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

Average Error: 0.0 → 0.0

Time: 28.8s

Precision: binary64

Cost: 13888

Math

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

↓

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

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
 (fma (+ y (+ t -2.0)) b (- x (fma (+ y -1.0) z (* a (+ t -1.0))))))

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 fma((y + (t + -2.0)), b, (x - fma((y + -1.0), z, (a * (t + -1.0)))));
}

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

   \[\leadsto \color{blue}{\mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + -1\right) \cdot a\right)\right)} \]
   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	\[ \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   sub-neg [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]
   associate-+l- [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x - \left(\left(y - 1\right) \cdot z - \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]
   fma-neg [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -\left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]
   sub-neg [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(\color{blue}{y + \left(-1\right)}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   metadata-eval [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + \color{blue}{-1}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   remove-double-neg [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right) \cdot a}\right)\right) \]
   remove-double-neg [<=] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a\right)\right) \]
   remove-double-neg [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]
   sub-neg [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot a\right)\right) \]
   metadata-eval [=>] 0.0	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + \color{blue}{-1}\right) \cdot a\right)\right) \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	36.9
Cost	2564

\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := a - t \cdot a\\ t_4 := x + t \cdot b\\ t_5 := x + y \cdot b\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{+61}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-110}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -7.5 \cdot 10^{-205}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;a \leq -1.38 \cdot 10^{-222}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -7.8 \cdot 10^{-258}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-302}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-249}:\\ \;\;\;\;b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 380:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+45}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	36.9
Cost	2300

\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := a - t \cdot a\\ t_4 := x + t \cdot b\\ t_5 := x + y \cdot b\\ \mathbf{if}\;a \leq -5.2 \cdot 10^{+161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.2 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.6 \cdot 10^{+59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2 \cdot 10^{-62}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-85}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -6.5 \cdot 10^{-203}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{-223}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 9.5 \cdot 10^{-280}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 1.45 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 7200:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.55 \cdot 10^{+72}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	27.4
Cost	2032

\[\begin{array}{l} t_1 := x - t \cdot \left(a - b\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ t_4 := b \cdot \left(y + -2\right)\\ \mathbf{if}\;a \leq -4 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6.4 \cdot 10^{+63}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-57}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-303}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-261}:\\ \;\;\;\;b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{-75}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.02 \cdot 10^{+21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.42 \cdot 10^{+29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.8 \cdot 10^{+71}:\\ \;\;\;\;x + t_4\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{+148}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	32.7
Cost	1900

\[\begin{array}{l} t_1 := x - t \cdot \left(a - b\right)\\ t_2 := b \cdot \left(y + -2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ t_4 := a - t \cdot a\\ t_5 := x + t_2\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+202}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -1.12 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{+60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -3.1 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-179}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.3 \cdot 10^{-231}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq -4.15 \cdot 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{-127}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.1 \cdot 10^{+140}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 5
Error	25.6
Cost	1896

\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := x + b \cdot \left(-2 + \left(y + t\right)\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -1.66 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-41}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -4.1 \cdot 10^{-57}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;a \leq -1.9 \cdot 10^{-168}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-252}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.1 \cdot 10^{-28}:\\ \;\;\;\;x - t \cdot \left(a - b\right)\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+60}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	33.3
Cost	1768

\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := a - t \cdot a\\ t_4 := x + b \cdot \left(y + -2\right)\\ \mathbf{if}\;a \leq -4.7 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.6 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-61}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -7.6 \cdot 10^{-103}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.2 \cdot 10^{-232}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq -4 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3 \cdot 10^{-127}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;a \leq 8.5 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{+142}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 7
Error	40.2
Cost	1640

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;x \leq -1.15 \cdot 10^{-37}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq -4.8 \cdot 10^{-168}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-220}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;x \leq 3.8 \cdot 10^{-203}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{-121}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-63}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;x \leq 0.0075:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+71}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+136}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8
Error	37.6
Cost	1640

\[\begin{array}{l} t_1 := b \cdot \left(t + -2\right)\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := x + t \cdot b\\ \mathbf{if}\;z \leq -6 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.35 \cdot 10^{-12}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-185}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-275}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-266}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{+24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+93}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{+167}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	49.8
Cost	1576

\[\begin{array}{l} t_1 := t \cdot \left(-a\right)\\ \mathbf{if}\;a \leq -2.2 \cdot 10^{+157}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3.3 \cdot 10^{+117}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -3 \cdot 10^{+117}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -3400000000:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -4.4 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.9 \cdot 10^{-57}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-96}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq -2.5 \cdot 10^{-182}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-202}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;a \leq 3.4 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 10
Error	23.1
Cost	1368

\[\begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{if}\;a \leq -3.9 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.6 \cdot 10^{+65}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.5 \cdot 10^{+97}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{elif}\;a \leq 7 \cdot 10^{+150}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	22.3
Cost	1368

\[\begin{array}{l} t_1 := x + \left(z - t \cdot \left(a - b\right)\right)\\ \mathbf{if}\;a \leq -9.5 \cdot 10^{+202}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;a \leq -4.5 \cdot 10^{-41}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-128}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;a \leq 9 \cdot 10^{-25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+65}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 12
Error	16.3
Cost	1364

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x + \left(z - t \cdot \left(a - b\right)\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -1.55 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -6.4 \cdot 10^{-152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.4 \cdot 10^{-298}:\\ \;\;\;\;a + t_3\\ \mathbf{elif}\;t \leq 5 \cdot 10^{-95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6 \cdot 10^{+61}:\\ \;\;\;\;t_3 + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	12.8
Cost	1361

\[\begin{array}{l} \mathbf{if}\;b \leq -1.8 \cdot 10^{+29}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;b \leq 8 \cdot 10^{-16} \lor \neg \left(b \leq 160000000000\right) \land b \leq 8.8 \cdot 10^{+64}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \end{array} \]

Alternative 14
Error	13.6
Cost	1360

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ t_3 := t_2 + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5 \cdot 10^{-10}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-149}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.5 \cdot 10^{-299}:\\ \;\;\;\;a + t_2\\ \mathbf{elif}\;t \leq 6.9 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 15
Error	8.2
Cost	1356

\[\begin{array}{l} t_1 := x + z \cdot \left(1 - y\right)\\ t_2 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_3 := t_2 + t_1\\ t_4 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1 \cdot 10^{+27}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-46}:\\ \;\;\;\;t_1 + t_4\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\left(x + t_2\right) + t_4\\ \end{array} \]

Alternative 16
Error	0.0
Cost	1344

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

Alternative 17
Error	15.6
Cost	1236

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x + \left(z - t \cdot \left(a - b\right)\right)\\ t_3 := a + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{if}\;t \leq -8.8 \cdot 10^{-10}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{-299}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.04 \cdot 10^{-94}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+42}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	8.1
Cost	1225

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -6.7 \cdot 10^{+44} \lor \neg \left(z \leq 8.2 \cdot 10^{+70}\right):\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(-2 + \left(y + t\right)\right)\right) + t_1\\ \end{array} \]

Alternative 19
Error	36.5
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -380000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.5 \cdot 10^{-228}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.8 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-281}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq 2.8 \cdot 10^{-262}:\\ \;\;\;\;b \cdot \left(y + -2\right)\\ \mathbf{elif}\;t \leq 4 \cdot 10^{+62}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	28.0
Cost	1108

\[\begin{array}{l} t_1 := x + b \cdot \left(y + -2\right)\\ t_2 := x - t \cdot \left(a - b\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{-16}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-148}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{-298}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 3.65 \cdot 10^{-97}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.4 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 21
Error	17.1
Cost	1104

\[\begin{array}{l} t_1 := a + \left(x + z \cdot \left(1 - y\right)\right)\\ t_2 := x + \left(z - t \cdot \left(a - b\right)\right)\\ \mathbf{if}\;t \leq -13000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{-277}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 7.8 \cdot 10^{-184}:\\ \;\;\;\;x + \left(z - b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Error	39.0
Cost	984

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+64}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-12}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq -9.4 \cdot 10^{-185}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-257}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+224}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 23
Error	45.1
Cost	856

\[\begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{-122}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-148}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3500000000000:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 5 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{+136}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	45.2
Cost	852

\[\begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{+26}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -9.4 \cdot 10^{-122}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{-149}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.22 \cdot 10^{-63}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 200000:\\ \;\;\;\;t \cdot b\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 25
Error	34.6
Cost	848

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -950000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.4 \cdot 10^{-228}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;t \leq -1.9 \cdot 10^{-305}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3 \cdot 10^{+43}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Error	38.0
Cost	720

\[\begin{array}{l} \mathbf{if}\;z \leq -7 \cdot 10^{+64}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-12}:\\ \;\;\;\;x + a\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-70}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+224}:\\ \;\;\;\;x + a\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 27
Error	33.6
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -680000000 \lor \neg \left(t \leq 5 \cdot 10^{+43}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + a\\ \end{array} \]

Alternative 28
Error	44.5
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+62}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+164}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 29
Error	49.1
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023066 
(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)))