Octave 3.8, jcobi/3

Average Error: 6.04% → 0.37%

Time: 22.4s

Precision: binary64

Cost: 1732

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

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

Math

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

↓

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ \mathbf{if}\;\beta \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;\frac{\alpha + 1}{\frac{-2 - \left(\alpha + \beta\right)}{-1 - \beta} \cdot \left(t_0 \cdot \left(\beta + \left(\alpha + 2\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\left(\beta + 3\right) + \alpha \cdot 2}}{t_0}\\ \end{array} \]

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 (+ alpha (+ beta 3.0))))
   (if (<= beta 9.6e+61)
     (/
      (+ alpha 1.0)
      (*
       (/ (- -2.0 (+ alpha beta)) (- -1.0 beta))
       (* t_0 (+ beta (+ alpha 2.0)))))
     (/ (/ (+ alpha 1.0) (+ (+ beta 3.0) (* alpha 2.0))) 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 = alpha + (beta + 3.0);
	double tmp;
	if (beta <= 9.6e+61) {
		tmp = (alpha + 1.0) / (((-2.0 - (alpha + beta)) / (-1.0 - beta)) * (t_0 * (beta + (alpha + 2.0))));
	} else {
		tmp = ((alpha + 1.0) / ((beta + 3.0) + (alpha * 2.0))) / t_0;
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = alpha + (beta + 3.0d0)
    if (beta <= 9.6d+61) then
        tmp = (alpha + 1.0d0) / ((((-2.0d0) - (alpha + beta)) / ((-1.0d0) - beta)) * (t_0 * (beta + (alpha + 2.0d0))))
    else
        tmp = ((alpha + 1.0d0) / ((beta + 3.0d0) + (alpha * 2.0d0))) / t_0
    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 t_0 = alpha + (beta + 3.0);
	double tmp;
	if (beta <= 9.6e+61) {
		tmp = (alpha + 1.0) / (((-2.0 - (alpha + beta)) / (-1.0 - beta)) * (t_0 * (beta + (alpha + 2.0))));
	} else {
		tmp = ((alpha + 1.0) / ((beta + 3.0) + (alpha * 2.0))) / t_0;
	}
	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):
	t_0 = alpha + (beta + 3.0)
	tmp = 0
	if beta <= 9.6e+61:
		tmp = (alpha + 1.0) / (((-2.0 - (alpha + beta)) / (-1.0 - beta)) * (t_0 * (beta + (alpha + 2.0))))
	else:
		tmp = ((alpha + 1.0) / ((beta + 3.0) + (alpha * 2.0))) / t_0
	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)
	t_0 = Float64(alpha + Float64(beta + 3.0))
	tmp = 0.0
	if (beta <= 9.6e+61)
		tmp = Float64(Float64(alpha + 1.0) / Float64(Float64(Float64(-2.0 - Float64(alpha + beta)) / Float64(-1.0 - beta)) * Float64(t_0 * Float64(beta + Float64(alpha + 2.0)))));
	else
		tmp = Float64(Float64(Float64(alpha + 1.0) / Float64(Float64(beta + 3.0) + Float64(alpha * 2.0))) / t_0);
	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)
	t_0 = alpha + (beta + 3.0);
	tmp = 0.0;
	if (beta <= 9.6e+61)
		tmp = (alpha + 1.0) / (((-2.0 - (alpha + beta)) / (-1.0 - beta)) * (t_0 * (beta + (alpha + 2.0))));
	else
		tmp = ((alpha + 1.0) / ((beta + 3.0) + (alpha * 2.0))) / t_0;
	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_] := Block[{t$95$0 = N[(alpha + N[(beta + 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[beta, 9.6e+61], N[(N[(alpha + 1.0), $MachinePrecision] / N[(N[(N[(-2.0 - N[(alpha + beta), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - beta), $MachinePrecision]), $MachinePrecision] * N[(t$95$0 * N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(alpha + 1.0), $MachinePrecision] / N[(N[(beta + 3.0), $MachinePrecision] + N[(alpha * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if beta < 9.5999999999999995e61

   1. Initial program 0.18

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

   2. Simplified 0.19

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

      [Start] 0.18	\[ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]

   3. Applied egg-rr 0.19

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

   4. Simplified 0.2

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

      [Start] 0.19	\[ \frac{\frac{1}{2 + \left(\alpha + \beta\right)} \cdot \frac{\alpha + 1}{\frac{-2 - \left(\alpha + \beta\right)}{-1 - \beta}}}{\alpha + \left(\beta + 3\right)} \]
      +-commutative [=>] 0.19	\[ \frac{\frac{1}{2 + \left(\alpha + \beta\right)} \cdot \frac{\color{blue}{1 + \alpha}}{\frac{-2 - \left(\alpha + \beta\right)}{-1 - \beta}}}{\alpha + \left(\beta + 3\right)} \]
      associate-*r/ [=>] 0.2	\[ \frac{\color{blue}{\frac{\frac{1}{2 + \left(\alpha + \beta\right)} \cdot \left(1 + \alpha\right)}{\frac{-2 - \left(\alpha + \beta\right)}{-1 - \beta}}}}{\alpha + \left(\beta + 3\right)} \]
      associate-+r+ [=>] 0.2	\[ \frac{\frac{\frac{1}{\color{blue}{\left(2 + \alpha\right) + \beta}} \cdot \left(1 + \alpha\right)}{\frac{-2 - \left(\alpha + \beta\right)}{-1 - \beta}}}{\alpha + \left(\beta + 3\right)} \]
      +-commutative [=>] 0.2	\[ \frac{\frac{\frac{1}{\left(2 + \alpha\right) + \beta} \cdot \left(1 + \alpha\right)}{\frac{-2 - \color{blue}{\left(\beta + \alpha\right)}}{-1 - \beta}}}{\alpha + \left(\beta + 3\right)} \]

   5. Applied egg-rr 0.18

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

   6. Simplified 0.17

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

      [Start] 0.18	\[ 1 \cdot \frac{1 + \alpha}{\left(\frac{\left(-2 - \beta\right) - \alpha}{-1 - \beta} \cdot \left(\alpha + \left(\beta + 3\right)\right)\right) \cdot \left(\left(\beta + 2\right) + \alpha\right)} \]
      *-lft-identity [=>] 0.18	\[ \color{blue}{\frac{1 + \alpha}{\left(\frac{\left(-2 - \beta\right) - \alpha}{-1 - \beta} \cdot \left(\alpha + \left(\beta + 3\right)\right)\right) \cdot \left(\left(\beta + 2\right) + \alpha\right)}} \]
      associate-*l* [=>] 0.17	\[ \frac{1 + \alpha}{\color{blue}{\frac{\left(-2 - \beta\right) - \alpha}{-1 - \beta} \cdot \left(\left(\alpha + \left(\beta + 3\right)\right) \cdot \left(\left(\beta + 2\right) + \alpha\right)\right)}} \]
      associate--l- [=>] 0.17	\[ \frac{1 + \alpha}{\frac{\color{blue}{-2 - \left(\beta + \alpha\right)}}{-1 - \beta} \cdot \left(\left(\alpha + \left(\beta + 3\right)\right) \cdot \left(\left(\beta + 2\right) + \alpha\right)\right)} \]
      +-commutative [=>] 0.17	\[ \frac{1 + \alpha}{\frac{-2 - \left(\beta + \alpha\right)}{-1 - \beta} \cdot \left(\color{blue}{\left(\left(\beta + 3\right) + \alpha\right)} \cdot \left(\left(\beta + 2\right) + \alpha\right)\right)} \]
      associate-+l+ [=>] 0.17	\[ \frac{1 + \alpha}{\frac{-2 - \left(\beta + \alpha\right)}{-1 - \beta} \cdot \left(\left(\left(\beta + 3\right) + \alpha\right) \cdot \color{blue}{\left(\beta + \left(2 + \alpha\right)\right)}\right)} \]

   if 9.5999999999999995e61 < beta

   1. Initial program 12.72

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

   2. Simplified 0.19

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

      [Start] 12.72	\[ \frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1} \]

   3. Taylor expanded in beta around inf 0.6

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

   4. Simplified 0.6

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

      [Start] 0.6	\[ \frac{\frac{\alpha + 1}{\beta + \left(3 + 2 \cdot \alpha\right)}}{\alpha + \left(\beta + 3\right)} \]
      associate-+r+ [=>] 0.6	\[ \frac{\frac{\alpha + 1}{\color{blue}{\left(\beta + 3\right) + 2 \cdot \alpha}}}{\alpha + \left(\beta + 3\right)} \]

3. Recombined 2 regimes into one program.

4. Final simplification 0.37

   \[\leadsto \begin{array}{l} \mathbf{if}\;\beta \leq 9.6 \cdot 10^{+61}:\\ \;\;\;\;\frac{\alpha + 1}{\frac{-2 - \left(\alpha + \beta\right)}{-1 - \beta} \cdot \left(\left(\alpha + \left(\beta + 3\right)\right) \cdot \left(\beta + \left(\alpha + 2\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\left(\beta + 3\right) + \alpha \cdot 2}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.4%
Cost	1732

\[\begin{array}{l} \mathbf{if}\;\beta \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;\left(\alpha + 1\right) \cdot \frac{-1 - \beta}{\left(-2 - \left(\alpha + \beta\right)\right) \cdot \left(\left(\beta + \left(\alpha + 2\right)\right) \cdot \left(\left(\alpha + \beta\right) + 3\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\left(\beta + 3\right) + \alpha \cdot 2}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 2
Error	0.43%
Cost	1604

\[\begin{array}{l} t_0 := \alpha + \left(2 + \beta\right)\\ t_1 := \alpha + \left(\beta + 3\right)\\ \mathbf{if}\;\beta \leq 10000000000:\\ \;\;\;\;\frac{\beta + \left(\alpha + 1\right)}{t_1 \cdot \left(t_0 \cdot t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\left(\beta + 3\right) + \alpha \cdot 2}}{t_1}\\ \end{array} \]

Alternative 3
Error	0.18%
Cost	1600

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

Alternative 4
Error	0.19%
Cost	1600

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

Alternative 5
Error	1.76%
Cost	1348

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.4:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\alpha + 2}}{\left(\alpha + \left(2 + \beta\right)\right) \cdot \left(\left(\alpha + \beta\right) + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\left(\beta + 3\right) + \alpha \cdot 2}}{\alpha + \left(\beta + 3\right)}\\ \end{array} \]

Alternative 6
Error	2.17%
Cost	1220

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ \mathbf{if}\;\beta \leq 0.45:\\ \;\;\;\;\frac{\frac{0.5}{2 + \beta}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\left(\beta + 3\right) + \alpha \cdot 2}}{t_0}\\ \end{array} \]

Alternative 7
Error	2.96%
Cost	836

\[\begin{array}{l} \mathbf{if}\;\beta \leq 10.5:\\ \;\;\;\;\frac{\frac{0.5}{2 + \beta}}{\alpha + \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{\beta}\\ \end{array} \]

Alternative 8
Error	2.92%
Cost	836

\[\begin{array}{l} t_0 := \alpha + \left(\beta + 3\right)\\ \mathbf{if}\;\beta \leq 4.5:\\ \;\;\;\;\frac{\frac{0.5}{2 + \beta}}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{t_0}\\ \end{array} \]

Alternative 9
Error	36.99%
Cost	712

\[\begin{array}{l} \mathbf{if}\;\beta \leq 5:\\ \;\;\;\;\frac{0.3333333333333333}{\alpha + \left(\beta + 3\right)}\\ \mathbf{elif}\;\beta \leq 1.32 \cdot 10^{+154}:\\ \;\;\;\;\frac{\alpha + 1}{\beta \cdot \beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 10
Error	3.39%
Cost	708

\[\begin{array}{l} \mathbf{if}\;\beta \leq 9.5:\\ \;\;\;\;\frac{0.5}{\left(\beta + 3\right) \cdot \left(2 + \beta\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{\beta}\\ \end{array} \]

Alternative 11
Error	39.51%
Cost	584

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.4:\\ \;\;\;\;\frac{0.3333333333333333}{\alpha + 3}\\ \mathbf{elif}\;\beta \leq 9.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 12
Error	39.51%
Cost	584

\[\begin{array}{l} \mathbf{if}\;\beta \leq 5.2:\\ \;\;\;\;\frac{0.3333333333333333}{\alpha + \left(\beta + 3\right)}\\ \mathbf{elif}\;\beta \leq 9.2 \cdot 10^{+157}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha}{\beta}}{\beta}\\ \end{array} \]

Alternative 13
Error	36.52%
Cost	580

\[\begin{array}{l} \mathbf{if}\;\beta \leq 5:\\ \;\;\;\;\frac{0.3333333333333333}{\alpha + \left(\beta + 3\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\alpha + 1}{\beta}}{\beta}\\ \end{array} \]

Alternative 14
Error	42.6%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.4:\\ \;\;\;\;\frac{0.3333333333333333}{\alpha + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\beta \cdot \beta}\\ \end{array} \]

Alternative 15
Error	42.15%
Cost	452

\[\begin{array}{l} \mathbf{if}\;\beta \leq 3.2:\\ \;\;\;\;\frac{0.3333333333333333}{\alpha + 3}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{1}{\beta}}{\beta}\\ \end{array} \]

Alternative 16
Error	88.43%
Cost	320

\[\frac{0.3333333333333333}{\alpha + 3} \]

Alternative 17
Error	97.47%
Cost	192

\[\frac{0.5}{\alpha} \]

Reproduce

herbie shell --seed 2023089 
(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)))