Octave 3.8, jcobi/3

Average Accuracy: 94.2% → 99.6%

Time: 24.6s

Precision: binary64

Cost: 7812

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

\[ \begin{array}{c}[alpha, beta] = \mathsf{sort}([alpha, beta])\\ \end{array} \]

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\beta \leq 5 \cdot 10^{+148}:\\ \;\;\;\;\frac{\left(\alpha + 1\right) \cdot {\left(\beta + \left(\alpha + 2\right)\right)}^{-2}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \beta}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

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
 (if (<= beta 5e+148)
   (/
    (* (+ alpha 1.0) (pow (+ beta (+ alpha 2.0)) -2.0))
    (/ (+ beta (+ alpha 3.0)) (+ 1.0 beta)))
   (/ (/ (+ alpha 1.0) beta) (+ 1.0 (+ 2.0 (+ alpha beta))))))

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 tmp;
	if (beta <= 5e+148) {
		tmp = ((alpha + 1.0) * pow((beta + (alpha + 2.0)), -2.0)) / ((beta + (alpha + 3.0)) / (1.0 + beta));
	} else {
		tmp = ((alpha + 1.0) / beta) / (1.0 + (2.0 + (alpha + beta)));
	}
	return tmp;
}

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) :: tmp
    if (beta <= 5d+148) then
        tmp = ((alpha + 1.0d0) * ((beta + (alpha + 2.0d0)) ** (-2.0d0))) / ((beta + (alpha + 3.0d0)) / (1.0d0 + beta))
    else
        tmp = ((alpha + 1.0d0) / beta) / (1.0d0 + (2.0d0 + (alpha + beta)))
    end if
    code = tmp
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 tmp;
	if (beta <= 5e+148) {
		tmp = ((alpha + 1.0) * Math.pow((beta + (alpha + 2.0)), -2.0)) / ((beta + (alpha + 3.0)) / (1.0 + beta));
	} else {
		tmp = ((alpha + 1.0) / beta) / (1.0 + (2.0 + (alpha + beta)));
	}
	return tmp;
}

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):
	tmp = 0
	if beta <= 5e+148:
		tmp = ((alpha + 1.0) * math.pow((beta + (alpha + 2.0)), -2.0)) / ((beta + (alpha + 3.0)) / (1.0 + beta))
	else:
		tmp = ((alpha + 1.0) / beta) / (1.0 + (2.0 + (alpha + beta)))
	return tmp

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)
	tmp = 0.0
	if (beta <= 5e+148)
		tmp = Float64(Float64(Float64(alpha + 1.0) * (Float64(beta + Float64(alpha + 2.0)) ^ -2.0)) / Float64(Float64(beta + Float64(alpha + 3.0)) / Float64(1.0 + beta)));
	else
		tmp = Float64(Float64(Float64(alpha + 1.0) / beta) / Float64(1.0 + Float64(2.0 + Float64(alpha + beta))));
	end
	return tmp
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_2 = code(alpha, beta)
	tmp = 0.0;
	if (beta <= 5e+148)
		tmp = ((alpha + 1.0) * ((beta + (alpha + 2.0)) ^ -2.0)) / ((beta + (alpha + 3.0)) / (1.0 + beta));
	else
		tmp = ((alpha + 1.0) / beta) / (1.0 + (2.0 + (alpha + beta)));
	end
	tmp_2 = tmp;
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_] := If[LessEqual[beta, 5e+148], N[(N[(N[(alpha + 1.0), $MachinePrecision] * N[Power[N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision] / N[(N[(beta + N[(alpha + 3.0), $MachinePrecision]), $MachinePrecision] / N[(1.0 + beta), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(alpha + 1.0), $MachinePrecision] / beta), $MachinePrecision] / N[(1.0 + N[(2.0 + N[(alpha + beta), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if beta < 5.00000000000000024e148

   1. Initial program 99.8%

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

   2. Simplified 99.8%

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

      [Start] 99.8	\[ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
      associate-/l/ [=>] 99.7	\[ \frac{\color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
      associate-/l/ [=>] 89.5	\[ \color{blue}{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)}} \]
      associate-+l+ [=>] 89.5	\[ \frac{\color{blue}{\left(\alpha + \left(\beta + \beta \cdot \alpha\right)\right)} + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      +-commutative [=>] 89.5	\[ \frac{\left(\alpha + \color{blue}{\left(\beta \cdot \alpha + \beta\right)}\right) + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      associate-+r+ [=>] 89.5	\[ \frac{\color{blue}{\left(\left(\alpha + \beta \cdot \alpha\right) + \beta\right)} + 1}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      associate-+l+ [=>] 89.5	\[ \frac{\color{blue}{\left(\alpha + \beta \cdot \alpha\right) + \left(\beta + 1\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      distribute-rgt1-in [=>] 89.5	\[ \frac{\color{blue}{\left(\beta + 1\right) \cdot \alpha} + \left(\beta + 1\right)}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      *-rgt-identity [<=] 89.5	\[ \frac{\left(\beta + 1\right) \cdot \alpha + \color{blue}{\left(\beta + 1\right) \cdot 1}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      distribute-lft-out [=>] 89.5	\[ \frac{\color{blue}{\left(\beta + 1\right) \cdot \left(\alpha + 1\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      +-commutative [=>] 89.5	\[ \frac{\left(\beta + 1\right) \cdot \color{blue}{\left(1 + \alpha\right)}}{\left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1\right) \cdot \left(\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)\right)} \]
      times-frac [=>] 99.8	\[ \color{blue}{\frac{\beta + 1}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \cdot \frac{1 + \alpha}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot 1\right)}} \]

   3. Applied egg-rr 99.9%

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

      [Start] 99.8	\[ \frac{\beta + 1}{\alpha + \left(\beta + 3\right)} \cdot \frac{\alpha + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)} \]
      *-commutative [=>] 99.8	\[ \color{blue}{\frac{\alpha + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)} \cdot \frac{\beta + 1}{\alpha + \left(\beta + 3\right)}} \]
      clear-num [=>] 99.7	\[ \frac{\alpha + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)} \cdot \color{blue}{\frac{1}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}}} \]
      un-div-inv [=>] 99.8	\[ \color{blue}{\frac{\frac{\alpha + 1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}}} \]
      div-inv [=>] 99.7	\[ \frac{\color{blue}{\left(\alpha + 1\right) \cdot \frac{1}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}} \]
      pow2 [=>] 99.7	\[ \frac{\left(\alpha + 1\right) \cdot \frac{1}{\color{blue}{{\left(\alpha + \left(\beta + 2\right)\right)}^{2}}}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}} \]
      pow-flip [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot \color{blue}{{\left(\alpha + \left(\beta + 2\right)\right)}^{\left(-2\right)}}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}} \]
      +-commutative [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot {\left(\alpha + \color{blue}{\left(2 + \beta\right)}\right)}^{\left(-2\right)}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}} \]
      associate-+r+ [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot {\color{blue}{\left(\left(\alpha + 2\right) + \beta\right)}}^{\left(-2\right)}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}} \]
      metadata-eval [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot {\left(\left(\alpha + 2\right) + \beta\right)}^{\color{blue}{-2}}}{\frac{\alpha + \left(\beta + 3\right)}{\beta + 1}} \]
      +-commutative [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot {\left(\left(\alpha + 2\right) + \beta\right)}^{-2}}{\frac{\alpha + \color{blue}{\left(3 + \beta\right)}}{\beta + 1}} \]
      associate-+r+ [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot {\left(\left(\alpha + 2\right) + \beta\right)}^{-2}}{\frac{\color{blue}{\left(\alpha + 3\right) + \beta}}{\beta + 1}} \]
      +-commutative [=>] 99.9	\[ \frac{\left(\alpha + 1\right) \cdot {\left(\left(\alpha + 2\right) + \beta\right)}^{-2}}{\frac{\left(\alpha + 3\right) + \beta}{\color{blue}{1 + \beta}}} \]

   if 5.00000000000000024e148 < beta

   1. Initial program 81.9%

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

   2. Taylor expanded in beta around inf 99.1%

      \[\leadsto \frac{\color{blue}{\frac{1 + \alpha}{\beta}}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\beta \leq 5 \cdot 10^{+148}:\\ \;\;\;\;\frac{\left(\alpha + 1\right) \cdot {\left(\beta + \left(\alpha + 2\right)\right)}^{-2}}{\frac{\beta + \left(\alpha + 3\right)}{1 + \beta}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternatives

Alternative 1
Accuracy	99.7%
Cost	14080

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

Alternative 2
Accuracy	99.5%
Cost	1860

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 2 \cdot 10^{+146}:\\ \;\;\;\;\frac{\frac{\left(\alpha + \beta\right) + \left(1 + \alpha \cdot \beta\right)}{t_0}}{t_0 \cdot \left(3 + \left(\alpha + \beta\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 3
Accuracy	99.3%
Cost	1732

\[\begin{array}{l} \mathbf{if}\;\beta \leq 7.1 \cdot 10^{+16}:\\ \;\;\;\;\left(1 + \beta\right) \cdot \frac{-1 - \alpha}{\left(\alpha + \left(\beta + 2\right)\right) \cdot \left(\left(\beta + \left(\alpha + 3\right)\right) \cdot \left(-2 - \left(\alpha + \beta\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 4
Accuracy	99.4%
Cost	1732

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 7.2 \cdot 10^{+105}:\\ \;\;\;\;\left(1 + \beta\right) \cdot \frac{\frac{\alpha + 1}{t_0}}{t_0 \cdot \left(\alpha + \left(\beta + 3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 5
Accuracy	99.5%
Cost	1732

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 2\right)\\ \mathbf{if}\;\beta \leq 10^{+148}:\\ \;\;\;\;\frac{1 + \beta}{\alpha + \left(\beta + 3\right)} \cdot \frac{\alpha + 1}{t_0 \cdot t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 6
Accuracy	98.2%
Cost	1220

\[\begin{array}{l} \mathbf{if}\;\beta \leq 50000000000000:\\ \;\;\;\;\left(1 + \beta\right) \cdot \frac{\frac{1}{\beta + 2}}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 7
Accuracy	98.3%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;\beta \leq 6 \cdot 10^{+15}:\\ \;\;\;\;\frac{\frac{1 + \beta}{\beta + 2}}{\left(\beta + 2\right) \cdot \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 8
Accuracy	96.4%
Cost	964

\[\begin{array}{l} \mathbf{if}\;\beta \leq 5.2:\\ \;\;\;\;\frac{0.5}{\left(\alpha + 3\right) \cdot \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{1 + \left(2 + \left(\alpha + \beta\right)\right)}\\ \end{array} \]

Alternative 9
Accuracy	96.3%
Cost	708

\[\begin{array}{l} \mathbf{if}\;\beta \leq 24:\\ \;\;\;\;\frac{0.5}{\left(\alpha + 3\right) \cdot \left(\alpha + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\alpha + 1}{\beta} \cdot \frac{1}{\beta}\\ \end{array} \]

Alternative 10
Accuracy	54.0%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\beta \leq 1.45 \cdot 10^{+154}:\\ \;\;\;\;\frac{\alpha + 1}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 11
Accuracy	54.3%
Cost	576

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

Alternative 12
Accuracy	53.8%
Cost	452

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

Alternative 13
Accuracy	48.9%
Cost	320

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

Alternative 14
Accuracy	49.3%
Cost	320

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

Alternative 15
Accuracy	29.9%
Cost	64

\[0 \]

Reproduce

herbie shell --seed 2023152 
(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)))