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

Average Error: 0.03% → 0.02%

Time: 34.0s

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 0.03

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

2. Simplified 0.02

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

   [Start] 0.03	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   +-commutative [=>] 0.03	\[ \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]
   fma-def [=>] 0.03	\[ \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]
   sub-neg [=>] 0.03	\[ \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   associate-+l+ [=>] 0.03	\[ \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   metadata-eval [=>] 0.03	\[ \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   sub-neg [=>] 0.03	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]
   associate-+l- [=>] 0.03	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x - \left(\left(y - 1\right) \cdot z - \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]
   fma-neg [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \color{blue}{\mathsf{fma}\left(y - 1, z, -\left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]
   sub-neg [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(\color{blue}{y + \left(-1\right)}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   metadata-eval [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + \color{blue}{-1}, z, -\left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   remove-double-neg [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right) \cdot a}\right)\right) \]
   remove-double-neg [<=] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(-\left(-\left(t - 1\right)\right)\right)} \cdot a\right)\right) \]
   remove-double-neg [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t - 1\right)} \cdot a\right)\right) \]
   sub-neg [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \color{blue}{\left(t + \left(-1\right)\right)} \cdot a\right)\right) \]
   metadata-eval [=>] 0.02	\[ \mathsf{fma}\left(y + \left(t + -2\right), b, x - \mathsf{fma}\left(y + -1, z, \left(t + \color{blue}{-1}\right) \cdot a\right)\right) \]

3. Final simplification 0.02

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

Alternatives

Alternative 1
Error	32.03%
Cost	2680

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := \left(x + t_1\right) + y \cdot b\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ t_4 := a \cdot \left(1 - t\right)\\ t_5 := t_4 + t_1\\ t_6 := b \cdot \left(-2 + \left(y + t\right)\right) + t_4\\ t_7 := \left(x + z\right) + t_4\\ \mathbf{if}\;b \leq -7.5 \cdot 10^{+120}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -9.5 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq -5 \cdot 10^{+25}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq -1.62 \cdot 10^{-12}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -3.5 \cdot 10^{-290}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 2.7 \cdot 10^{-288}:\\ \;\;\;\;\left(x - y \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;b \leq 1.3 \cdot 10^{-237}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 6.4 \cdot 10^{-202}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 3.65 \cdot 10^{+18}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;b \leq 1.45 \cdot 10^{+75}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;b \leq 9 \cdot 10^{+109}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+194}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 2
Error	27.69%
Cost	2284

\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ t_3 := t_1 + \left(x - y \cdot z\right)\\ t_4 := a \cdot \left(1 - t\right)\\ t_5 := \left(x + z\right) + t_4\\ \mathbf{if}\;y \leq -2.5 \cdot 10^{-19}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -1.32 \cdot 10^{-216}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq -2.9 \cdot 10^{-242}:\\ \;\;\;\;t_1 + t_4\\ \mathbf{elif}\;y \leq -1.35 \cdot 10^{-294}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 5.6 \cdot 10^{-189}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-39}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.3 \cdot 10^{-7}:\\ \;\;\;\;t_4 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 18000000000:\\ \;\;\;\;x + t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 3
Error	31.16%
Cost	2156

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(x + z\right) + t_1\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ t_4 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;y \leq -50000000000000:\\ \;\;\;\;\left(x - y \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-72}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{elif}\;y \leq -4.5 \cdot 10^{-208}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-290}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 10^{-128}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{-39}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.6 \cdot 10^{-24}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 0.006:\\ \;\;\;\;t_1 + t_4\\ \mathbf{elif}\;y \leq 98000000000:\\ \;\;\;\;x + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + t_4\right) + y \cdot b\\ \end{array} \]

Alternative 4
Error	35.2%
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(x + z\right) + t_1\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;y \leq -3.2 \cdot 10^{+16}:\\ \;\;\;\;\left(x - y \cdot z\right) + t \cdot b\\ \mathbf{elif}\;y \leq -2.75 \cdot 10^{-292}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-189}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.7 \cdot 10^{-22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{-5}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+89}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 5
Error	34.79%
Cost	1764

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := \left(x + z\right) + t_1\\ t_3 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;y \leq -1.15 \cdot 10^{+14}:\\ \;\;\;\;\left(x - y \cdot z\right) + t \cdot b\\ \mathbf{elif}\;y \leq -2.05 \cdot 10^{-287}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 1.82 \cdot 10^{-187}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.25 \cdot 10^{-129}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{-38}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{-22}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 0.000135:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+89}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6
Error	19.31%
Cost	1756

\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := t_1 + \left(x - y \cdot z\right)\\ t_3 := a \cdot \left(1 - t\right)\\ t_4 := \left(x + z \cdot \left(1 - y\right)\right) + t_3\\ t_5 := t_1 + t_3\\ \mathbf{if}\;b \leq -2.6 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -12500000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq -4.4 \cdot 10^{-25}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq 4.7 \cdot 10^{+18}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;b \leq 5.8 \cdot 10^{+75}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;b \leq 1.8 \cdot 10^{+109}:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;b \leq 1.22 \cdot 10^{+194}:\\ \;\;\;\;a + \left(x - b \cdot \left(2 - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 7
Error	42.91%
Cost	1636

\[\begin{array}{l} t_1 := x + b \cdot \left(t + -2\right)\\ t_2 := x - b \cdot \left(2 - y\right)\\ t_3 := x + z \cdot \left(1 - y\right)\\ t_4 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -1.22 \cdot 10^{+93}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -10500000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-215}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-277}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-198}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-53}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 8
Error	54.01%
Cost	1504

\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ t_3 := a - t \cdot a\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5200000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.8 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-230}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	49.12%
Cost	1504

\[\begin{array}{l} t_1 := x + b \cdot \left(t + -2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ t_3 := a - t \cdot a\\ \mathbf{if}\;z \leq -6 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-81}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-178}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-152}:\\ \;\;\;\;b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-81}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-52}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	27.08%
Cost	1496

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := a + \left(x - b \cdot \left(2 - y\right)\right)\\ t_3 := \left(x - y \cdot z\right) + t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4.7 \cdot 10^{+23}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq -0.09:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-23}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq -1.62 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.12 \cdot 10^{-185}:\\ \;\;\;\;\left(x + z\right) + t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{-6}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 11
Error	58.6%
Cost	1376

\[\begin{array}{l} t_1 := b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := a - t \cdot a\\ t_3 := z - y \cdot z\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+94}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -44000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-181}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-231}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-178}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{-53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+93}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 12
Error	39.04%
Cost	1368

\[\begin{array}{l} t_1 := x + b \cdot \left(-2 + \left(y + t\right)\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ t_3 := x + a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -205000000:\\ \;\;\;\;x + b \cdot \left(t + -2\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-179}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-230}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-198}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-9}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	35%
Cost	1368

\[\begin{array}{l} t_1 := \left(x + z\right) + a \cdot \left(1 - t\right)\\ t_2 := x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{if}\;y \leq -1.5 \cdot 10^{+16}:\\ \;\;\;\;\left(x - y \cdot z\right) + t \cdot b\\ \mathbf{elif}\;y \leq -7.2 \cdot 10^{-294}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 9.8 \cdot 10^{-231}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{-189}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.3 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 14
Error	0.03%
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 15
Error	0.03%
Cost	1344

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

Alternative 16
Error	59.15%
Cost	1244

\[\begin{array}{l} t_1 := x + y \cdot b\\ t_2 := a - t \cdot a\\ \mathbf{if}\;a \leq -5 \cdot 10^{+56}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -5.5 \cdot 10^{-40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq -5.8 \cdot 10^{-156}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -2.8 \cdot 10^{-300}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+108}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	38.88%
Cost	1236

\[\begin{array}{l} t_1 := x + a \cdot \left(1 - t\right)\\ t_2 := x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{if}\;z \leq -1750000000:\\ \;\;\;\;x + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-232}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-198}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-9}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 18
Error	12.61%
Cost	1225

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+93} \lor \neg \left(z \leq 1.7 \cdot 10^{-8}\right):\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(-2 + \left(y + t\right)\right)\right) + t_1\\ \end{array} \]

Alternative 19
Error	12.44%
Cost	1224

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -1.7 \cdot 10^{+97}:\\ \;\;\;\;\left(x + y \cdot \left(b - z\right)\right) + \left(z + b \cdot \left(t + -2\right)\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-9}:\\ \;\;\;\;\left(x + b \cdot \left(-2 + \left(y + t\right)\right)\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;\left(x + z \cdot \left(1 - y\right)\right) + t_1\\ \end{array} \]

Alternative 20
Error	78.47%
Cost	1180

\[\begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -86000000:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-54}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-233}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-122}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;z \leq 10^{+91}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 21
Error	57.03%
Cost	1112

\[\begin{array}{l} t_1 := a - t \cdot a\\ t_2 := x + y \cdot b\\ t_3 := z - y \cdot z\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+92}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-134}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-228}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-180}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+89}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 22
Error	45.59%
Cost	1108

\[\begin{array}{l} t_1 := x + b \cdot \left(t + -2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+92}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-82}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;z \leq -9.2 \cdot 10^{-278}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-53}:\\ \;\;\;\;x - b \cdot \left(2 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 23
Error	28.39%
Cost	1106

\[\begin{array}{l} \mathbf{if}\;b \leq -1.76 \cdot 10^{+52} \lor \neg \left(b \leq -820000\right) \land \left(b \leq -7.8 \cdot 10^{-16} \lor \neg \left(b \leq 2.65 \cdot 10^{+53}\right)\right):\\ \;\;\;\;x + b \cdot \left(-2 + \left(y + t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + z\right) + a \cdot \left(1 - t\right)\\ \end{array} \]

Alternative 24
Error	66.84%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -34000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2.25 \cdot 10^{-184}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.6 \cdot 10^{+51}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 25
Error	61.03%
Cost	980

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -4400000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.55 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;t \leq -2.5 \cdot 10^{-106}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;t \leq 3.9 \cdot 10^{-171}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq 5.3 \cdot 10^{+48}:\\ \;\;\;\;x + y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Error	68.14%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-69} \lor \neg \left(t \leq 6.2 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 27
Error	59.73%
Cost	585

\[\begin{array}{l} \mathbf{if}\;t \leq -24000000000 \lor \neg \left(t \leq 4.5 \cdot 10^{+50}\right):\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot b\\ \end{array} \]

Alternative 28
Error	76.96%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 9 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 29
Error	76.23%
Cost	456

\[\begin{array}{l} \mathbf{if}\;t \leq -1.12 \cdot 10^{-69}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;t \leq 7 \cdot 10^{+66}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 30
Error	76.99%
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023121 
(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)))