739348 \cdot 10^{-225}:\\ \;\;\;\;\left(x + b \cdot \left(y + -2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6.410991055704619 \cdot 10^{-116}:\\ \;\;\;\;x + \left(a + z\right)\\ \mathbf{elif}\;t \leq 2916.315739342115:\\ \;\;\;\;\left(x + b \cdot \left(y + -2\right)\right) + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x - \left(t + -1\right) \cdot a\right) + t \cdot b\\ \end{array} \]

Alternatives

Alternative 1
Error	38.3
Cost	1772

\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := z - y \cdot z\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -4.908571517904543 \cdot 10^{-10}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.008545031922205 \cdot 10^{-77}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;x \leq -6.432191492546112 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;x \leq -1.1140655086702975 \cdot 10^{-159}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -3.4904607590011354 \cdot 10^{-231}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;x \leq 5.361786587318497 \cdot 10^{-191}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 8.797173011027828 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.1637418200907455 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.8745680873397529:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 7.73874449609612 \cdot 10^{+106}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.979418264783029 \cdot 10^{+196}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + z\\ \end{array} \]

Alternative 2
Error	27.3
Cost	1632

\[\begin{array}{l} t_1 := x + b \cdot \left(-2 + \left(t + y\right)\right)\\ t_2 := a \cdot \left(1 - t\right)\\ t_3 := x - z \cdot \left(y + -1\right)\\ \mathbf{if}\;a \leq -1.8426532857969448 \cdot 10^{+28}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.3331988442633054 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.0412127176822209 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5.4926942540199806 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.551762021893823 \cdot 10^{-271}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 8.607889128858485 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.012855454405422 \cdot 10^{-144}:\\ \;\;\;\;b \cdot y + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;a \leq 29.274290580877597:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+172}:\\ \;\;\;\;x + \left(a + z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 3
Error	23.6
Cost	1496

\[\begin{array}{l} t_1 := \left(x - \left(t + -1\right) \cdot a\right) + t \cdot b\\ t_2 := \left(x + b \cdot \left(y + -2\right)\right) + z\\ \mathbf{if}\;b \leq -54.95269838053092:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -5.9559471691959226 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.786870050354409 \cdot 10^{-299}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;b \leq 2.0294780616480287 \cdot 10^{-103}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.806003588238974 \cdot 10^{-71}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(t + y\right)\right)\\ \end{array} \]

Alternative 4
Error	36.9
Cost	1376

\[\begin{array}{l} t_1 := b \cdot \left(y + -2\right)\\ t_2 := x - t \cdot a\\ \mathbf{if}\;t \leq -3179.6749671733455:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.106378692354201 \cdot 10^{-75}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -3.1488478664116253 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2352339306147185 \cdot 10^{-221}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -2.69051687500648 \cdot 10^{-303}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.521420401100466 \cdot 10^{-239}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.8015929858970816 \cdot 10^{-221}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;t \leq 2.7472433807280564 \cdot 10^{-27}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	29.9
Cost	1376

\[\begin{array}{l} t_1 := x - z \cdot \left(y + -1\right)\\ t_2 := x + \left(a + z\right)\\ t_3 := x - t \cdot a\\ t_4 := a + b \cdot \left(y + -2\right)\\ \mathbf{if}\;t \leq -1.5999351883990136 \cdot 10^{+40}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.928484976876344 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.1488478664116253 \cdot 10^{-168}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -3.2352339306147185 \cdot 10^{-221}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.4882689135838257 \cdot 10^{-230}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.3523958354620057 \cdot 10^{-250}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.3058393724601264 \cdot 10^{-285}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 831441.7102027182:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	25.8
Cost	1368

\[\begin{array}{l} t_1 := x + b \cdot \left(-2 + \left(t + y\right)\right)\\ t_2 := \left(x + b \cdot \left(y + -2\right)\right) + z\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -1.8426532857969448 \cdot 10^{+28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -2.3331988442633054 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.0412127176822209 \cdot 10^{-215}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;a \leq 2.551762021893823 \cdot 10^{-271}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.900856420031732 \cdot 10^{-194}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	30.0
Cost	1112

\[\begin{array}{l} t_1 := x + \left(a + z\right)\\ t_2 := b \cdot \left(y + -2\right)\\ t_3 := x - t \cdot a\\ \mathbf{if}\;t \leq -8.511935691559604 \cdot 10^{+33}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.0663959499885217 \cdot 10^{-83}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.9080861308979917 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2352339306147185 \cdot 10^{-221}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.4882689135838257 \cdot 10^{-230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 831441.7102027182:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	40.2
Cost	984

\[\begin{array}{l} \mathbf{if}\;b \leq -1.76 \cdot 10^{+186}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq 2.572648219310054 \cdot 10^{-62}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 7.932072411628089 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.3110229640825212 \cdot 10^{-12}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;b \leq 3.7 \cdot 10^{+136}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+236}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]

Alternative 9
Error	38.7
Cost	980

\[\begin{array}{l} t_1 := b \cdot \left(y + -2\right)\\ t_2 := x - t \cdot a\\ \mathbf{if}\;t \leq -1.75278588784042 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.1488478664116253 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.2352339306147185 \cdot 10^{-221}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -3.4882689135838257 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 831441.7102027182:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	38.5
Cost	848

\[\begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ \mathbf{if}\;b \leq -1.76 \cdot 10^{+186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.572648219310054 \cdot 10^{-62}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 7.932072411628089 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.3110229640825212 \cdot 10^{-12}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	38.4
Cost	848

\[\begin{array}{l} \mathbf{if}\;b \leq -1.4734104756830015 \cdot 10^{+32}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;b \leq 2.572648219310054 \cdot 10^{-62}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 7.932072411628089 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.3110229640825212 \cdot 10^{-12}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \end{array} \]

Alternative 12
Error	37.1
Cost	848

\[\begin{array}{l} t_1 := x - t \cdot a\\ \mathbf{if}\;y \leq -2.988850179617078 \cdot 10^{-45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -6.169352425639303 \cdot 10^{-80}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;y \leq -1.7450287997095854 \cdot 10^{-185}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 506079796276037.4:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 13
Error	40.3
Cost	720

\[\begin{array}{l} \mathbf{if}\;t \leq -3.1 \cdot 10^{+181}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{+95}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.4 \cdot 10^{+211}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+305}:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 14
Error	38.8
Cost	720

\[\begin{array}{l} \mathbf{if}\;b \leq -1.76 \cdot 10^{+186}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq 2.572648219310054 \cdot 10^{-62}:\\ \;\;\;\;x + z\\ \mathbf{elif}\;b \leq 9.887511769989365 \cdot 10^{-27}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+236}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]

Alternative 15
Error	38.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;b \leq -1.76 \cdot 10^{+186}:\\ \;\;\;\;b \cdot -2\\ \mathbf{elif}\;b \leq 1.6 \cdot 10^{+236}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot -2\\ \end{array} \]

Alternative 16
Error	44.2
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -4584861104611533300:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.162751807186277 \cdot 10^{+44}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 17
Error	39.8
Cost	324

\[\begin{array}{l} \mathbf{if}\;y \leq 9.8 \cdot 10^{+61}:\\ \;\;\;\;x + z\\ \mathbf{else}:\\ \;\;\;\;b \cdot y\\ \end{array} \]

Alternative 18
Error	53.7
Cost	64

\[z \]

Reproduce

herbie shell --seed 2022228 
(FPCore (x y z t a b)
  :name "Statistics.Distribution.Beta:$centropy from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (- x (* (- y 1.0) z)) (* (- t 1.0) a)) (* (- (+ y t) 2.0) b)))