Octave 3.8, jcobi/3

Percentage Accurate: 94.0% → 99.8%

Time: 18.4s

Precision: binary64

Cost: 1600

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

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

Math

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

↓

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

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 (+ alpha (+ beta 2.0))))
   (/ (/ (* (+ beta 1.0) (/ (+ 1.0 alpha) t_0)) t_0) (+ alpha (+ beta 3.0)))))

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 = alpha + (beta + 2.0);
	return (((beta + 1.0) * ((1.0 + alpha) / t_0)) / t_0) / (alpha + (beta + 3.0));
}

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 = alpha + (beta + 2.0d0)
    code = (((beta + 1.0d0) * ((1.0d0 + alpha) / t_0)) / t_0) / (alpha + (beta + 3.0d0))
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 = alpha + (beta + 2.0);
	return (((beta + 1.0) * ((1.0 + alpha) / t_0)) / t_0) / (alpha + (beta + 3.0));
}

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 = alpha + (beta + 2.0)
	return (((beta + 1.0) * ((1.0 + alpha) / t_0)) / t_0) / (alpha + (beta + 3.0))

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(alpha + Float64(beta + 2.0))
	return Float64(Float64(Float64(Float64(beta + 1.0) * Float64(Float64(1.0 + alpha) / t_0)) / t_0) / Float64(alpha + Float64(beta + 3.0)))
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 = alpha + (beta + 2.0);
	tmp = (((beta + 1.0) * ((1.0 + alpha) / t_0)) / t_0) / (alpha + (beta + 3.0));
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[(alpha + N[(beta + 2.0), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(N[(beta + 1.0), $MachinePrecision] * N[(N[(1.0 + alpha), $MachinePrecision] / t$95$0), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision] / N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 93.7%

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

2. Simplified 91.3%

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

   [Start] 93.7%	\[ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
   associate-/l/ [=>] 91.5%	\[ \color{blue}{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}} \]
   associate-+l+ [=>] 91.5%	\[ \frac{\frac{\color{blue}{\left(\alpha + \left(\beta + \beta \cdot \alpha\right)\right)} + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   +-commutative [=>] 91.5%	\[ \frac{\frac{\left(\alpha + \color{blue}{\left(\beta \cdot \alpha + \beta\right)}\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   associate-+r+ [=>] 91.5%	\[ \frac{\frac{\color{blue}{\left(\left(\alpha + \beta \cdot \alpha\right) + \beta\right)} + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   associate-+l+ [=>] 91.5%	\[ \frac{\frac{\color{blue}{\left(\alpha + \beta \cdot \alpha\right) + \left(\beta + 1\right)}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   distribute-rgt1-in [=>] 91.5%	\[ \frac{\frac{\color{blue}{\left(\beta + 1\right) \cdot \alpha} + \left(\beta + 1\right)}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   *-rgt-identity [<=] 91.5%	\[ \frac{\frac{\left(\beta + 1\right) \cdot \alpha + \color{blue}{\left(\beta + 1\right) \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   distribute-lft-out [=>] 91.5%	\[ \frac{\frac{\color{blue}{\left(\beta + 1\right) \cdot \left(\alpha + 1\right)}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   +-commutative [=>] 91.5%	\[ \frac{\frac{\left(\beta + 1\right) \cdot \color{blue}{\left(1 + \alpha\right)}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   associate-*l/ [<=] 94.6%	\[ \frac{\color{blue}{\frac{\beta + 1}{\left(\alpha + \beta\right) + 2 \cdot 1} \cdot \left(1 + \alpha\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   *-commutative [=>] 94.6%	\[ \frac{\color{blue}{\left(1 + \alpha\right) \cdot \frac{\beta + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)} \]
   associate-*r/ [<=] 91.3%	\[ \color{blue}{\left(1 + \alpha\right) \cdot \frac{\frac{\beta + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}} \]

3. Applied egg-rr 94.6%

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

   [Start] 91.3%	\[ \left(\alpha + 1\right) \cdot \frac{\frac{\beta + 1}{\alpha + \left(\beta + 2\right)}}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 3\right)\right)} \]
   associate-*r/ [=>] 94.6%	\[ \color{blue}{\frac{\left(\alpha + 1\right) \cdot \frac{\beta + 1}{\alpha + \left(\beta + 2\right)}}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 3\right)\right)}} \]
   +-commutative [=>] 94.6%	\[ \frac{\left(\alpha + 1\right) \cdot \frac{\color{blue}{1 + \beta}}{\alpha + \left(\beta + 2\right)}}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 3\right)\right)} \]

4. Simplified 99.8%

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

   [Start] 94.6%	\[ \frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\alpha + \left(\beta + 2\right)}}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 3\right)\right)} \]
   associate-/r* [=>] 99.8%	\[ \color{blue}{\frac{\frac{\left(\alpha + 1\right) \cdot \frac{1 + \beta}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)}} \]
   associate-*r/ [=>] 93.7%	\[ \frac{\frac{\color{blue}{\frac{\left(\alpha + 1\right) \cdot \left(1 + \beta\right)}{\alpha + \left(\beta + 2\right)}}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [=>] 93.7%	\[ \frac{\frac{\frac{\color{blue}{\left(1 + \alpha\right)} \cdot \left(1 + \beta\right)}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [<=] 93.7%	\[ \frac{\frac{\frac{\left(1 + \alpha\right) \cdot \color{blue}{\left(\beta + 1\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   *-commutative [=>] 93.7%	\[ \frac{\frac{\frac{\color{blue}{\left(\beta + 1\right) \cdot \left(1 + \alpha\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [=>] 93.7%	\[ \frac{\frac{\frac{\color{blue}{\left(1 + \beta\right)} \cdot \left(1 + \alpha\right)}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [<=] 93.7%	\[ \frac{\frac{\frac{\left(1 + \beta\right) \cdot \color{blue}{\left(\alpha + 1\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   associate-*r/ [<=] 99.8%	\[ \frac{\frac{\color{blue}{\left(1 + \beta\right) \cdot \frac{\alpha + 1}{\alpha + \left(\beta + 2\right)}}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [<=] 99.8%	\[ \frac{\frac{\color{blue}{\left(\beta + 1\right)} \cdot \frac{\alpha + 1}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [=>] 99.8%	\[ \frac{\frac{\left(\beta + 1\right) \cdot \frac{\color{blue}{1 + \alpha}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [=>] 99.8%	\[ \frac{\frac{\left(\beta + 1\right) \cdot \frac{1 + \alpha}{\color{blue}{\left(\beta + 2\right) + \alpha}}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [=>] 99.8%	\[ \frac{\frac{\left(\beta + 1\right) \cdot \frac{1 + \alpha}{\left(\beta + 2\right) + \alpha}}{\color{blue}{\left(\beta + 2\right) + \alpha}}}{\alpha + \left(\beta + 3\right)} \]
   +-commutative [=>] 99.8%	\[ \frac{\frac{\left(\beta + 1\right) \cdot \frac{1 + \alpha}{\left(\beta + 2\right) + \alpha}}{\left(\beta + 2\right) + \alpha}}{\color{blue}{\left(\beta + 3\right) + \alpha}} \]

5. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	99.8%
Cost	1600

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

Alternative 2
Accuracy	91.5%
Cost	1732

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ t_1 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 2.8 \cdot 10^{+39}:\\ \;\;\;\;\left(1 + \alpha\right) \cdot \frac{\frac{\beta + 1}{t_1}}{t_1 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(1 + \alpha\right) \cdot \left(1 + \frac{-1 - \alpha}{\beta}\right)}{t_0}}{2 + \left(\beta + \alpha\right)}\\ \end{array} \]

Alternative 3
Accuracy	94.9%
Cost	1732

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ t_1 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 10^{+39}:\\ \;\;\;\;\left(\beta + 1\right) \cdot \frac{\frac{1 + \alpha}{t_1}}{t_1 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(1 + \alpha\right) \cdot \left(1 + \frac{-1 - \alpha}{\beta}\right)}{t_0}}{2 + \left(\beta + \alpha\right)}\\ \end{array} \]

Alternative 4
Accuracy	72.6%
Cost	1604

\[\begin{array}{l} \mathbf{if}\;\beta \leq 13500000000:\\ \;\;\;\;\frac{\beta + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\left(\beta + 2\right) \cdot \left(\beta + 3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\left(1 + \alpha\right) \cdot \left(1 + \frac{-1 - \alpha}{\beta}\right)}{\alpha + \left(\beta + 3\right)}}{2 + \left(\beta + \alpha\right)}\\ \end{array} \]

Alternative 5
Accuracy	99.8%
Cost	1600

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

Alternative 6
Accuracy	72.7%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;\beta \leq 2.8 \cdot 10^{+17}:\\ \;\;\;\;\frac{\beta + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\left(\beta + 2\right) \cdot \left(\beta + 3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 3\right)}}{2 + \left(\beta + \alpha\right)}\\ \end{array} \]

Alternative 7
Accuracy	92.2%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;\beta \leq 2.8:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + 2}}{\left(\alpha + 3\right) \cdot \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 8
Accuracy	92.4%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;\beta \leq 1.75:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + 2}}{\left(\alpha + 3\right) \cdot \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha + \left(\beta + 3\right)}}{2 + \left(\beta + \alpha\right)}\\ \end{array} \]

Alternative 9
Accuracy	72.1%
Cost	836

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ \mathbf{if}\;\beta \leq 4.5:\\ \;\;\;\;\frac{0.25}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{t_0}\\ \end{array} \]

Alternative 10
Accuracy	70.2%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\beta \leq 6.5:\\ \;\;\;\;\frac{0.25}{\alpha + \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \end{array} \]

Alternative 11
Accuracy	71.4%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\beta \leq 8:\\ \;\;\;\;\frac{0.25}{\alpha + \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{1 + \alpha}{\beta \cdot \beta}\\ \end{array} \]

Alternative 12
Accuracy	61.3%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 2.8:\\ \;\;\;\;\frac{0.25}{\alpha + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{\beta \cdot \beta}\\ \end{array} \]

Alternative 13
Accuracy	69.7%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.7:\\ \;\;\;\;\frac{0.25}{\alpha + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\beta \cdot \beta}\\ \end{array} \]

Alternative 14
Accuracy	69.8%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.7:\\ \;\;\;\;\frac{0.25}{\alpha + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \end{array} \]

Alternative 15
Accuracy	46.0%
Cost	320

\[\frac{0.25}{\alpha + 3} \]

Alternative 16
Accuracy	4.3%
Cost	192

\[\frac{0.2}{\beta} \]

Reproduce

herbie shell --seed 2023167 
(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)))