\[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]

⬇

\[\begin{array}{l} \mathbf{if}\;\beta \le 7.672284614270702 \cdot 10^{+191}:\\ \;\;\;\;\frac{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta \cdot \alpha + \beta\right)}{\alpha + \left(\beta + 2\right)}}{{\left(\sqrt[3]{\left(\alpha + 1.0\right) + \left(\beta + 2\right)}\right)}^3}}{\alpha + \left(\beta + 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\alpha + \beta\right) \cdot 0.25 + 0.5}{\left(\alpha + \left(2 + \beta\right)\right) \cdot \left(\left(2 + \beta\right) + \left(\alpha + 1.0\right)\right)}\\ \end{array}\]

Derivation

Split input into 2 regimes.
if beta < 7.672284614270702e+191
1. Initial program 1.7
  \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
2. Applied simplify 2.5
  \[\leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta \cdot \alpha + \beta\right)}{\alpha + \left(\beta + 2\right)}}{\left(\left(\alpha + 1.0\right) + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}}\]
3. Using strategy rm
4. Applied associate-/r* 1.7
  \[\leadsto \color{blue}{\frac{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta \cdot \alpha + \beta\right)}{\alpha + \left(\beta + 2\right)}}{\left(\alpha + 1.0\right) + \left(\beta + 2\right)}}{\alpha + \left(\beta + 2\right)}}\]
5. Using strategy rm
6. Applied add-cube-cbrt 2.0
  \[\leadsto \frac{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta \cdot \alpha + \beta\right)}{\alpha + \left(\beta + 2\right)}}{\color{blue}{{\left(\sqrt[3]{\left(\alpha + 1.0\right) + \left(\beta + 2\right)}\right)}^3}}}{\alpha + \left(\beta + 2\right)}\]
if 7.672284614270702e+191 < beta
1. Initial program 60.2
  \[\frac{\frac{\frac{\left(\left(\alpha + \beta\right) + \beta \cdot \alpha\right) + 1.0}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\alpha + \beta\right) + 2 \cdot 1}}{\left(\left(\alpha + \beta\right) + 2 \cdot 1\right) + 1.0}\]
2. Applied simplify 60.2
  \[\leadsto \color{blue}{\frac{\frac{\left(\alpha + 1.0\right) + \left(\beta \cdot \alpha + \beta\right)}{\alpha + \left(\beta + 2\right)}}{\left(\left(\alpha + 1.0\right) + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}}\]
3. Applied taylor 59.0
  \[\leadsto \frac{0.5 + \left(0.25 \cdot \beta + 0.25 \cdot \alpha\right)}{\left(\left(\alpha + 1.0\right) + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}\]
4. Taylor expanded around 0 59.0
  
  \[\leadsto \frac{\color{blue}{0.5 + \left(0.25 \cdot \beta + 0.25 \cdot \alpha\right)}}{\left(\left(\alpha + 1.0\right) + \left(\beta + 2\right)\right) \cdot \left(\alpha + \left(\beta + 2\right)\right)}\]
5. Applied simplify 59.0
  \[\leadsto \color{blue}{\frac{\left(\alpha + \beta\right) \cdot 0.25 + 0.5}{\left(\alpha + \left(2 + \beta\right)\right) \cdot \left(\left(2 + \beta\right) + \left(\alpha + 1.0\right)\right)}}\]
Recombined 2 regimes into one program.
Removed slow pow expressions

Runtime

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (alpha beta)
  :name "Octave 3.8, jcobi/3"
  :pre (and (> alpha -1) (> beta -1))
  (/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2 1))) (+ (+ alpha beta) (* 2 1))) (+ (+ (+ alpha beta) (* 2 1)) 1.0)))

Error

Derivation

`if beta < 7.672284614270702e+191`

`if 7.672284614270702e+191 < beta`

Runtime