Octave 3.8, jcobi/3

Percentage Accurate: 94.9% → 99.8%

Time: 26.9s

Precision: binary64

Cost: 1600

• Unsound rule application detected in e-graph. Results may not be sound.

\[\alpha > -1 \land \beta > -1\]

Math

\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]

↓

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\beta + \left(\alpha + 3\right)}}{t_0}}{t_0} \end{array} \]

FPCore

(FPCore (alpha beta)
 :precision binary64
 (/
  (/
   (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))
   (+ (+ alpha beta) (* 2.0 1.0)))
  (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))

↓

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ beta (+ alpha 2.0))))
   (/ (/ (* (+ alpha 1.0) (/ (+ 1.0 beta) (+ beta (+ alpha 3.0)))) t_0) t_0)))

C

double code(double alpha, double beta) {
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0);
}

↓

double code(double alpha, double beta) {
	double t_0 = beta + (alpha + 2.0);
	return (((alpha + 1.0) * ((1.0 + beta) / (beta + (alpha + 3.0)))) / t_0) / t_0;
}

Fortran

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    code = (((((alpha + beta) + (beta * alpha)) + 1.0d0) / ((alpha + beta) + (2.0d0 * 1.0d0))) / ((alpha + beta) + (2.0d0 * 1.0d0))) / (((alpha + beta) + (2.0d0 * 1.0d0)) + 1.0d0)
end function

↓

real(8) function code(alpha, beta)
    real(8), intent (in) :: alpha
    real(8), intent (in) :: beta
    real(8) :: t_0
    t_0 = beta + (alpha + 2.0d0)
    code = (((alpha + 1.0d0) * ((1.0d0 + beta) / (beta + (alpha + 3.0d0)))) / t_0) / t_0
end function

Java

public static double code(double alpha, double beta) {
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0);
}

↓

public static double code(double alpha, double beta) {
	double t_0 = beta + (alpha + 2.0);
	return (((alpha + 1.0) * ((1.0 + beta) / (beta + (alpha + 3.0)))) / t_0) / t_0;
}

Python

def code(alpha, beta):
	return (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0)

↓

def code(alpha, beta):
	t_0 = beta + (alpha + 2.0)
	return (((alpha + 1.0) * ((1.0 + beta) / (beta + (alpha + 3.0)))) / t_0) / t_0

Julia

function code(alpha, beta)
	return Float64(Float64(Float64(Float64(Float64(Float64(alpha + beta) + Float64(beta * alpha)) + 1.0) / Float64(Float64(alpha + beta) + Float64(2.0 * 1.0))) / Float64(Float64(alpha + beta) + Float64(2.0 * 1.0))) / Float64(Float64(Float64(alpha + beta) + Float64(2.0 * 1.0)) + 1.0))
end

↓

function code(alpha, beta)
	t_0 = Float64(beta + Float64(alpha + 2.0))
	return Float64(Float64(Float64(Float64(alpha + 1.0) * Float64(Float64(1.0 + beta) / Float64(beta + Float64(alpha + 3.0)))) / t_0) / t_0)
end

MATLAB

function tmp = code(alpha, beta)
	tmp = (((((alpha + beta) + (beta * alpha)) + 1.0) / ((alpha + beta) + (2.0 * 1.0))) / ((alpha + beta) + (2.0 * 1.0))) / (((alpha + beta) + (2.0 * 1.0)) + 1.0);
end

↓

function tmp = code(alpha, beta)
	t_0 = beta + (alpha + 2.0);
	tmp = (((alpha + 1.0) * ((1.0 + beta) / (beta + (alpha + 3.0)))) / t_0) / t_0;
end

Wolfram

code[alpha_, beta_] := N[(N[(N[(N[(N[(N[(alpha + beta), $MachinePrecision] + N[(beta * alpha), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision] / N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[(N[(alpha + beta), $MachinePrecision] + N[(2.0 * 1.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]

↓

code[alpha_, beta_] := Block[{t$95$0 = N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(alpha + 1.0), $MachinePrecision] * N[(N[(1.0 + beta), $MachinePrecision] / N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / t$95$0), $MachinePrecision]]

Derivation

1. Initial program 92.5%

   \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]

2. Simplified 96.2%

   \[\leadsto \color{blue}{\frac{\beta + 1}{\alpha + \left(\beta + 3\right)} \cdot \frac{\alpha + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}} \]
   Step-by-step derivation

   [Start] 92.5	\[ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
   associate-/l/ [=>] 91.7	\[ \frac{\color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
   associate-/l/ [=>] 83.9	\[ \color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)}} \]
   associate-+l+ [=>] 83.9	\[ \frac{\color{blue}{\left(\alpha + \left(\beta + \beta \cdot \alpha\right)\right)} + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   +-commutative [=>] 83.9	\[ \frac{\left(\alpha + \color{blue}{\left(\beta \cdot \alpha + \beta\right)}\right) + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   associate-+r+ [=>] 83.9	\[ \frac{\color{blue}{\left(\left(\alpha + \beta \cdot \alpha\right) + \beta\right)} + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   associate-+l+ [=>] 83.9	\[ \frac{\color{blue}{\left(\alpha + \beta \cdot \alpha\right) + \left(\beta + 1\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   distribute-rgt1-in [=>] 83.9	\[ \frac{\color{blue}{\left(\beta + 1\right) \cdot \alpha} + \left(\beta + 1\right)}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   *-rgt-identity [<=] 83.9	\[ \frac{\left(\beta + 1\right) \cdot \alpha + \color{blue}{\left(\beta + 1\right) \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   distribute-lft-out [=>] 83.9	\[ \frac{\color{blue}{\left(\beta + 1\right) \cdot \left(\alpha + 1\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   +-commutative [=>] 83.9	\[ \frac{\left(\beta + 1\right) \cdot \color{blue}{\left(1 + \alpha\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
   times-frac [=>] 96.2	\[ \color{blue}{\frac{\beta + 1}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \cdot \frac{1 + \alpha}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}} \]

3. Applied egg-rr 99.8%

   \[\leadsto \color{blue}{\frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\left(\alpha + 3\right) + \beta}}{\left(\alpha + 2\right) + \beta}}{\left(\alpha + 2\right) + \beta}} \]
   Step-by-step derivation

   [Start] 96.2	\[ \frac{\beta + 1}{\alpha + \left(\beta + 3\right)} \cdot \frac{\alpha + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)} \]
   associate-*r/ [=>] 96.2	\[ \color{blue}{\frac{\frac{\beta + 1}{\alpha + \left(\beta + 3\right)} \cdot \left(\alpha + 1\right)}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}} \]
   associate-/r* [=>] 99.8	\[ \color{blue}{\frac{\frac{\frac{\beta + 1}{\alpha + \left(\beta + 3\right)} \cdot \left(\alpha + 1\right)}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}} \]
   *-commutative [=>] 99.8	\[ \frac{\frac{\color{blue}{\left(\alpha + 1\right) \cdot \frac{\beta + 1}{\alpha + \left(\beta + 3\right)}}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{\color{blue}{1 + \beta}}{\alpha + \left(\beta + 3\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\alpha + \color{blue}{\left(3 + \beta\right)}}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)} \]
   associate-+r+ [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\color{blue}{\left(\alpha + 3\right) + \beta}}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\left(\alpha + 3\right) + \beta}}{\alpha + \color{blue}{\left(2 + \beta\right)}}}{\alpha + \left(\beta + 2\right)} \]
   associate-+r+ [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\left(\alpha + 3\right) + \beta}}{\color{blue}{\left(\alpha + 2\right) + \beta}}}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\left(\alpha + 3\right) + \beta}}{\left(\alpha + 2\right) + \beta}}{\alpha + \color{blue}{\left(2 + \beta\right)}} \]
   associate-+r+ [=>] 99.8	\[ \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\left(\alpha + 3\right) + \beta}}{\left(\alpha + 2\right) + \beta}}{\color{blue}{\left(\alpha + 2\right) + \beta}} \]

4. Final simplification 99.8%

   \[\leadsto \frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\beta + \left(\alpha + 3\right)}}{\beta + \left(\alpha + 2\right)}}{\beta + \left(\alpha + 2\right)} \]

Alternatives

Alternative 1
Accuracy	93.4%
Cost	1732

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ t_1 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 10^{+97}:\\ \;\;\;\;\left(\alpha + 1\right) \cdot \frac{\frac{1 + \beta}{t_1}}{\left(\alpha + \left(\beta + 3\right)\right) \cdot t_1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\alpha + 1\right) \cdot \left(1 - \frac{\alpha}{\beta}\right)}{t_0}}{t_0}\\ \end{array} \]

Alternative 2
Accuracy	97.2%
Cost	1732

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ t_1 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 2 \cdot 10^{+108}:\\ \;\;\;\;\frac{1 + \beta}{\alpha + \left(\beta + 3\right)} \cdot \frac{\alpha + 1}{t_0 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\alpha + 1\right) \cdot \left(1 - \frac{\alpha}{\beta}\right)}{t_1}}{t_1}\\ \end{array} \]

Alternative 3
Accuracy	74.3%
Cost	1604

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 455000000:\\ \;\;\;\;\frac{\frac{1 + \beta}{6 + \beta \cdot \left(\beta + 5\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\alpha + 1\right) \cdot \left(1 - \frac{\alpha + 2}{\beta}\right)}{t_0}}{t_0}\\ \end{array} \]

Alternative 4
Accuracy	99.8%
Cost	1600

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \frac{\frac{1 + \beta}{t_0}}{\alpha + \left(\beta + 3\right)} \cdot \frac{\alpha + 1}{t_0} \end{array} \]

Alternative 5
Accuracy	74.3%
Cost	1476

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 1.7 \cdot 10^{+27}:\\ \;\;\;\;\frac{\frac{1 + \beta}{6 + \beta \cdot \left(\beta + 5\right)}}{\beta + \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 - \frac{\alpha}{\beta}}{t_0} \cdot \frac{\alpha + 1}{t_0}\\ \end{array} \]

Alternative 6
Accuracy	74.3%
Cost	1476

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 2 \cdot 10^{+21}:\\ \;\;\;\;\frac{\frac{1 + \beta}{6 + \beta \cdot \left(\beta + 5\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(\alpha + 1\right) \cdot \left(1 - \frac{\alpha}{\beta}\right)}{t_0}}{t_0}\\ \end{array} \]

Alternative 7
Accuracy	74.6%
Cost	1220

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 5.2 \cdot 10^{+25}:\\ \;\;\;\;\frac{1 + \beta}{\left(\beta + 3\right) \cdot \left(t_0 \cdot \left(\beta + 2\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{t_0}}{t_0}\\ \end{array} \]

Alternative 8
Accuracy	74.5%
Cost	1220

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 5.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{\frac{1 + \beta}{6 + \beta \cdot \left(\beta + 5\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{t_0}}{t_0}\\ \end{array} \]

Alternative 9
Accuracy	73.5%
Cost	1092

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 2.4:\\ \;\;\;\;\frac{0.16666666666666666 + \beta \cdot 0.027777777777777776}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{t_0}}{t_0}\\ \end{array} \]

Alternative 10
Accuracy	73.5%
Cost	1092

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 3.2:\\ \;\;\;\;\frac{\frac{1 + \beta}{6 + \beta \cdot 5}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{t_0}}{t_0}\\ \end{array} \]

Alternative 11
Accuracy	73.3%
Cost	964

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.3:\\ \;\;\;\;\frac{0.16666666666666666 + \beta \cdot 0.027777777777777776}{\beta + \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 12
Accuracy	73.2%
Cost	836

\[\begin{array}{l} \mathbf{if}\;\beta \leq 4.8:\\ \;\;\;\;\frac{0.16666666666666666 + \beta \cdot 0.027777777777777776}{\beta + \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{\beta}\\ \end{array} \]

Alternative 13
Accuracy	73.3%
Cost	836

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\beta \leq 4:\\ \;\;\;\;\frac{0.16666666666666666 + \beta \cdot 0.027777777777777776}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{t_0}\\ \end{array} \]

Alternative 14
Accuracy	71.5%
Cost	712

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.7:\\ \;\;\;\;\frac{0.16666666666666666}{\alpha + 2}\\ \mathbf{elif}\;\beta \leq 2 \cdot 10^{+159}:\\ \;\;\;\;\frac{1}{\beta} \cdot \frac{1}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 15
Accuracy	71.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.6:\\ \;\;\;\;\frac{0.16666666666666666}{\alpha + 2}\\ \mathbf{elif}\;\beta \leq 2.1 \cdot 10^{+161}:\\ \;\;\;\;\frac{1}{\beta} \cdot \frac{1}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha}{\beta} \cdot \frac{1}{\beta}\\ \end{array} \]

Alternative 16
Accuracy	71.4%
Cost	712

\[\begin{array}{l} \mathbf{if}\;\beta \leq 8.5:\\ \;\;\;\;\frac{0.16666666666666666}{\beta + \left(\alpha + 2\right)}\\ \mathbf{elif}\;\beta \leq 8.2 \cdot 10^{+160}:\\ \;\;\;\;\frac{1}{\beta} \cdot \frac{1}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha}{\beta} \cdot \frac{1}{\beta}\\ \end{array} \]

Alternative 17
Accuracy	72.7%
Cost	712

\[\begin{array}{l} \mathbf{if}\;\beta \leq 9.5:\\ \;\;\;\;\frac{0.16666666666666666}{\beta + \left(\alpha + 2\right)}\\ \mathbf{elif}\;\beta \leq 1.4 \cdot 10^{+154}:\\ \;\;\;\;\frac{\alpha + 1}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha}{\beta} \cdot \frac{1}{\beta}\\ \end{array} \]

Alternative 18
Accuracy	71.4%
Cost	584

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.6:\\ \;\;\;\;\frac{0.16666666666666666}{\alpha + 2}\\ \mathbf{elif}\;\beta \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 19
Accuracy	72.9%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\beta \leq 9:\\ \;\;\;\;\frac{0.16666666666666666}{\beta + \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{\beta}\\ \end{array} \]

Alternative 20
Accuracy	62.4%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 2.6:\\ \;\;\;\;\frac{0.16666666666666666}{\alpha + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\beta \cdot \beta}\\ \end{array} \]

Alternative 21
Accuracy	70.8%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 4.5:\\ \;\;\;\;\frac{0.16666666666666666}{\alpha + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\beta \cdot \beta}\\ \end{array} \]

Alternative 22
Accuracy	47.1%
Cost	320

\[\frac{0.16666666666666666}{\alpha + 2} \]

Alternative 23
Accuracy	3.6%
Cost	192

\[\frac{-1}{\beta} \]

Reproduce

herbie shell --seed 2023161 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))