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

Average Error: 0.0 → 0.0

Time: 24.8s

Precision: binary64

Cost: 1344

Math

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

↓

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

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

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

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 = ((((b - z) * y) + x) + ((t + (-2.0d0)) * b)) + (z + (a * (1.0d0 - t)))
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 ((((b - z) * y) + x) + ((t + -2.0) * b)) + (z + (a * (1.0 - t)));
}

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

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

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

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

3. Taylor expanded in y around 0 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	39.5
Cost	1508

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -1.6 \cdot 10^{+17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -46000000000:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-80}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -7.8 \cdot 10^{-84}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 3.7 \cdot 10^{-164}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 2
Error	39.1
Cost	1508

\[\begin{array}{l} t_1 := a - t \cdot a\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := x - z \cdot y\\ t_4 := t \cdot \left(b - a\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+186}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -1.55 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -2.6 \cdot 10^{+77}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -0.00065:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq -5.4 \cdot 10^{-70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-270}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-162}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+49}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 3
Error	39.0
Cost	1508

\[\begin{array}{l} t_1 := a - t \cdot a\\ t_2 := x - z \cdot y\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{+77}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -6.6 \cdot 10^{-5}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{-271}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-165}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+49}:\\ \;\;\;\;z - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 4
Error	38.1
Cost	1508

\[\begin{array}{l} t_1 := a - t \cdot a\\ t_2 := x - z \cdot y\\ t_3 := t \cdot \left(b - a\right)\\ \mathbf{if}\;x \leq -9.6 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -5 \cdot 10^{+76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -0.00038:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-71}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{-270}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq 1.42 \cdot 10^{-161}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) + -2\right)\\ \mathbf{elif}\;x \leq 1.32 \cdot 10^{-76}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+49}:\\ \;\;\;\;z - z \cdot y\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 5
Error	41.0
Cost	1376

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq -1.4 \cdot 10^{-81}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-83}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq -3.05 \cdot 10^{-270}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 2.15 \cdot 10^{-165}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 6
Error	7.0
Cost	1357

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -9 \cdot 10^{+74}:\\ \;\;\;\;x + \left(t_1 - z \cdot \left(y + -1\right)\right)\\ \mathbf{elif}\;z \leq -3.1 \cdot 10^{-38} \lor \neg \left(z \leq 5.2 \cdot 10^{-24}\right):\\ \;\;\;\;a + \left(z \cdot \left(1 - y\right) + \left(x + b \cdot \left(y + -2\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) + -2\right)\right) + t_1\\ \end{array} \]

Alternative 7
Error	0.0
Cost	1344

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

Alternative 8
Error	21.9
Cost	1244

\[\begin{array}{l} t_1 := a + \left(b \cdot -2 + \left(z + x\right)\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := x - t \cdot a\\ t_4 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;t \leq -8 \cdot 10^{+36}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{-132}:\\ \;\;\;\;a + \left(x + t_4\right)\\ \mathbf{elif}\;t \leq 160000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 2.9 \cdot 10^{+34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;t \leq 9.6 \cdot 10^{+119}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Error	17.0
Cost	1232

\[\begin{array}{l} t_1 := a + \left(b \cdot -2 + \left(z + x\right)\right)\\ t_2 := x - \left(z \cdot \left(y + -1\right) + t \cdot a\right)\\ \mathbf{if}\;t \leq -2.5 \cdot 10^{-24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 6.5 \cdot 10^{-281}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 5.5 \cdot 10^{-131}:\\ \;\;\;\;a + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 0.6:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Error	7.4
Cost	1225

\[\begin{array}{l} \mathbf{if}\;t \leq -3.9 \cdot 10^{-7} \lor \neg \left(t \leq 32000\right):\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + \left(z \cdot \left(1 - y\right) + \left(x + b \cdot \left(y + -2\right)\right)\right)\\ \end{array} \]

Alternative 11
Error	38.5
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -6.2 \cdot 10^{+171}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -4.4 \cdot 10^{-70}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;x \leq -3.8 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.55 \cdot 10^{-165}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 2.75 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 12
Error	38.6
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;x \leq -5.8 \cdot 10^{-69}:\\ \;\;\;\;a - t \cdot a\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-164}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-76}:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;x \leq 2 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 13
Error	33.7
Cost	1112

\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := b \cdot \left(\left(t + y\right) + -2\right)\\ \mathbf{if}\;a \leq -2.35 \cdot 10^{-11}:\\ \;\;\;\;a + \left(x + b \cdot -2\right)\\ \mathbf{elif}\;a \leq -6 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.7 \cdot 10^{-95}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.22 \cdot 10^{-164}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 3.65 \cdot 10^{-79}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.9 \cdot 10^{+94}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;a - t \cdot a\\ \end{array} \]

Alternative 14
Error	18.9
Cost	1104

\[\begin{array}{l} t_1 := a + \left(b \cdot -2 + \left(z + x\right)\right)\\ t_2 := x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{if}\;t \leq -7.5 \cdot 10^{-8}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 4.35 \cdot 10^{-280}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 8.8 \cdot 10^{-135}:\\ \;\;\;\;a + \left(x + z \cdot \left(1 - y\right)\right)\\ \mathbf{elif}\;t \leq 0.49:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	16.6
Cost	1096

\[\begin{array}{l} t_1 := x + b \cdot \left(y + -2\right)\\ \mathbf{if}\;a \leq -1.15 \cdot 10^{+70}:\\ \;\;\;\;a + t_1\\ \mathbf{elif}\;a \leq 2.3 \cdot 10^{-70}:\\ \;\;\;\;z \cdot \left(1 - y\right) + t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 16
Error	12.3
Cost	1096

\[\begin{array}{l} t_1 := x + b \cdot \left(y + -2\right)\\ \mathbf{if}\;b \leq -5.5 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(1 - y\right) + t_1\\ \mathbf{elif}\;b \leq 1.14 \cdot 10^{+36}:\\ \;\;\;\;x + \left(a \cdot \left(1 - t\right) - z \cdot \left(y + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;a + t_1\\ \end{array} \]

Alternative 17
Error	21.5
Cost	980

\[\begin{array}{l} t_1 := x - t \cdot a\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -5.8 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 160000000:\\ \;\;\;\;a + \left(b \cdot -2 + \left(z + x\right)\right)\\ \mathbf{elif}\;t \leq 5.8 \cdot 10^{+30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq 1.38 \cdot 10^{+35}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 4.9 \cdot 10^{+120}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Error	29.5
Cost	976

\[\begin{array}{l} \mathbf{if}\;a \leq -7 \cdot 10^{-10}:\\ \;\;\;\;a + \left(x + b \cdot -2\right)\\ \mathbf{elif}\;a \leq -1.8 \cdot 10^{-79}:\\ \;\;\;\;x - t \cdot a\\ \mathbf{elif}\;a \leq -9.5 \cdot 10^{-82}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) + -2\right)\\ \mathbf{elif}\;a \leq 3600000:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;a - t \cdot a\\ \end{array} \]

Alternative 19
Error	40.1
Cost	916

\[\begin{array}{l} \mathbf{if}\;x \leq -3400000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-77}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -5.3 \cdot 10^{-270}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{-163}:\\ \;\;\;\;\left(t + -2\right) \cdot b\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-92}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 20
Error	44.8
Cost	784

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-77}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 5.1 \cdot 10^{-303}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{-90}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Error	45.3
Cost	724

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-72}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{-271}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-76}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq 3.4 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	25.6
Cost	713

\[\begin{array}{l} \mathbf{if}\;a \leq -4.6 \cdot 10^{-73} \lor \neg \left(a \leq 3.2 \cdot 10^{-41}\right):\\ \;\;\;\;x - \left(t + -1\right) \cdot a\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(1 - y\right)\\ \end{array} \]

Alternative 23
Error	44.1
Cost	460

\[\begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+169}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{-73}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+86}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 24
Error	35.8
Cost	456

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+160}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 9 \cdot 10^{+94}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 25
Error	43.7
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -1.35 \cdot 10^{+137}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 4.8 \cdot 10^{+96}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 26
Error	53.5
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023060 
(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)))