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

Percentage Accurate: 95.3% → 98.4%

Time: 24.8s

Precision: binary64

Cost: 15172

• 35.7% of points produce a very large (infinite) output. You may want to add a precondition.

Math

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

↓

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;\left(t_2 + a \cdot \left(1 - t\right)\right) + t_1 \leq \infty:\\ \;\;\;\;t_1 + \left(t_2 - \mathsf{fma}\left(a, t, -a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z - b \cdot \left(2 - t\right)\right)\right)\\ \end{array} \]

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
 (let* ((t_1 (* b (- (+ t y) 2.0))) (t_2 (+ x (* z (- 1.0 y)))))
   (if (<= (+ (+ t_2 (* a (- 1.0 t))) t_1) INFINITY)
     (+ t_1 (- t_2 (fma a t (- a))))
     (fma a (- 1.0 t) (fma (- b z) y (- z (* b (- 2.0 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) {
	double t_1 = b * ((t + y) - 2.0);
	double t_2 = x + (z * (1.0 - y));
	double tmp;
	if (((t_2 + (a * (1.0 - t))) + t_1) <= ((double) INFINITY)) {
		tmp = t_1 + (t_2 - fma(a, t, -a));
	} else {
		tmp = fma(a, (1.0 - t), fma((b - z), y, (z - (b * (2.0 - t)))));
	}
	return tmp;
}

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)
	t_1 = Float64(b * Float64(Float64(t + y) - 2.0))
	t_2 = Float64(x + Float64(z * Float64(1.0 - y)))
	tmp = 0.0
	if (Float64(Float64(t_2 + Float64(a * Float64(1.0 - t))) + t_1) <= Inf)
		tmp = Float64(t_1 + Float64(t_2 - fma(a, t, Float64(-a))));
	else
		tmp = fma(a, Float64(1.0 - t), fma(Float64(b - z), y, Float64(z - Float64(b * Float64(2.0 - t)))));
	end
	return tmp
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_] := Block[{t$95$1 = N[(b * N[(N[(t + y), $MachinePrecision] - 2.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x + N[(z * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(t$95$2 + N[(a * N[(1.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(t$95$1 + N[(t$95$2 - N[(a * t + (-a)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(a * N[(1.0 - t), $MachinePrecision] + N[(N[(b - z), $MachinePrecision] * y + N[(z - N[(b * N[(2.0 - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b)) < +inf.0

   1. Initial program 100.0%

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

   2. Taylor expanded in t around 0 100.0%

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

   3. Simplified 100.0%

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

      [Start] 100.0%	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(a \cdot t + -1 \cdot a\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
      fma-def [=>] 100.0%	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \color{blue}{\mathsf{fma}\left(a, t, -1 \cdot a\right)}\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
      neg-mul-1 [<=] 100.0%	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \mathsf{fma}\left(a, t, \color{blue}{-a}\right)\right) + \left(\left(y + t\right) - 2\right) \cdot b \]

   if +inf.0 < (+.f64 (-.f64 (-.f64 x (*.f64 (-.f64 y 1) z)) (*.f64 (-.f64 t 1) a)) (*.f64 (-.f64 (+.f64 y t) 2) b))

   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 66.7%

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

      [Start] 0.0%	\[ \left(\left(x - \left(y - 1\right) \cdot z\right) - \left(t - 1\right) \cdot a\right) + \left(\left(y + t\right) - 2\right) \cdot b \]
      sub-neg [=>] 0.0%	\[ \color{blue}{\left(\left(x - \left(y - 1\right) \cdot z\right) + \left(-\left(t - 1\right) \cdot a\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
      +-commutative [=>] 0.0%	\[ \color{blue}{\left(\left(-\left(t - 1\right) \cdot a\right) + \left(x - \left(y - 1\right) \cdot z\right)\right)} + \left(\left(y + t\right) - 2\right) \cdot b \]
      associate-+l+ [=>] 0.0%	\[ \color{blue}{\left(-\left(t - 1\right) \cdot a\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right)} \]
      *-commutative [=>] 0.0%	\[ \left(-\color{blue}{a \cdot \left(t - 1\right)}\right) + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]
      distribute-rgt-neg-in [=>] 0.0%	\[ \color{blue}{a \cdot \left(-\left(t - 1\right)\right)} + \left(\left(x - \left(y - 1\right) \cdot z\right) + \left(\left(y + t\right) - 2\right) \cdot b\right) \]
      +-commutative [<=] 0.0%	\[ a \cdot \left(-\left(t - 1\right)\right) + \color{blue}{\left(\left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]
      fma-def [=>] 33.3%	\[ \color{blue}{\mathsf{fma}\left(a, -\left(t - 1\right), \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right)} \]
      neg-sub0 [=>] 33.3%	\[ \mathsf{fma}\left(a, \color{blue}{0 - \left(t - 1\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]
      associate--r- [=>] 33.3%	\[ \mathsf{fma}\left(a, \color{blue}{\left(0 - t\right) + 1}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]
      neg-sub0 [<=] 33.3%	\[ \mathsf{fma}\left(a, \color{blue}{\left(-t\right)} + 1, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]
      +-commutative [=>] 33.3%	\[ \mathsf{fma}\left(a, \color{blue}{1 + \left(-t\right)}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]
      sub-neg [<=] 33.3%	\[ \mathsf{fma}\left(a, \color{blue}{1 - t}, \left(\left(y + t\right) - 2\right) \cdot b + \left(x - \left(y - 1\right) \cdot z\right)\right) \]
      fma-def [=>] 66.7%	\[ \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(\left(y + t\right) - 2, b, x - \left(y - 1\right) \cdot z\right)}\right) \]
      sub-neg [=>] 66.7%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{\left(y + t\right) + \left(-2\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]
      associate-+l+ [=>] 66.7%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{y + \left(t + \left(-2\right)\right)}, b, x - \left(y - 1\right) \cdot z\right)\right) \]
      metadata-eval [=>] 66.7%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + \color{blue}{-2}\right), b, x - \left(y - 1\right) \cdot z\right)\right) \]
      sub-neg [=>] 66.7%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{x + \left(-\left(y - 1\right) \cdot z\right)}\right)\right) \]
      +-commutative [=>] 66.7%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(y + \left(t + -2\right), b, \color{blue}{\left(-\left(y - 1\right) \cdot z\right) + x}\right)\right) \]

   3. Taylor expanded in y around 0 77.8%

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

   4. Simplified 77.8%

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

      [Start] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \left(-1 \cdot z + b\right) \cdot y + \left(z + \left(b \cdot \left(t - 2\right) + x\right)\right)\right) \]
      fma-def [=>] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \color{blue}{\mathsf{fma}\left(-1 \cdot z + b, y, z + \left(b \cdot \left(t - 2\right) + x\right)\right)}\right) \]
      +-commutative [=>] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{b + -1 \cdot z}, y, z + \left(b \cdot \left(t - 2\right) + x\right)\right)\right) \]
      mul-1-neg [=>] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b + \color{blue}{\left(-z\right)}, y, z + \left(b \cdot \left(t - 2\right) + x\right)\right)\right) \]
      sub-neg [<=] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(\color{blue}{b - z}, y, z + \left(b \cdot \left(t - 2\right) + x\right)\right)\right) \]
      fma-def [=>] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z + \color{blue}{\mathsf{fma}\left(b, t - 2, x\right)}\right)\right) \]
      sub-neg [=>] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z + \mathsf{fma}\left(b, \color{blue}{t + \left(-2\right)}, x\right)\right)\right) \]
      metadata-eval [=>] 77.8%	\[ \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z + \mathsf{fma}\left(b, t + \color{blue}{-2}, x\right)\right)\right) \]

   5. Taylor expanded in b around inf 77.8%

      \[\leadsto \mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z + \color{blue}{\left(t - 2\right) \cdot b}\right)\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(x + z \cdot \left(1 - y\right)\right) + a \cdot \left(1 - t\right)\right) + b \cdot \left(\left(t + y\right) - 2\right) \leq \infty:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) + \left(\left(x + z \cdot \left(1 - y\right)\right) - \mathsf{fma}\left(a, t, -a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z - b \cdot \left(2 - t\right)\right)\right)\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	98.4%
Cost	15172

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;\left(t_2 + a \cdot \left(1 - t\right)\right) + t_1 \leq \infty:\\ \;\;\;\;t_1 + \left(t_2 - \mathsf{fma}\left(a, t, -a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(a, 1 - t, \mathsf{fma}\left(b - z, y, z - b \cdot \left(2 - t\right)\right)\right)\\ \end{array} \]

Alternative 2
Accuracy	97.6%
Cost	20160

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

Alternative 3
Accuracy	97.9%
Cost	9092

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;\left(t_2 + a \cdot \left(1 - t\right)\right) + t_1 \leq \infty:\\ \;\;\;\;t_1 + \left(t_2 - \mathsf{fma}\left(a, t, -a\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 4
Accuracy	97.9%
Cost	2756

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

Alternative 5
Accuracy	97.9%
Cost	2756

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_2 := x + z \cdot \left(1 - y\right)\\ \mathbf{if}\;\left(t_2 + a \cdot \left(1 - t\right)\right) + t_1 \leq \infty:\\ \;\;\;\;t_1 + \left(t_2 + \left(a - a \cdot t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \end{array} \]

Alternative 6
Accuracy	82.7%
Cost	1356

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_2 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;b \leq -1.25 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 2.15 \cdot 10^{+23}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t_2\right)\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{+173}:\\ \;\;\;\;\left(z + \left(x + b \cdot \left(t - 2\right)\right)\right) + t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Accuracy	33.8%
Cost	1244

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;a \leq -2.25 \cdot 10^{+45}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-84}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -4.8 \cdot 10^{-181}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq -2.15 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.75 \cdot 10^{-159}:\\ \;\;\;\;z\\ \mathbf{elif}\;a \leq 5.4 \cdot 10^{-90}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 2700000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	37.2%
Cost	1244

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ t_2 := b \cdot \left(t - 2\right)\\ \mathbf{if}\;a \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -1.32 \cdot 10^{-74}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq -6.8 \cdot 10^{-182}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;a \leq 8.6 \cdot 10^{-303}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1.65 \cdot 10^{-144}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq 1.5 \cdot 10^{-31}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;a \leq 145000000000:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 9
Accuracy	61.7%
Cost	1240

\[\begin{array}{l} t_1 := x + \left(a - a \cdot t\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ t_3 := z \cdot \left(1 - y\right)\\ \mathbf{if}\;b \leq -2.4 \cdot 10^{+53}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.3 \cdot 10^{-144}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -6.7 \cdot 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 7.2 \cdot 10^{-286}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 5.2 \cdot 10^{-276}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;b \leq 2.6 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 10
Accuracy	55.8%
Cost	1240

\[\begin{array}{l} t_1 := x + \left(z - y \cdot z\right)\\ t_2 := x + \left(a - a \cdot t\right)\\ t_3 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;a \leq -5.6 \cdot 10^{+89}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;a \leq -3.5 \cdot 10^{-146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq -7 \cdot 10^{-197}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 4.2 \cdot 10^{-247}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;a \leq 10^{-161}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;a \leq 6.1 \cdot 10^{+44}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 11
Accuracy	67.5%
Cost	1233

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right) - a \cdot t\\ \mathbf{if}\;t \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.5 \cdot 10^{+52}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;t \leq -1.96 \cdot 10^{-7} \lor \neg \left(t \leq 8 \cdot 10^{-11}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x + \left(a - \left(y \cdot z - z\right)\right)\\ \end{array} \]

Alternative 12
Accuracy	86.5%
Cost	1225

\[\begin{array}{l} t_1 := a \cdot \left(1 - t\right)\\ \mathbf{if}\;z \leq -1.8 \cdot 10^{+66} \lor \neg \left(z \leq 1.1 \cdot 10^{+69}\right):\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + t_1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + b \cdot \left(\left(t + y\right) - 2\right)\right) + t_1\\ \end{array} \]

Alternative 13
Accuracy	41.6%
Cost	1112

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.96 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -7 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-306}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 3.95 \cdot 10^{-200}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 5.2 \cdot 10^{-125}:\\ \;\;\;\;y \cdot \left(-z\right)\\ \mathbf{elif}\;t \leq 56:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 14
Accuracy	46.7%
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ t_3 := y \cdot \left(b - z\right)\\ \mathbf{if}\;t \leq -1.96 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.2 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -4.9 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -8.2 \cdot 10^{-302}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;t \leq 1.25 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Accuracy	46.0%
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.96 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-295}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 1.16 \cdot 10^{+85}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 16
Accuracy	45.1%
Cost	1112

\[\begin{array}{l} t_1 := z \cdot \left(1 - y\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -5.5 \cdot 10^{-124}:\\ \;\;\;\;x - a \cdot t\\ \mathbf{elif}\;t \leq -3.2 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-295}:\\ \;\;\;\;b \cdot \left(y - 2\right)\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 6.3 \cdot 10^{+84}:\\ \;\;\;\;y \cdot \left(b - z\right)\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Accuracy	69.1%
Cost	1104

\[\begin{array}{l} t_1 := x + \left(a - \left(y \cdot z - z\right)\right)\\ t_2 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.05 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;b \leq -1.25 \cdot 10^{-47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq -2.25 \cdot 10^{-256}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \mathbf{elif}\;b \leq 3.2 \cdot 10^{+82}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 18
Accuracy	82.0%
Cost	1096

\[\begin{array}{l} t_1 := b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{if}\;b \leq -1.2 \cdot 10^{+154}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;b \leq 8.2 \cdot 10^{+63}:\\ \;\;\;\;x + \left(z \cdot \left(1 - y\right) + a \cdot \left(1 - t\right)\right)\\ \mathbf{else}:\\ \;\;\;\;t_1 - a \cdot t\\ \end{array} \]

Alternative 19
Accuracy	26.6%
Cost	1048

\[\begin{array}{l} t_1 := a \cdot \left(-t\right)\\ \mathbf{if}\;t \leq -85000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -4 \cdot 10^{-178}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -5.1 \cdot 10^{-298}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 2.6 \cdot 10^{-91}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+85}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 1.35 \cdot 10^{+174}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 20
Accuracy	25.0%
Cost	1048

\[\begin{array}{l} t_1 := y \cdot \left(-z\right)\\ \mathbf{if}\;x \leq -1.1 \cdot 10^{+109}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq -3.5 \cdot 10^{+19}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-148}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{-158}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-46}:\\ \;\;\;\;a\\ \mathbf{elif}\;x \leq 3.55 \cdot 10^{+115}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 21
Accuracy	48.9%
Cost	980

\[\begin{array}{l} t_1 := y \cdot \left(b - z\right)\\ t_2 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.96 \cdot 10^{-7}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;t \leq -2 \cdot 10^{-178}:\\ \;\;\;\;x - y \cdot z\\ \mathbf{elif}\;t \leq -5.8 \cdot 10^{-300}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq 2 \cdot 10^{-89}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{elif}\;t \leq 3.1 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 22
Accuracy	68.3%
Cost	968

\[\begin{array}{l} \mathbf{if}\;t \leq -1.3 \cdot 10^{-7}:\\ \;\;\;\;\left(z - b \cdot \left(2 - t\right)\right) + a \cdot \left(1 - t\right)\\ \mathbf{elif}\;t \leq 7.6 \cdot 10^{-11}:\\ \;\;\;\;x + \left(a - \left(y \cdot z - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right) - a \cdot t\\ \end{array} \]

Alternative 23
Accuracy	23.2%
Cost	852

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq -1.35 \cdot 10^{-175}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq -6.6 \cdot 10^{-298}:\\ \;\;\;\;y \cdot b\\ \mathbf{elif}\;t \leq 4.2 \cdot 10^{-93}:\\ \;\;\;\;z\\ \mathbf{elif}\;t \leq 8.5 \cdot 10^{+169}:\\ \;\;\;\;y \cdot b\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 24
Accuracy	69.2%
Cost	841

\[\begin{array}{l} \mathbf{if}\;b \leq -1.05 \cdot 10^{+154} \lor \neg \left(b \leq 1.22 \cdot 10^{+85}\right):\\ \;\;\;\;b \cdot \left(\left(t + y\right) - 2\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(z + a \cdot \left(1 - t\right)\right)\\ \end{array} \]

Alternative 25
Accuracy	45.4%
Cost	716

\[\begin{array}{l} t_1 := t \cdot \left(b - a\right)\\ \mathbf{if}\;t \leq -1.9 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t \leq -5.4 \cdot 10^{-124}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 1.2 \cdot 10^{+84}:\\ \;\;\;\;z \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 26
Accuracy	23.5%
Cost	588

\[\begin{array}{l} \mathbf{if}\;t \leq -1.85 \cdot 10^{+146}:\\ \;\;\;\;t \cdot b\\ \mathbf{elif}\;t \leq 1.75 \cdot 10^{-198}:\\ \;\;\;\;x\\ \mathbf{elif}\;t \leq 2.15 \cdot 10^{+105}:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;t \cdot b\\ \end{array} \]

Alternative 27
Accuracy	19.2%
Cost	460

\[\begin{array}{l} \mathbf{if}\;a \leq -1.05 \cdot 10^{+90}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq -2.1 \cdot 10^{-257}:\\ \;\;\;\;x\\ \mathbf{elif}\;a \leq 1300000000000:\\ \;\;\;\;z\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 28
Accuracy	21.2%
Cost	328

\[\begin{array}{l} \mathbf{if}\;a \leq -5.5 \cdot 10^{+90}:\\ \;\;\;\;a\\ \mathbf{elif}\;a \leq 7.7 \cdot 10^{+183}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;a\\ \end{array} \]

Alternative 29
Accuracy	11.5%
Cost	64

\[a \]

Reproduce

herbie shell --seed 2023272 
(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)))