Octave 3.8, jcobi/1

Average Error: 16.3 → 0.1

Time: 8.5s

Precision: binary64

Cost: 8324

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

Math

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

↓

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.99995:\\ \;\;\;\;\frac{\frac{-2 + \beta \cdot -2}{\alpha} \cdot \left(-1 + \frac{\beta + 2}{\alpha}\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-\alpha, \frac{1}{t_0}, 1 + \frac{\beta}{t_0}\right)}{2}\\ \end{array} \]

FPCore

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

↓

(FPCore (alpha beta)
 :precision binary64
 (let* ((t_0 (+ beta (+ alpha 2.0))))
   (if (<= (/ (- beta alpha) (+ (+ beta alpha) 2.0)) -0.99995)
     (/
      (* (/ (+ -2.0 (* beta -2.0)) alpha) (+ -1.0 (/ (+ beta 2.0) alpha)))
      2.0)
     (/ (fma (- alpha) (/ 1.0 t_0) (+ 1.0 (/ beta t_0))) 2.0))))

C

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

↓

double code(double alpha, double beta) {
	double t_0 = beta + (alpha + 2.0);
	double tmp;
	if (((beta - alpha) / ((beta + alpha) + 2.0)) <= -0.99995) {
		tmp = (((-2.0 + (beta * -2.0)) / alpha) * (-1.0 + ((beta + 2.0) / alpha))) / 2.0;
	} else {
		tmp = fma(-alpha, (1.0 / t_0), (1.0 + (beta / t_0))) / 2.0;
	}
	return tmp;
}

Julia

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

↓

function code(alpha, beta)
	t_0 = Float64(beta + Float64(alpha + 2.0))
	tmp = 0.0
	if (Float64(Float64(beta - alpha) / Float64(Float64(beta + alpha) + 2.0)) <= -0.99995)
		tmp = Float64(Float64(Float64(Float64(-2.0 + Float64(beta * -2.0)) / alpha) * Float64(-1.0 + Float64(Float64(beta + 2.0) / alpha))) / 2.0);
	else
		tmp = Float64(fma(Float64(-alpha), Float64(1.0 / t_0), Float64(1.0 + Float64(beta / t_0))) / 2.0);
	end
	return tmp
end

Wolfram

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

↓

code[alpha_, beta_] := Block[{t$95$0 = N[(beta + N[(alpha + 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(beta - alpha), $MachinePrecision] / N[(N[(beta + alpha), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision], -0.99995], N[(N[(N[(N[(-2.0 + N[(beta * -2.0), $MachinePrecision]), $MachinePrecision] / alpha), $MachinePrecision] * N[(-1.0 + N[(N[(beta + 2.0), $MachinePrecision] / alpha), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision], N[(N[((-alpha) * N[(1.0 / t$95$0), $MachinePrecision] + N[(1.0 + N[(beta / t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) < -0.999950000000000006

   1. Initial program 59.1

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

   2. Taylor expanded in alpha around -inf 3.1

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

   3. Simplified 0.2

      \[\leadsto \frac{\color{blue}{\frac{\beta \cdot -2 + -2}{\alpha} \cdot \left(-1 - \frac{-2 - \beta}{\alpha}\right)}}{2} \]
      Proof
      (*.f64 (/.f64 (+.f64 (*.f64 beta -2) -2) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (*.f64 beta (Rewrite<= metadata-eval (+.f64 -1 -1))) -2) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 -1 beta) (*.f64 -1 beta))) -2) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (+.f64 (*.f64 -1 beta) (Rewrite=> mul-1-neg_binary64 (neg.f64 beta))) -2) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (Rewrite<= sub-neg_binary64 (-.f64 (*.f64 -1 beta) beta)) -2) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (+.f64 (-.f64 (*.f64 -1 beta) beta) (Rewrite<= metadata-eval (neg.f64 2))) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= sub-neg_binary64 (-.f64 (-.f64 (*.f64 -1 beta) beta) 2)) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (Rewrite<= associate--r+_binary64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2))) alpha) (-.f64 -1 (/.f64 (-.f64 -2 beta) alpha))): 2 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (/.f64 (-.f64 (Rewrite<= metadata-eval (*.f64 2 -1)) beta) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (*.f64 2 -1) (neg.f64 beta))) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (/.f64 (+.f64 (*.f64 2 -1) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 beta))) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (/.f64 (+.f64 (*.f64 2 -1) (Rewrite=> *-commutative_binary64 (*.f64 beta -1))) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (/.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 -1 (+.f64 2 beta))) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (/.f64 (*.f64 -1 (Rewrite<= +-commutative_binary64 (+.f64 beta 2))) alpha))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (-.f64 -1 (Rewrite<= associate-*r/_binary64 (*.f64 -1 (/.f64 (+.f64 beta 2) alpha))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (Rewrite<= unsub-neg_binary64 (+.f64 -1 (neg.f64 (*.f64 -1 (/.f64 (+.f64 beta 2) alpha)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (+.f64 -1 (neg.f64 (Rewrite=> mul-1-neg_binary64 (neg.f64 (/.f64 (+.f64 beta 2) alpha)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha) (+.f64 -1 (Rewrite=> remove-double-neg_binary64 (/.f64 (+.f64 beta 2) alpha)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (*.f64 (/.f64 (+.f64 beta 2) alpha) (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)))): 1 points increase in error, 2 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (Rewrite<= times-frac_binary64 (/.f64 (*.f64 (+.f64 beta 2) (-.f64 (*.f64 -1 beta) (+.f64 beta 2))) (*.f64 alpha alpha)))): 18 points increase in error, 20 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (/.f64 (*.f64 (+.f64 beta 2) (-.f64 (*.f64 -1 beta) (+.f64 beta 2))) (Rewrite<= unpow2_binary64 (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (-.f64 (*.f64 -1 beta) (+.f64 beta 2))))): 3 points increase in error, 14 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (-.f64 (*.f64 -1 beta) (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (+.f64 beta 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (-.f64 (*.f64 -1 beta) (neg.f64 (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (+.f64 beta 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (-.f64 (*.f64 -1 beta) (Rewrite=> neg-mul-1_binary64 (*.f64 -1 (*.f64 -1 (+.f64 beta 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (Rewrite=> distribute-lft-out--_binary64 (*.f64 -1 (-.f64 beta (*.f64 -1 (+.f64 beta 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (Rewrite<= neg-mul-1_binary64 (neg.f64 (-.f64 beta (*.f64 -1 (+.f64 beta 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (Rewrite=> distribute-rgt-neg-out_binary64 (neg.f64 (*.f64 (/.f64 (+.f64 beta 2) (pow.f64 alpha 2)) (-.f64 beta (*.f64 -1 (+.f64 beta 2))))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (+.f64 beta 2) (/.f64 (pow.f64 alpha 2) (-.f64 beta (*.f64 -1 (+.f64 beta 2)))))))): 5 points increase in error, 5 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 beta 2) (-.f64 beta (*.f64 -1 (+.f64 beta 2)))) (pow.f64 alpha 2))))): 14 points increase in error, 3 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (/.f64 (*.f64 (+.f64 beta 2) (Rewrite=> cancel-sign-sub-inv_binary64 (+.f64 beta (*.f64 (neg.f64 -1) (+.f64 beta 2))))) (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (/.f64 (*.f64 (+.f64 beta 2) (+.f64 beta (*.f64 (Rewrite=> metadata-eval 1) (+.f64 beta 2)))) (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (/.f64 (*.f64 (+.f64 beta 2) (+.f64 beta (Rewrite=> *-lft-identity_binary64 (+.f64 beta 2)))) (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (/.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 beta (+.f64 beta 2)) (*.f64 (+.f64 beta 2) (+.f64 beta 2)))) (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (/.f64 (+.f64 (*.f64 beta (+.f64 beta 2)) (Rewrite<= unpow2_binary64 (pow.f64 (+.f64 beta 2) 2))) (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (neg.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (pow.f64 (+.f64 beta 2) 2) (*.f64 beta (+.f64 beta 2)))) (pow.f64 alpha 2)))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 -1 (/.f64 (-.f64 (*.f64 -1 beta) (+.f64 beta 2)) alpha)) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (/.f64 (+.f64 (pow.f64 (+.f64 beta 2) 2) (*.f64 beta (+.f64 beta 2))) (pow.f64 alpha 2))))): 0 points increase in error, 0 points decrease in error

   if -0.999950000000000006 < (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))

   1. Initial program 0.0

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

   2. Applied egg-rr 0.0

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

   3. Applied egg-rr 0.0

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

4. Final simplification 0.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.99995:\\ \;\;\;\;\frac{\frac{-2 + \beta \cdot -2}{\alpha} \cdot \left(-1 + \frac{\beta + 2}{\alpha}\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(-\alpha, \frac{1}{\beta + \left(\alpha + 2\right)}, 1 + \frac{\beta}{\beta + \left(\alpha + 2\right)}\right)}{2}\\ \end{array} \]

Alternatives

Alternative 1
Error	0.1
Cost	1860

\[\begin{array}{l} t_0 := \beta + \left(\alpha + 2\right)\\ \mathbf{if}\;\frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2} \leq -0.99995:\\ \;\;\;\;\frac{\frac{-2 + \beta \cdot -2}{\alpha} \cdot \left(-1 + \frac{\beta + 2}{\alpha}\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(1 + \frac{\beta}{t_0}\right) - \frac{\alpha}{t_0}}{2}\\ \end{array} \]

Alternative 2
Error	0.1
Cost	1732

\[\begin{array}{l} t_0 := \frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2}\\ \mathbf{if}\;t_0 \leq -0.99995:\\ \;\;\;\;\frac{\frac{-2 + \beta \cdot -2}{\alpha} \cdot \left(-1 + \frac{\beta + 2}{\alpha}\right)}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 + 1}{2}\\ \end{array} \]

Alternative 3
Error	0.3
Cost	1476

\[\begin{array}{l} t_0 := \frac{\beta - \alpha}{\left(\beta + \alpha\right) + 2}\\ \mathbf{if}\;t_0 \leq -0.99995:\\ \;\;\;\;\frac{\frac{2 + \left(\beta + \beta\right)}{\alpha}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{t_0 + 1}{2}\\ \end{array} \]

Alternative 4
Error	17.7
Cost	1236

\[\begin{array}{l} t_0 := \frac{1 - \frac{\alpha}{\alpha + 2}}{2}\\ \mathbf{if}\;\alpha \leq -6.0899653888988816 \cdot 10^{-86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\alpha \leq -3.4353413598737325 \cdot 10^{-135}:\\ \;\;\;\;1\\ \mathbf{elif}\;\alpha \leq -1.5569750566321883 \cdot 10^{-307}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\alpha \leq 3.549104777889903 \cdot 10^{-269}:\\ \;\;\;\;1\\ \mathbf{elif}\;\alpha \leq 30594.135145607757:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2 + \left(\beta + \beta\right)}{\alpha}}{2}\\ \end{array} \]

Alternative 5
Error	18.2
Cost	972

\[\begin{array}{l} t_0 := \frac{1 - \frac{\alpha}{\alpha + 2}}{2}\\ \mathbf{if}\;\beta \leq 2.3066403972338685 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\beta \leq 2.377065411610965 \cdot 10^{-130}:\\ \;\;\;\;\frac{\frac{2}{\alpha}}{2}\\ \mathbf{elif}\;\beta \leq 0.0030235064129672047:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6
Error	19.6
Cost	844

\[\begin{array}{l} t_0 := \frac{1 + \beta \cdot 0.5}{2}\\ \mathbf{if}\;\beta \leq 2.3066403972338685 \cdot 10^{-168}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;\beta \leq 3.717500748633203 \cdot 10^{-100}:\\ \;\;\;\;\frac{\frac{2}{\alpha}}{2}\\ \mathbf{elif}\;\beta \leq 0.0030235064129672047:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7
Error	5.0
Cost	708

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 2.1268744325725516 \cdot 10^{+28}:\\ \;\;\;\;\frac{1 + \frac{\beta}{\beta + 2}}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2 + \left(\beta + \beta\right)}{\alpha}}{2}\\ \end{array} \]

Alternative 8
Error	30.4
Cost	580

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 2.1268744325725516 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\beta + 2}{\alpha}}{2}\\ \end{array} \]

Alternative 9
Error	30.9
Cost	452

\[\begin{array}{l} \mathbf{if}\;\alpha \leq 2.1268744325725516 \cdot 10^{+28}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{\alpha}}{2}\\ \end{array} \]

Alternative 10
Error	61.6
Cost	64

\[0 \]

Alternative 11
Error	40.2
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2022291 
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/1"
  :precision binary64
  :pre (and (> alpha -1.0) (> beta -1.0))
  (/ (+ (/ (- beta alpha) (+ (+ alpha beta) 2.0)) 1.0) 2.0))