Octave 3.8, jcobi/3

Average Accuracy: 94.2% → 99.8%

Time: 26.1s

Precision: binary64

Cost: 1600

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

Math

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

↓

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

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

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

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

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

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

Derivation

1. Initial program 94.2%

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

2. Simplified 92.9%

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

   [Start] 94.2	\[ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
   associate-/l/ [=>] 92.8	\[ \frac{\color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
   associate-/r* [<=] 84.7	\[ \color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right)}} \]
   associate-/l/ [<=] 92.9	\[ \color{blue}{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}} \]

3. Applied egg-rr 99.4%

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

   [Start] 92.9	\[ \frac{\frac{\left(\beta + 1\right) \cdot \left(\alpha + 1\right)}{\left(\alpha + \beta\right) + 3}}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)} \]
   associate-/r* [=>] 94.2	\[ \color{blue}{\frac{\frac{\frac{\left(\beta + 1\right) \cdot \left(\alpha + 1\right)}{\left(\alpha + \beta\right) + 3}}{\alpha + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}} \]
   div-inv [=>] 94.1	\[ \color{blue}{\frac{\frac{\left(\beta + 1\right) \cdot \left(\alpha + 1\right)}{\left(\alpha + \beta\right) + 3}}{\alpha + \left(\beta + 2\right)} \cdot \frac{1}{\alpha + \left(\beta + 2\right)}} \]
   associate-/l* [=>] 99.7	\[ \frac{\color{blue}{\frac{\beta + 1}{\frac{\left(\alpha + \beta\right) + 3}{\alpha + 1}}}}{\alpha + \left(\beta + 2\right)} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   associate-/l/ [=>] 99.4	\[ \color{blue}{\frac{\beta + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \frac{\left(\alpha + \beta\right) + 3}{\alpha + 1}}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   associate-+r+ [=>] 99.4	\[ \frac{\beta + 1}{\color{blue}{\left(\left(\alpha + \beta\right) + 2\right)} \cdot \frac{\left(\alpha + \beta\right) + 3}{\alpha + 1}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.4	\[ \frac{\beta + 1}{\left(\color{blue}{\left(\beta + \alpha\right)} + 2\right) \cdot \frac{\left(\alpha + \beta\right) + 3}{\alpha + 1}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   associate-+l+ [=>] 99.4	\[ \frac{\beta + 1}{\color{blue}{\left(\beta + \left(\alpha + 2\right)\right)} \cdot \frac{\left(\alpha + \beta\right) + 3}{\alpha + 1}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\color{blue}{\left(\beta + \alpha\right)} + 3}{\alpha + 1}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   associate-+l+ [=>] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\color{blue}{\beta + \left(\alpha + 3\right)}}{\alpha + 1}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   +-commutative [=>] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\beta + \left(\alpha + 3\right)}{\color{blue}{1 + \alpha}}} \cdot \frac{1}{\alpha + \left(\beta + 2\right)} \]
   associate-+r+ [=>] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \cdot \frac{1}{\color{blue}{\left(\alpha + \beta\right) + 2}} \]
   +-commutative [=>] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \cdot \frac{1}{\color{blue}{\left(\beta + \alpha\right)} + 2} \]
   associate-+l+ [=>] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \cdot \frac{1}{\color{blue}{\beta + \left(\alpha + 2\right)}} \]

4. Applied egg-rr 99.8%

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

   [Start] 99.4	\[ \frac{\beta + 1}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \cdot \frac{1}{\beta + \left(\alpha + 2\right)} \]
   associate-*l/ [=>] 99.5	\[ \color{blue}{\frac{\left(\beta + 1\right) \cdot \frac{1}{\beta + \left(\alpha + 2\right)}}{\left(\beta + \left(\alpha + 2\right)\right) \cdot \frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}}} \]
   associate-/r* [=>] 99.8	\[ \color{blue}{\frac{\frac{\left(\beta + 1\right) \cdot \frac{1}{\beta + \left(\alpha + 2\right)}}{\beta + \left(\alpha + 2\right)}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}}} \]
   div-inv [<=] 99.8	\[ \frac{\frac{\color{blue}{\frac{\beta + 1}{\beta + \left(\alpha + 2\right)}}}{\beta + \left(\alpha + 2\right)}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \]
   associate-+r+ [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{\color{blue}{\left(\beta + \alpha\right) + 2}}}{\beta + \left(\alpha + 2\right)}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{\color{blue}{2 + \left(\beta + \alpha\right)}}}{\beta + \left(\alpha + 2\right)}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \]
   associate-+r+ [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{2 + \left(\beta + \alpha\right)}}{\color{blue}{\left(\beta + \alpha\right) + 2}}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{2 + \left(\beta + \alpha\right)}}{\color{blue}{2 + \left(\beta + \alpha\right)}}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \alpha}} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{2 + \left(\beta + \alpha\right)}}{2 + \left(\beta + \alpha\right)}}{\frac{\color{blue}{\left(\alpha + 3\right) + \beta}}{1 + \alpha}} \]
   associate-+l+ [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{2 + \left(\beta + \alpha\right)}}{2 + \left(\beta + \alpha\right)}}{\frac{\color{blue}{\alpha + \left(3 + \beta\right)}}{1 + \alpha}} \]
   +-commutative [=>] 99.8	\[ \frac{\frac{\frac{\beta + 1}{2 + \left(\beta + \alpha\right)}}{2 + \left(\beta + \alpha\right)}}{\frac{\alpha + \color{blue}{\left(\beta + 3\right)}}{1 + \alpha}} \]

5. Final simplification 99.8%

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

Alternatives

Alternative 1
Accuracy	96.3%
Cost	1732

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 3.6 \cdot 10^{+142}:\\ \;\;\;\;\frac{\frac{\left(\beta + 1\right) \cdot \left(1 + \alpha\right)}{\left(\beta + \alpha\right) + 3}}{t_0 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\left(\beta + 3\right) + 2 \cdot \alpha}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 2
Accuracy	99.5%
Cost	1600

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

Alternative 3
Accuracy	93.7%
Cost	1476

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ \mathbf{if}\;\beta \leq 1.4:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\alpha \cdot \left(2 + \alpha\right) + 2 \cdot \left(2 + \alpha\right)}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\left(\beta + 3\right) + 2 \cdot \alpha}}{t_0}\\ \end{array} \]

Alternative 4
Accuracy	93.3%
Cost	1348

\[\begin{array}{l} \mathbf{if}\;\beta \leq 7:\\ \;\;\;\;\frac{1 + \alpha}{\left(2 + \alpha\right) \cdot \left(\alpha + 3\right)} \cdot \frac{1}{\beta + \left(2 + \alpha\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\left(\beta + 3\right) + 2 \cdot \alpha}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 5
Accuracy	93.3%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;\beta \leq 0.98:\\ \;\;\;\;\frac{\frac{1 + \alpha}{2 + \alpha}}{\left(2 + \alpha\right) \cdot \left(\alpha + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\left(\beta + 3\right) + 2 \cdot \alpha}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 6
Accuracy	92.8%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;\beta \leq 4.9:\\ \;\;\;\;\frac{\frac{1 + \alpha}{2 + \alpha}}{\left(2 + \alpha\right) \cdot \left(\alpha + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\frac{\alpha + \left(\beta + 3\right)}{1 + \alpha}}\\ \end{array} \]

Alternative 7
Accuracy	82.5%
Cost	964

\[\begin{array}{l} \mathbf{if}\;\beta \leq 4.2:\\ \;\;\;\;\frac{0.5 + \alpha \cdot 0.25}{\left(2 + \alpha\right) \cdot \left(\alpha + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 8
Accuracy	82.5%
Cost	964

\[\begin{array}{l} \mathbf{if}\;\beta \leq 15:\\ \;\;\;\;\frac{0.5 + \alpha \cdot 0.25}{\left(2 + \alpha\right) \cdot \left(\alpha + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\frac{\alpha + \left(\beta + 3\right)}{1 + \alpha}}\\ \end{array} \]

Alternative 9
Accuracy	71.0%
Cost	836

\[\begin{array}{l} \mathbf{if}\;\beta \leq 4.6:\\ \;\;\;\;\frac{0.5}{\left(\beta + 3\right) \cdot \left(\beta + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 10
Accuracy	70.9%
Cost	708

\[\begin{array}{l} \mathbf{if}\;\beta \leq 10.2:\\ \;\;\;\;\frac{0.5}{\left(\beta + 3\right) \cdot \left(\beta + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1 + \alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 11
Accuracy	27.5%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\beta \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 12
Accuracy	27.7%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 13
Accuracy	22.7%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 4.2 \cdot 10^{+98}:\\ \;\;\;\;\frac{1}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\alpha \cdot \alpha}\\ \end{array} \]

Alternative 14
Accuracy	26.6%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{1}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha}{\beta \cdot \beta}\\ \end{array} \]

Alternative 15
Accuracy	26.9%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha}{\beta \cdot \beta}\\ \end{array} \]

Alternative 16
Accuracy	27.5%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 3.9 \cdot 10^{-13}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 17
Accuracy	28.0%
Cost	448

\[\frac{\frac{1 + \alpha}{\beta}}{\beta} \]

Alternative 18
Accuracy	25.9%
Cost	320

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

Alternative 19
Accuracy	4.2%
Cost	192

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

Alternative 20
Accuracy	4.2%
Cost	192

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

Reproduce

herbie shell --seed 2023138 
(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)))