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

Average Error: 0.0 → 0.0

Time: 32.1s

Precision: binary64

Cost: 1344

Math

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

↓

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

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
 (+ a (+ (* b -2.0) (+ (+ (+ z x) (* (- b z) y)) (* t (- b a))))))

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

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
    code = a + ((b * (-2.0d0)) + (((z + x) + ((b - z) * y)) + (t * (b - a))))
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) {
	return a + ((b * -2.0) + (((z + x) + ((b - z) * y)) + (t * (b - a))));
}

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):
	return a + ((b * -2.0) + (((z + x) + ((b - z) * y)) + (t * (b - a))))

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)
	return Float64(a + Float64(Float64(b * -2.0) + Float64(Float64(Float64(z + x) + Float64(Float64(b - z) * y)) + Float64(t * Float64(b - a)))))
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 = code(x, y, z, t, a, b)
	tmp = a + ((b * -2.0) + (((z + x) + ((b - z) * y)) + (t * (b - a))));
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_] := N[(a + N[(N[(b * -2.0), $MachinePrecision] + N[(N[(N[(z + x), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

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 y around 0 0.0

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

3. Simplified 0.0

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

   [Start] 0.0	\[ \left(\left(t - 2\right) \cdot b + \left(\left(b - z\right) \cdot y + x\right)\right) - \left(-1 \cdot z + \left(t - 1\right) \cdot a\right) \]
   rational_best.json-simplify-2 [=>] 0.0	\[ \left(\color{blue}{b \cdot \left(t - 2\right)} + \left(\left(b - z\right) \cdot y + x\right)\right) - \left(-1 \cdot z + \left(t - 1\right) \cdot a\right) \]
   rational_best.json-simplify-1 [=>] 0.0	\[ \left(b \cdot \left(t - 2\right) + \color{blue}{\left(x + \left(b - z\right) \cdot y\right)}\right) - \left(-1 \cdot z + \left(t - 1\right) \cdot a\right) \]
   rational_best.json-simplify-2 [=>] 0.0	\[ \left(b \cdot \left(t - 2\right) + \left(x + \color{blue}{y \cdot \left(b - z\right)}\right)\right) - \left(-1 \cdot z + \left(t - 1\right) \cdot a\right) \]
   rational_best.json-simplify-2 [=>] 0.0	\[ \left(b \cdot \left(t - 2\right) + \left(x + y \cdot \left(b - z\right)\right)\right) - \left(\color{blue}{z \cdot -1} + \left(t - 1\right) \cdot a\right) \]
   rational_best.json-simplify-12 [=>] 0.0	\[ \left(b \cdot \left(t - 2\right) + \left(x + y \cdot \left(b - z\right)\right)\right) - \left(\color{blue}{\left(-z\right)} + \left(t - 1\right) \cdot a\right) \]
   rational_best.json-simplify-2 [=>] 0.0	\[ \left(b \cdot \left(t - 2\right) + \left(x + y \cdot \left(b - z\right)\right)\right) - \left(\left(-z\right) + \color{blue}{a \cdot \left(t - 1\right)}\right) \]
   rational_best.json-simplify-18 [<=] 0.0	\[ \left(b \cdot \left(t - 2\right) + \left(x + y \cdot \left(b - z\right)\right)\right) - \left(\left(-z\right) + a \cdot \color{blue}{\left(t + -1\right)}\right) \]

4. Taylor expanded in t around 0 0.0

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

5. Simplified 0.0

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

   [Start] 0.0	\[ \left(t \cdot \left(b - a\right) + \left(-2 \cdot b + \left(z + \left(\left(b - z\right) \cdot y + x\right)\right)\right)\right) - -1 \cdot a \]
   rational_best.json-simplify-2 [=>] 0.0	\[ \left(t \cdot \left(b - a\right) + \left(-2 \cdot b + \left(z + \left(\left(b - z\right) \cdot y + x\right)\right)\right)\right) - \color{blue}{a \cdot -1} \]
   rational_best.json-simplify-12 [=>] 0.0	\[ \left(t \cdot \left(b - a\right) + \left(-2 \cdot b + \left(z + \left(\left(b - z\right) \cdot y + x\right)\right)\right)\right) - \color{blue}{\left(-a\right)} \]
   rational_best.json-simplify-11 [=>] 0.0	\[ \left(t \cdot \left(b - a\right) + \left(-2 \cdot b + \left(z + \left(\left(b - z\right) \cdot y + x\right)\right)\right)\right) - \color{blue}{\left(0 - a\right)} \]
   rational_best.json-simplify-46 [=>] 0.0	\[ \color{blue}{a + \left(\left(t \cdot \left(b - a\right) + \left(-2 \cdot b + \left(z + \left(\left(b - z\right) \cdot y + x\right)\right)\right)\right) - 0\right)} \]
   rational_best.json-simplify-6 [=>] 0.0	\[ a + \color{blue}{\left(t \cdot \left(b - a\right) + \left(-2 \cdot b + \left(z + \left(\left(b - z\right) \cdot y + x\right)\right)\right)\right)} \]
   rational_best.json-simplify-1 [=>] 0.0	\[ a + \left(t \cdot \left(b - a\right) + \color{blue}{\left(\left(z + \left(\left(b - z\right) \cdot y + x\right)\right) + -2 \cdot b\right)}\right) \]
   rational_best.json-simplify-43 [=>] 0.0	\[ a + \color{blue}{\left(-2 \cdot b + \left(\left(z + \left(\left(b - z\right) \cdot y + x\right)\right) + t \cdot \left(b - a\right)\right)\right)} \]
   rational_best.json-simplify-2 [=>] 0.0	\[ a + \left(\color{blue}{b \cdot -2} + \left(\left(z + \left(\left(b - z\right) \cdot y + x\right)\right) + t \cdot \left(b - a\right)\right)\right) \]
   rational_best.json-simplify-1 [=>] 0.0	\[ a + \left(b \cdot -2 + \left(\left(z + \color{blue}{\left(x + \left(b - z\right) \cdot y\right)}\right) + t \cdot \left(b - a\right)\right)\right) \]
   rational_best.json-simplify-2 [<=] 0.0	\[ a + \left(b \cdot -2 + \left(\left(z + \left(x + \color{blue}{y \cdot \left(b - z\right)}\right)\right) + t \cdot \left(b - a\right)\right)\right) \]
   rational_best.json-simplify-43 [=>] 0.0	\[ a + \left(b \cdot -2 + \left(\color{blue}{\left(y \cdot \left(b - z\right) + \left(x + z\right)\right)} + t \cdot \left(b - a\right)\right)\right) \]
   rational_best.json-simplify-1 [<=] 0.0	\[ a + \left(b \cdot -2 + \left(\left(y \cdot \left(b - z\right) + \color{blue}{\left(z + x\right)}\right) + t \cdot \left(b - a\right)\right)\right) \]
   rational_best.json-simplify-1 [=>] 0.0	\[ a + \left(b \cdot -2 + \left(\color{blue}{\left(\left(z + x\right) + y \cdot \left(b - z\right)\right)} + t \cdot \left(b - a\right)\right)\right) \]
   rational_best.json-simplify-2 [=>] 0.0	\[ a + \left(b \cdot -2 + \left(\left(\left(z + x\right) + \color{blue}{\left(b - z\right) \cdot y}\right) + t \cdot \left(b - a\right)\right)\right) \]

6. Final simplification 0.0

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

Alternatives

Alternative 1
Error	37.5
Cost	2036

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+22}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.05 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 8.6 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 10500000000000:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+59}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+72}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+133}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 2
Error	37.8
Cost	2036

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -1.05 \cdot 10^{+20}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{-272}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;x \leq 3.3 \cdot 10^{-165}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+16}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+71}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.4 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+133}:\\ \;\;\;\;b \cdot \left(t - 2\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 3
Error	29.3
Cost	1900

\[\begin{array}{l} t_1 := a + \left(z + x\right)\\ t_2 := x - z \cdot \left(y - 1\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;a + \left(b \cdot -2 + x\right)\\ \mathbf{elif}\;b \leq -7 \cdot 10^{-15}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;b \leq -1.5 \cdot 10^{-75}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -1.05 \cdot 10^{-191}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.8 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 4.6 \cdot 10^{-288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 2 \cdot 10^{-260}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.1 \cdot 10^{+78}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 4
Error	25.5
Cost	1896

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(t - 2\right)\right) + z\\ t_2 := x - \left(t - 1\right) \cdot a\\ t_3 := x - z \cdot \left(y - 1\right)\\ \mathbf{if}\;b \leq -0.0032:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.6 \cdot 10^{-49}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -6.5 \cdot 10^{-135}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;b \leq -4.5 \cdot 10^{-147}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -1.1 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 5.3 \cdot 10^{-287}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.2 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.35 \cdot 10^{-98}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	28.4
Cost	1768

\[\begin{array}{l} t_1 := x - z \cdot \left(y - 1\right)\\ t_2 := x - \left(t - 1\right) \cdot a\\ \mathbf{if}\;b \leq -2.8 \cdot 10^{+15}:\\ \;\;\;\;a + \left(b \cdot -2 + x\right)\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{-15}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;b \leq -1.7 \cdot 10^{-41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -4.3 \cdot 10^{-147}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;b \leq -4 \cdot 10^{-191}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -9.2 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-168}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.1 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 3.1 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\left(\left(y + t\right) - 2\right) \cdot b\\ \end{array} \]

Alternative 6
Error	28.0
Cost	1632

\[\begin{array}{l} t_1 := x - z \cdot \left(y - 1\right)\\ t_2 := -\left(y \cdot z + a \cdot \left(-1 + t\right)\right)\\ t_3 := x - \left(t - 1\right) \cdot a\\ t_4 := \left(x + b \cdot \left(t - 2\right)\right) + z\\ \mathbf{if}\;b \leq -0.0145:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -2.5 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -7.5 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -3 \cdot 10^{-297}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.7 \cdot 10^{-153}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 1.4 \cdot 10^{-98}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.5 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 7
Error	16.4
Cost	1624

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(t - 2\right)\right) + z\\ t_2 := x - \left(\left(t - 1\right) \cdot a + z \cdot \left(y - 1\right)\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{-121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.25 \cdot 10^{-150}:\\ \;\;\;\;t \cdot \left(-a\right) + \left(\left(y + t\right) - 2\right) \cdot b\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-219}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{-108}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 5.6 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	19.8
Cost	1496

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(t - 2\right)\right) + z\\ t_2 := x - \left(\left(t - 1\right) \cdot a + \left(-z\right)\right)\\ t_3 := a + \left(b \cdot -2 + \left(b - z\right) \cdot y\right)\\ \mathbf{if}\;y \leq -5.5 \cdot 10^{+41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -7.8 \cdot 10^{-87}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7 \cdot 10^{+69}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	8.5
Cost	1488

\[\begin{array}{l} t_1 := \left(t - 1\right) \cdot a\\ t_2 := z \cdot \left(y - 1\right)\\ t_3 := x - \left(t_1 + t_2\right)\\ t_4 := \left(\left(\left(y + t\right) - 2\right) \cdot b + x\right) - t_2\\ \mathbf{if}\;a \leq -2.15 \cdot 10^{+139}:\\ \;\;\;\;x - \left(t_1 + \left(-z\right)\right)\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{+83}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{-12}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	22.9
Cost	1432

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(t - 2\right)\right) + z\\ t_2 := x - \left(\left(t - 1\right) \cdot a + \left(-z\right)\right)\\ \mathbf{if}\;y \leq -1.1 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+133}:\\ \;\;\;\;-\left(y \cdot z + a \cdot \left(-1 + t\right)\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+178}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]

Alternative 11
Error	17.8
Cost	1232

\[\begin{array}{l} t_1 := \left(t - 1\right) \cdot a\\ t_2 := x - \left(t_1 + z \cdot y\right)\\ \mathbf{if}\;y \leq -9000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-63}:\\ \;\;\;\;x - \left(t_1 + \left(-z\right)\right)\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-11}:\\ \;\;\;\;\left(x + b \cdot \left(t - 2\right)\right) + z\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{+171}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;a + \left(b \cdot -2 + \left(b - z\right) \cdot y\right)\\ \end{array} \]

Alternative 12
Error	7.2
Cost	1224

\[\begin{array}{l} t_1 := \left(t - 1\right) \cdot a\\ t_2 := \left(\left(y + t\right) - 2\right) \cdot b + x\\ t_3 := z \cdot \left(y - 1\right)\\ \mathbf{if}\;a \leq -2.65 \cdot 10^{+38}:\\ \;\;\;\;t_2 - t_1\\ \mathbf{elif}\;a \leq 2.4 \cdot 10^{-12}:\\ \;\;\;\;t_2 - t_3\\ \mathbf{else}:\\ \;\;\;\;x - \left(t_1 + t_3\right)\\ \end{array} \]

Alternative 13
Error	7.6
Cost	1224

\[\begin{array}{l} t_1 := \left(\left(y + t\right) - 2\right) \cdot b + x\\ \mathbf{if}\;y \leq -3 \cdot 10^{+49}:\\ \;\;\;\;t_1 - \left(t - 1\right) \cdot a\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+33}:\\ \;\;\;\;\left(\left(z + x\right) + b \cdot \left(t - 2\right)\right) - a \cdot \left(-1 + t\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - z \cdot \left(y - 1\right)\\ \end{array} \]

Alternative 14
Error	34.8
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -20000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-160}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-198}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 7.2 \cdot 10^{+35}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 1.8 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{+136}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	27.0
Cost	848

\[\begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -9 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.6 \cdot 10^{+35}:\\ \;\;\;\;a + \left(z + x\right)\\ \mathbf{elif}\;y \leq 1.04 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+173}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	27.1
Cost	848

\[\begin{array}{l} t_1 := a + \left(z + x\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.6 \cdot 10^{+39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-264}:\\ \;\;\;\;a + \left(b \cdot -2 + x\right)\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	35.2
Cost	652

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 16000000000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 1.6 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 18
Error	44.6
Cost	592

\[\begin{array}{l} \mathbf{if}\;a \leq -1.5 \cdot 10^{+119}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{+79}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -5.9 \cdot 10^{+37}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 1400000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 19
Error	33.8
Cost	584

\[\begin{array}{l} \mathbf{if}\;a \leq -6.5 \cdot 10^{+37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 10500000000:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 20
Error	35.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -6.5 \cdot 10^{+187}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+211}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 21
Error	33.7
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -2.75 \cdot 10^{+38}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+122}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 22
Error	53.8
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023090 
(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)))