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

Average Error: 0.04% → 0.03%

Time: 27.1s

Precision: binary64

Cost: 7616

Math

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

↓

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

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

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

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

Derivation

1. Initial program 0.04

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

2. Simplified 0.02

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

   [Start] 0.04	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   +-commutative [=>] 0.04	\[ \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]
   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	\[ \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   metadata-eval [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + \color{blue}{-2}, b, \left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) \]
   sub-neg [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \color{blue}{\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)}\right) \]
   sub-neg [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \color{blue}{\left(x + \left(-\left(y - 1\right) \cdot z\right)\right)} + \left(-\left(t - 1\right) \cdot a\right)\right) \]
   +-commutative [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \color{blue}{\left(\left(-\left(y - 1\right) \cdot z\right) + x\right)} + \left(-\left(t - 1\right) \cdot a\right)\right) \]
   associate-+l+ [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)}\right) \]
   distribute-lft-neg-in [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \color{blue}{\left(-\left(y - 1\right)\right) \cdot z} + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   remove-double-neg [<=] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \left(-\left(y - 1\right)\right) \cdot \color{blue}{\left(-\left(-z\right)\right)} + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   mul-1-neg [<=] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \left(-\left(y - 1\right)\right) \cdot \left(-\color{blue}{-1 \cdot z}\right) + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   metadata-eval [<=] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \left(-\left(y - 1\right)\right) \cdot \left(-\color{blue}{\left(-1\right)} \cdot z\right) + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   *-commutative [<=] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \left(-\left(y - 1\right)\right) \cdot \left(-\color{blue}{z \cdot \left(-1\right)}\right) + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   distribute-lft-neg-in [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \left(-\left(y - 1\right)\right) \cdot \color{blue}{\left(\left(-z\right) \cdot \left(-1\right)\right)} + \left(x + \left(-\left(t - 1\right) \cdot a\right)\right)\right) \]
   +-commutative [=>] 0.03	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \left(-\left(y - 1\right)\right) \cdot \left(\left(-z\right) \cdot \left(-1\right)\right) + \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + x\right)}\right) \]
   fma-def [=>] 0.02	\[ \mathsf{fma}\left(\left(y + t\right) + -2, b, \color{blue}{\mathsf{fma}\left(-\left(y - 1\right), \left(-z\right) \cdot \left(-1\right), \left(-\left(t - 1\right) \cdot a\right) + x\right)}\right) \]

3. Applied egg-rr 0.03

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

4. Final simplification 0.03

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

Alternatives

Alternative 1
Error	55.34%
Cost	2428

\[\begin{array}{l} t_1 := a + \left(x + y \cdot b\right)\\ t_2 := z - y \cdot z\\ t_3 := a + \left(x + -2 \cdot b\right)\\ t_4 := x - a \cdot \left(t + -1\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -0.09:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-96}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.28 \cdot 10^{-185}:\\ \;\;\;\;b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-174}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9500000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+36}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+144}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+209}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	57.32%
Cost	2296

\[\begin{array}{l} t_1 := a + \left(x + -2 \cdot b\right)\\ t_2 := z - y \cdot z\\ t_3 := t \cdot \left(b - a\right)\\ t_4 := a + \left(x + y \cdot b\right)\\ \mathbf{if}\;x \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -4.6:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -7 \cdot 10^{-156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.35 \cdot 10^{-208}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-247}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-286}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{-226}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-187}:\\ \;\;\;\;b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{-177}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{-124}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3200000:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+37}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+146}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	60.47%
Cost	2168

\[\begin{array}{l} t_1 := z - y \cdot z\\ t_2 := x - y \cdot z\\ t_3 := \left(1 - t\right) \cdot a\\ t_4 := b \cdot \left(y + -2\right)\\ \mathbf{if}\;x \leq -1.9 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{+54}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.9:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq -1.12 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{-96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -4.2 \cdot 10^{-173}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-286}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-227}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-172}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-126}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-94}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;x \leq 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	58.9%
Cost	1900

\[\begin{array}{l} t_1 := z - y \cdot z\\ t_2 := x - y \cdot z\\ t_3 := \left(1 - t\right) \cdot a\\ t_4 := b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{if}\;x \leq -3.2 \cdot 10^{+136}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -0.82:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{-96}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.1 \cdot 10^{-153}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{-167}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{-288}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-228}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+36}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 5
Error	36.96%
Cost	1633

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x + \left(z - a \cdot \left(t + -1\right)\right)\\ \mathbf{if}\;a \leq -1.55 \cdot 10^{+19}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -1.45 \cdot 10^{-147}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -9 \cdot 10^{-255}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;a \leq 2.6 \cdot 10^{-12}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{elif}\;a \leq 1.2 \cdot 10^{+48}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 3.3 \cdot 10^{+134} \lor \neg \left(a \leq 9.2 \cdot 10^{+167}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6
Error	34.34%
Cost	1628

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x + \left(z - a \cdot \left(t + -1\right)\right)\\ t_3 := x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ \mathbf{if}\;a \leq -4.2 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -7.2 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-256}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.8 \cdot 10^{-172}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{elif}\;a \leq 1.86 \cdot 10^{+58}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.5 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+167}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 7
Error	39.95%
Cost	1505

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x - a \cdot \left(t + -1\right)\\ \mathbf{if}\;a \leq -3 \cdot 10^{+81}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -6.1 \cdot 10^{-145}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.25 \cdot 10^{-254}:\\ \;\;\;\;x - z \cdot \left(y + -1\right)\\ \mathbf{elif}\;a \leq 2.05 \cdot 10^{-7}:\\ \;\;\;\;x + b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 8.2 \cdot 10^{+132} \lor \neg \left(a \leq 9.2 \cdot 10^{+167}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 8
Error	44.01%
Cost	1504

\[\begin{array}{l} t_1 := a + \left(x + y \cdot b\right)\\ t_2 := x - a \cdot \left(t + -1\right)\\ t_3 := x - z \cdot \left(y + -1\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{+14}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{-25}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 2.2 \cdot 10^{+47}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{+84}:\\ \;\;\;\;z - y \cdot z\\ \mathbf{elif}\;a \leq 1.85 \cdot 10^{+140}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 7.5 \cdot 10^{+161}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+176}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	31.59%
Cost	1496

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x + \left(z \cdot \left(1 - y\right) - t \cdot a\right)\\ t_3 := x + \left(z - a \cdot \left(t + -1\right)\right)\\ \mathbf{if}\;a \leq -4.5 \cdot 10^{+18}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq -9.6 \cdot 10^{-139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 2.9 \cdot 10^{-129}:\\ \;\;\;\;z + \left(x - b \cdot \left(2 - t\right)\right)\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 3.7 \cdot 10^{+113}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+167}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 10
Error	15.84%
Cost	1490

\[\begin{array}{l} t_1 := x + b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{if}\;a \leq -7 \cdot 10^{-139} \lor \neg \left(a \leq 6.5 \cdot 10^{-26} \lor \neg \left(a \leq 1.3 \cdot 10^{+46}\right) \land a \leq 1.25 \cdot 10^{+176}\right):\\ \;\;\;\;t_1 + \left(1 - t\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;t_1 + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 11
Error	65.65%
Cost	1376

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;a \leq -1.35 \cdot 10^{+20}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -4.2 \cdot 10^{-21}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-239}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{-7}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 5.5 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq 6.2 \cdot 10^{+47}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 12
Error	65.6%
Cost	1376

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ \mathbf{if}\;a \leq -1.7 \cdot 10^{+19}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;a \leq -1.48 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -5.2 \cdot 10^{-137}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-239}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 1.7 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 6.6 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq 1.3 \cdot 10^{+48}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 9.2 \cdot 10^{+167}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a - t \cdot a\\ \end{array} \]

Alternative 13
Error	0.04%
Cost	1344

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

Alternative 14
Error	51.38%
Cost	1244

\[\begin{array}{l} t_1 := a + \left(x + -2 \cdot b\right)\\ t_2 := y \cdot \left(b - z\right)\\ \mathbf{if}\;y \leq -9 \cdot 10^{+220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -3 \cdot 10^{-246}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -3.9 \cdot 10^{-299}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.22 \cdot 10^{-198}:\\ \;\;\;\;z\\ \mathbf{elif}\;y \leq 6400000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 4.5 \cdot 10^{+111}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	35.62%
Cost	1236

\[\begin{array}{l} t_1 := a + \left(x + b \cdot \left(y + -2\right)\right)\\ t_2 := x - z \cdot \left(y + -1\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+201}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-175}:\\ \;\;\;\;x - a \cdot \left(t + -1\right)\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Error	12.33%
Cost	1225

\[\begin{array}{l} \mathbf{if}\;a \leq -1.4 \cdot 10^{+22} \lor \neg \left(a \leq 1.75 \cdot 10^{-8}\right):\\ \;\;\;\;x + \left(\left(1 - t\right) \cdot a - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(-2 + \left(t + y\right)\right)\right) + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 17
Error	58.07%
Cost	1112

\[\begin{array}{l} t_1 := x - y \cdot z\\ \mathbf{if}\;a \leq -4.4 \cdot 10^{+21}:\\ \;\;\;\;\left(1 - t\right) \cdot a\\ \mathbf{elif}\;a \leq -1.85 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-239}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 2 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 5.2 \cdot 10^{+45}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;a \leq 1.25 \cdot 10^{+176}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a - t \cdot a\\ \end{array} \]

Alternative 18
Error	18.57%
Cost	1097

\[\begin{array}{l} \mathbf{if}\;b \leq -3.8 \cdot 10^{+88} \lor \neg \left(b \leq 3.9 \cdot 10^{+116}\right):\\ \;\;\;\;x + b \cdot \left(-2 + \left(t + y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(1 - t\right) \cdot a - z \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 19
Error	68.96%
Cost	916

\[\begin{array}{l} \mathbf{if}\;a \leq -1.7 \cdot 10^{+88}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -2.7 \cdot 10^{-138}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-239}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5 \cdot 10^{+14}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;a \leq 4.9 \cdot 10^{+125}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 20
Error	61.06%
Cost	848

\[\begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-183}:\\ \;\;\;\;-2 \cdot b\\ \mathbf{elif}\;x \leq 3 \cdot 10^{+64}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	61.12%
Cost	848

\[\begin{array}{l} t_1 := \left(1 - t\right) \cdot a\\ \mathbf{if}\;x \leq -1.75 \cdot 10^{+136}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5.6 \cdot 10^{-227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-151}:\\ \;\;\;\;b \cdot \left(t + -2\right)\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+63}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	68.63%
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -3.6 \cdot 10^{+58}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -1.75 \cdot 10^{-152}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+60}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 23
Error	68.32%
Cost	328

\[\begin{array}{l} \mathbf{if}\;x \leq -1.1 \cdot 10^{+68}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+58}:\\ \;\;\;\;a\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	83.39%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023088 
(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)))