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

Average Error: 0.0 → 0.0

Time: 23.7s

Precision: binary64

Cost: 1344

Math

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

↓

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

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

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

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

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

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

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

   [Start] 0.0	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
   rational_best_oopsla_all_46_json_45_simplify-35 [=>] 0.0	\[ \color{blue}{\left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.0	\[ \left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{a \cdot \left(t - 1\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-13 [=>] 0.0	\[ \left(\left(y + t\right) - 2\right) \cdot b + \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\left(t \cdot a - a \cdot 1\right)}\right) \]
   rational_best_oopsla_all_46_json_45_simplify-36 [=>] 0.0	\[ \left(\left(y + t\right) - 2\right) \cdot b + \color{blue}{\left(a \cdot 1 - \left(t \cdot a - \left(x - \left(y - 1\right) \cdot z\right)\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.0	\[ \left(\left(y + t\right) - 2\right) \cdot b + \left(\color{blue}{a} - \left(t \cdot a - \left(x - \left(y - 1\right) \cdot z\right)\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-108 [=>] 0.0	\[ \color{blue}{\left(a + \left(\left(y + t\right) - 2\right) \cdot b\right) - \left(t \cdot a - \left(x - \left(y - 1\right) \cdot z\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-35 [=>] 0.0	\[ \left(a + \left(\color{blue}{\left(t + y\right)} - 2\right) \cdot b\right) - \left(t \cdot a - \left(x - \left(y - 1\right) \cdot z\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-107 [=>] 0.0	\[ \left(a + \color{blue}{\left(y + \left(t - 2\right)\right)} \cdot b\right) - \left(t \cdot a - \left(x - \left(y - 1\right) \cdot z\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-36 [=>] 0.0	\[ \left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - \color{blue}{\left(\left(y - 1\right) \cdot z - \left(x - t \cdot a\right)\right)} \]
   rational_best_oopsla_all_46_json_45_simplify-74 [=>] 0.0	\[ \left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - \left(\color{blue}{z \cdot \left(y - 1\right)} - \left(x - t \cdot a\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-13 [=>] 0.0	\[ \left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - \left(\color{blue}{\left(y \cdot z - z \cdot 1\right)} - \left(x - t \cdot a\right)\right) \]
   rational_best_oopsla_all_46_json_45_simplify-52 [=>] 0.0	\[ \left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - \left(\left(y \cdot z - \color{blue}{z}\right) - \left(x - t \cdot a\right)\right) \]

3. Taylor expanded in t around 0 0.0

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

4. Final simplification 0.0

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

Alternatives

Alternative 1
Error	38.1
Cost	1904

\[\begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := z \cdot \left(1 - y\right)\\ t_3 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+168}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -2.8 \cdot 10^{+89}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -1.46 \cdot 10^{-136}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -6 \cdot 10^{-174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.25 \cdot 10^{-210}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -5.2 \cdot 10^{-273}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+62}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+133}:\\ \;\;\;\;\left(t - 2\right) \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 2
Error	37.0
Cost	1640

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+168}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7 \cdot 10^{+88}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-137}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -5.5 \cdot 10^{-174}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -1.45 \cdot 10^{-220}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.08 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.02 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 3
Error	37.5
Cost	1640

\[\begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -1.5 \cdot 10^{+170}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{+127}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+89}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -4 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-174}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;x \leq -3.6 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{-272}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{-164}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-101}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 4
Error	19.4
Cost	1492

\[\begin{array}{l} t_1 := -2 \cdot b + \left(z + \left(a + t \cdot \left(b - a\right)\right)\right)\\ \mathbf{if}\;x \leq -5.3 \cdot 10^{+154}:\\ \;\;\;\;z + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;x \leq -2.2 \cdot 10^{+37}:\\ \;\;\;\;\left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - -1 \cdot x\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+65}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + b \cdot \left(-2 + t\right)\\ \end{array} \]

Alternative 5
Error	18.6
Cost	1492

\[\begin{array}{l} t_1 := -2 \cdot b + \left(z + \left(a + t \cdot \left(b - a\right)\right)\right)\\ t_2 := a + \left(y + \left(t - 2\right)\right) \cdot b\\ \mathbf{if}\;x \leq -7.8 \cdot 10^{+154}:\\ \;\;\;\;z + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{+29}:\\ \;\;\;\;t_2 - -1 \cdot x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-259}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;t_2 - t \cdot a\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + b \cdot \left(-2 + t\right)\\ \end{array} \]

Alternative 6
Error	8.6
Cost	1492

\[\begin{array}{l} t_1 := \left(z + \left(a + x\right)\right) - \left(y \cdot z + t \cdot a\right)\\ \mathbf{if}\;y \leq -1.95 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;\left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - t \cdot a\\ \mathbf{elif}\;y \leq -4 \cdot 10^{+23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3200000000000:\\ \;\;\;\;t \cdot \left(b - a\right) + \left(a + \left(-2 \cdot b + \left(z + x\right)\right)\right)\\ \mathbf{elif}\;y \leq 6.7 \cdot 10^{+183}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \end{array} \]

Alternative 7
Error	7.3
Cost	1488

\[\begin{array}{l} t_1 := \left(\left(\left(y + t\right) - 2\right) \cdot b + \left(z + x\right)\right) - y \cdot z\\ \mathbf{if}\;y \leq -1.85 \cdot 10^{+105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -9.2 \cdot 10^{+49}:\\ \;\;\;\;\left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - t \cdot a\\ \mathbf{elif}\;y \leq -5 \cdot 10^{+28}:\\ \;\;\;\;\left(z + \left(a + x\right)\right) - \left(y \cdot z + t \cdot a\right)\\ \mathbf{elif}\;y \leq 4.8 \cdot 10^{+44}:\\ \;\;\;\;t \cdot \left(b - a\right) + \left(a + \left(-2 \cdot b + \left(z + x\right)\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Error	22.6
Cost	1376

\[\begin{array}{l} t_1 := -2 \cdot b + \left(a + \left(z + x\right)\right)\\ t_2 := z + \left(x + a \cdot \left(1 - t\right)\right)\\ t_3 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -6.4 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-264}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{-76}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 4.9 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1000000000000:\\ \;\;\;\;t \cdot \left(b - a\right)\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{+132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+176}:\\ \;\;\;\;z + \left(a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Error	19.3
Cost	1360

\[\begin{array}{l} t_1 := -2 \cdot b + \left(z + \left(a + t \cdot \left(b - a\right)\right)\right)\\ \mathbf{if}\;x \leq -2.2 \cdot 10^{+34}:\\ \;\;\;\;z + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;\left(b - z\right) \cdot y\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\left(z + x\right) + b \cdot \left(-2 + t\right)\\ \end{array} \]

Alternative 10
Error	0.0
Cost	1344

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

Alternative 11
Error	0.0
Cost	1344

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

Alternative 12
Error	22.3
Cost	1244

\[\begin{array}{l} t_1 := z + \left(x + a \cdot \left(1 - t\right)\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.4 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.3 \cdot 10^{-264}:\\ \;\;\;\;-2 \cdot b + \left(a + \left(z + x\right)\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{-62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-32}:\\ \;\;\;\;\left(z + x\right) + b \cdot \left(-2 + t\right)\\ \mathbf{elif}\;y \leq 7.4 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+131}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+174}:\\ \;\;\;\;z + \left(a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 13
Error	37.8
Cost	1112

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;x \leq -2 \cdot 10^{+168}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -3.9 \cdot 10^{+127}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq -3.3 \cdot 10^{+89}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-164}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-101}:\\ \;\;\;\;z \cdot \left(-y\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+61}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 14
Error	26.8
Cost	1112

\[\begin{array}{l} t_1 := z + \left(a + x\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -8.4 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-239}:\\ \;\;\;\;\left(z + x\right) + b \cdot -2\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+129}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.7 \cdot 10^{+177}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	10.3
Cost	1096

\[\begin{array}{l} t_1 := \left(a + \left(y + \left(t - 2\right)\right) \cdot b\right) - -1 \cdot x\\ \mathbf{if}\;b \leq -0.017:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 1.75 \cdot 10^{-98}:\\ \;\;\;\;\left(z + \left(a + x\right)\right) - \left(y \cdot z + t \cdot a\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 16
Error	23.6
Cost	980

\[\begin{array}{l} t_1 := \left(b - z\right) \cdot y\\ t_2 := z + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{-89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -4.8 \cdot 10^{-158}:\\ \;\;\;\;\left(z + x\right) + b \cdot -2\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 7.5 \cdot 10^{+174}:\\ \;\;\;\;z + \left(a + x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 17
Error	18.0
Cost	972

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right) - y \cdot z\\ \mathbf{if}\;t \leq -3.8 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 4 \cdot 10^{-9}:\\ \;\;\;\;-2 \cdot b + \left(a + \left(z + x\right)\right)\\ \mathbf{elif}\;t \leq 1.15 \cdot 10^{+134}:\\ \;\;\;\;z + \left(x + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 18
Error	27.1
Cost	848

\[\begin{array}{l} t_1 := z + \left(a + x\right)\\ t_2 := \left(b - z\right) \cdot y\\ \mathbf{if}\;y \leq -1.35 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 19
Error	27.3
Cost	848

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.15 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 3.25 \cdot 10^{+38}:\\ \;\;\;\;z + \left(a + x\right)\\ \mathbf{elif}\;t \leq 4.8 \cdot 10^{+89}:\\ \;\;\;\;z + a \cdot \left(-t\right)\\ \mathbf{elif}\;t \leq 2 \cdot 10^{+137}:\\ \;\;\;\;z + x\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 20
Error	40.7
Cost	784

\[\begin{array}{l} t_1 := z \cdot \left(-y\right)\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{-126}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-243}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-258}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{-100}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 21
Error	44.5
Cost	592

\[\begin{array}{l} \mathbf{if}\;x \leq -2 \cdot 10^{+23}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 5 \cdot 10^{-252}:\\ \;\;\;\;z\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{-101}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 6.6 \cdot 10^{-35}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 22
Error	40.8
Cost	520

\[\begin{array}{l} \mathbf{if}\;a \leq 16000000000000:\\ \;\;\;\;z + x\\ \mathbf{elif}\;a \leq 2.7 \cdot 10^{+160}:\\ \;\;\;\;t \cdot \left(-a\right)\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 23
Error	40.4
Cost	456

\[\begin{array}{l} \mathbf{if}\;x \leq 1.9 \cdot 10^{-251}:\\ \;\;\;\;z + x\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{-100}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;z + x\\ \end{array} \]

Alternative 24
Error	43.9
Cost	328

\[\begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+109}:\\ \;\;\;\;z\\ \mathbf{elif}\;z \leq 5 \cdot 10^{+211}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z\\ \end{array} \]

Alternative 25
Error	49.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2023090 
(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)))