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

Average Error: 0.0 → 0.0

Time: 35.5s

Precision: binary64

Cost: 1344

Math

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

↓

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

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 (+ (+ (* z (- 1.0 y)) (+ (* b (- y 2.0)) x)) (* 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 + (((z * (1.0 - y)) + ((b * (y - 2.0)) + x)) + (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 + (((z * (1.0d0 - y)) + ((b * (y - 2.0d0)) + x)) + (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 + (((z * (1.0 - y)) + ((b * (y - 2.0)) + x)) + (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 + (((z * (1.0 - y)) + ((b * (y - 2.0)) + x)) + (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(Float64(z * Float64(1.0 - y)) + Float64(Float64(b * Float64(y - 2.0)) + x)) + 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 + (((z * (1.0 - y)) + ((b * (y - 2.0)) + x)) + (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[(N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision] + N[(N[(b * N[(y - 2.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]), $MachinePrecision] + N[(t * N[(b - a), $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. Simplified 0.0

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

   [Start] 0.0	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   +-commutative [=>] 0.0	\[ \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]
   fma-def [=>] 0.0	\[ \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]
   sub-neg [=>] 0.0	\[ \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   associate-+l+ [=>] 0.0	\[ \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   metadata-eval [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   cancel-sign-sub-inv [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right)\right) \cdot a}\right) \]
   +-commutative [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(t - 1\right)\right) \cdot a + \left(x - \left(y - 1\right) \cdot z\right)}\right) \]
   *-commutative [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(x - \left(y - 1\right) \cdot z\right)\right) \]
   fma-def [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), x - \left(y - 1\right) \cdot z\right)}\right) \]
   neg-sub0 [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, x - \left(y - 1\right) \cdot z\right)\right) \]
   associate--r- [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, x - \left(y - 1\right) \cdot z\right)\right) \]
   neg-sub0 [<=] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, x - \left(y - 1\right) \cdot z\right)\right) \]
   +-commutative [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, x - \left(y - 1\right) \cdot z\right)\right) \]
   sub-neg [<=] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, \color{blue}{1 - t}, x - \left(y - 1\right) \cdot z\right)\right) \]
   cancel-sign-sub-inv [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \color{blue}{x + \left(-\left(y - 1\right)\right) \cdot z}\right)\right) \]
   +-commutative [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \color{blue}{\left(-\left(y - 1\right)\right) \cdot z + x}\right)\right) \]
   *-commutative [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \color{blue}{z \cdot \left(-\left(y - 1\right)\right)} + x\right)\right) \]
   fma-def [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(z, -\left(y - 1\right), x\right)}\right)\right) \]
   neg-sub0 [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, \color{blue}{0 - \left(y - 1\right)}, x\right)\right)\right) \]
   associate--r- [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, \color{blue}{\left(0 - y\right) + 1}, x\right)\right)\right) \]
   neg-sub0 [<=] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, \color{blue}{\left(-y\right)} + 1, x\right)\right)\right) \]
   +-commutative [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, \color{blue}{1 + \left(-y\right)}, x\right)\right)\right) \]
   sub-neg [<=] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(z, \color{blue}{1 - y}, x\right)\right)\right) \]

3. Taylor expanded in t around inf 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	33.0
Cost	2561

\[\begin{array}{l} t_1 := z \cdot \left(-1 + y\right)\\ t_2 := x - t_1\\ t_3 := a + y \cdot \left(b - z\right)\\ t_4 := t \cdot \left(b - a\right)\\ t_5 := x + b \cdot \left(\left(t + y\right) + -2\right)\\ \mathbf{if}\;t \leq -1.7 \cdot 10^{+115}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -8.6 \cdot 10^{+31}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.22 \cdot 10^{-80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -4.4 \cdot 10^{-159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.75 \cdot 10^{-197}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq -1.56 \cdot 10^{-214}:\\ \;\;\;\;a - t_1\\ \mathbf{elif}\;t \leq -2.6 \cdot 10^{-306}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;t \leq 1.05 \cdot 10^{-144}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-68}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.08 \cdot 10^{-20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 27500:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1050000000000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.6 \cdot 10^{+77} \lor \neg \left(t \leq 4.2 \cdot 10^{+183}\right):\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 2
Error	33.6
Cost	2297

\[\begin{array}{l} t_1 := x - z \cdot \left(-1 + y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2.4 \cdot 10^{-28}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.8 \cdot 10^{-81}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{-73}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 50000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1250000000000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+77} \lor \neg \left(t \leq 2.4 \cdot 10^{+183}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 3
Error	33.6
Cost	2297

\[\begin{array}{l} t_1 := x - z \cdot \left(-1 + y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -9.2 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -7.4 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-82}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t + y\right) + b \cdot -2\\ \mathbf{elif}\;t \leq -6 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.6 \cdot 10^{-74}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2.2 \cdot 10^{-27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 275000:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 1020000000000:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{+77} \lor \neg \left(t \leq 5.8 \cdot 10^{+190}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Error	36.5
Cost	2036

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1 \cdot 10^{+67}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-76}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;t \leq -5.3 \cdot 10^{-198}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -2.9 \cdot 10^{-243}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-71}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.22 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	33.4
Cost	2033

\[\begin{array}{l} t_1 := x - z \cdot \left(-1 + y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.9 \cdot 10^{+114}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.08 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.04 \cdot 10^{+32}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.9 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1 \cdot 10^{-81}:\\ \;\;\;\;a + y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-308}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.02 \cdot 10^{-72}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1250000000000 \lor \neg \left(t \leq 4.5 \cdot 10^{+76}\right) \land t \leq 2.3 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 6
Error	37.3
Cost	1904

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := b \cdot \left(y - 2\right)\\ \mathbf{if}\;t \leq -2.3 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -6.2 \cdot 10^{-179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-244}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-305}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 3.8 \cdot 10^{-68}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-23}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	37.4
Cost	1904

\[\begin{array}{l} t_1 := b \cdot \left(y - 2\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.28 \cdot 10^{+73}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.5 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -4.1 \cdot 10^{-82}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-158}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.7 \cdot 10^{-244}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.6 \cdot 10^{-306}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-70}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-26}:\\ \;\;\;\;z - z \cdot y\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	35.7
Cost	1904

\[\begin{array}{l} t_1 := a + y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.08 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.1 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -1.95 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{-86}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-242}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-307}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-68}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-29}:\\ \;\;\;\;z - z \cdot y\\ \mathbf{elif}\;t \leq 1450:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	35.2
Cost	1900

\[\begin{array}{l} t_1 := a - z \cdot \left(-1 + y\right)\\ t_2 := a + y \cdot \left(b - z\right)\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -2.25 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{+31}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5 \cdot 10^{-23}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.45 \cdot 10^{-86}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{-243}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.85 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 10^{-69}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1020000000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	36.1
Cost	1772

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.15 \cdot 10^{+46}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -1.12 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -2.3 \cdot 10^{-25}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.28 \cdot 10^{-86}:\\ \;\;\;\;a - z \cdot y\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq -2.02 \cdot 10^{-230}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.1 \cdot 10^{-26}:\\ \;\;\;\;z - z \cdot y\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	16.8
Cost	1756

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := x + \left(z \cdot \left(1 - y\right) + t_1\right)\\ t_3 := x + b \cdot \left(\left(t + y\right) + -2\right)\\ t_4 := \left(x + b \cdot y\right) + t_1\\ \mathbf{if}\;z \leq -8 \cdot 10^{+15}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-49}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-57}:\\ \;\;\;\;x - z \cdot \left(-1 + y\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-223}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-293}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-174}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7.9 \cdot 10^{-125}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	34.9
Cost	1640

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.2 \cdot 10^{+46}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.3 \cdot 10^{+31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.2 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -3.5 \cdot 10^{-75}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;t \leq 7.1 \cdot 10^{-67}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 3.5 \cdot 10^{-32}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 13
Error	35.5
Cost	1640

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.5 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.4 \cdot 10^{+46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.86 \cdot 10^{+31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -1.05 \cdot 10^{-75}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;t \leq 1.55 \cdot 10^{-68}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	39.4
Cost	1577

\[\begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -2 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -3.4 \cdot 10^{-72}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq -3.45 \cdot 10^{-159}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq -9 \cdot 10^{-179}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;t \leq 1.3 \cdot 10^{-67}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.65 \cdot 10^{-27}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+77} \lor \neg \left(t \leq 3.25 \cdot 10^{+168}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 15
Error	20.3
Cost	1496

\[\begin{array}{l} t_1 := x + b \cdot \left(\left(t + y\right) + -2\right)\\ t_2 := a + \left(z \cdot \left(1 - y\right) - a \cdot t\right)\\ t_3 := a \cdot \left(1 - t\right)\\ t_4 := \left(x + b \cdot y\right) + t_3\\ \mathbf{if}\;z \leq -4.2 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-224}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-293}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-173}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-125}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+70}:\\ \;\;\;\;x + \left(t_3 - z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	7.9
Cost	1488

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -9.4 \cdot 10^{+30}:\\ \;\;\;\;x + \left(t_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-21}:\\ \;\;\;\;a + \left(t_1 + \left(b \cdot \left(y - 2\right) + x\right)\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{+77}:\\ \;\;\;\;a + \left(\left(x - z \cdot \left(-1 + y\right)\right) - a \cdot t\right)\\ \mathbf{elif}\;t \leq 1.9 \cdot 10^{+255}:\\ \;\;\;\;t_1 + \left(x + b \cdot \left(\left(t + y\right) + -2\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(t_1 - a \cdot t\right)\\ \end{array} \]

Alternative 17
Error	45.1
Cost	1384

\[\begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-18}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-125}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.15 \cdot 10^{-178}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -8.5 \cdot 10^{-293}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 5.3 \cdot 10^{-236}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-160}:\\ \;\;\;\;b \cdot y\\ \mathbf{elif}\;x \leq 8 \cdot 10^{-69}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+26}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 18
Error	24.6
Cost	1372

\[\begin{array}{l} t_1 := x + b \cdot \left(\left(t + y\right) + -2\right)\\ t_2 := x - z \cdot \left(-1 + y\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+55}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 8.2 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-108}:\\ \;\;\;\;a - z \cdot y\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-89}:\\ \;\;\;\;\left(x + b \cdot y\right) - a \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	24.2
Cost	1372

\[\begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(\left(t + y\right) + -2\right)\\ t_3 := a + \left(z \cdot \left(1 - y\right) - a \cdot t\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -5.4 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-108}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-84}:\\ \;\;\;\;\left(x + b \cdot y\right) - a \cdot t\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x - z \cdot \left(-1 + y\right)\\ \end{array} \]

Alternative 20
Error	22.6
Cost	1364

\[\begin{array}{l} t_1 := x + \left(a \cdot \left(1 - t\right) - z \cdot y\right)\\ t_2 := x + b \cdot \left(\left(t + y\right) + -2\right)\\ t_3 := a + \left(z \cdot \left(1 - y\right) - a \cdot t\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+15}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-296}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+73}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 21
Error	11.9
Cost	1362

\[\begin{array}{l} \mathbf{if}\;b \leq -1.25 \cdot 10^{-71} \lor \neg \left(b \leq 3.6 \cdot 10^{+47} \lor \neg \left(b \leq 2.1 \cdot 10^{+100}\right) \land b \leq 3.15 \cdot 10^{+153}\right):\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) + -2\right)\right) - a \cdot t\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 22
Error	12.0
Cost	1361

\[\begin{array}{l} t_1 := \left(x + b \cdot \left(\left(t + y\right) + -2\right)\right) - a \cdot t\\ \mathbf{if}\;b \leq -1.22 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.58 \cdot 10^{+38}:\\ \;\;\;\;a + \left(\left(x - z \cdot \left(-1 + y\right)\right) - a \cdot t\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{+98} \lor \neg \left(b \leq 1.65 \cdot 10^{+155}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 23
Error	6.9
Cost	1353

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+56} \lor \neg \left(z \leq 8.8 \cdot 10^{-36}\right):\\ \;\;\;\;a + \left(z \cdot \left(1 - y\right) + \left(b \cdot \left(y - 2\right) + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + \left(b \cdot \left(t + y\right) + b \cdot -2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 24
Error	0.0
Cost	1344

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

Alternative 25
Error	0.0
Cost	1344

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

Alternative 26
Error	6.9
Cost	1225

\[\begin{array}{l} \mathbf{if}\;z \leq -1.1 \cdot 10^{+57} \lor \neg \left(z \leq 4.8 \cdot 10^{-36}\right):\\ \;\;\;\;a + \left(z \cdot \left(1 - y\right) + \left(b \cdot \left(y - 2\right) + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) + -2\right)\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 27
Error	7.9
Cost	1224

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+30}:\\ \;\;\;\;x + \left(t_1 + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-20}:\\ \;\;\;\;a + \left(t_1 + \left(b \cdot \left(y - 2\right) + x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(\left(x - z \cdot \left(-1 + y\right)\right) - a \cdot t\right)\\ \end{array} \]

Alternative 28
Error	38.2
Cost	1181

\[\begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;t \leq -8.5 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-67}:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 1.5 \cdot 10^{-30}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;t \leq 2900:\\ \;\;\;\;a + x\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{+76} \lor \neg \left(t \leq 1.72 \cdot 10^{+171}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 29
Error	44.5
Cost	988

\[\begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+119}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.95 \cdot 10^{-19}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -2 \cdot 10^{-61}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.85 \cdot 10^{-127}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-179}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.65 \cdot 10^{-98}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.45 \cdot 10^{+26}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 30
Error	36.2
Cost	456

\[\begin{array}{l} \mathbf{if}\;z \leq -2.65 \cdot 10^{+159}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+91}:\\ \;\;\;\;a + x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 31
Error	44.0
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{+93}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+70}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 32
Error	53.6
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023039 
(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)))