\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]

↓

\[\left(\left({a}^{2} \cdot {b}^{2}\right) \cdot 2 + \left({b}^{4} + {a}^{4}\right)\right) + \left(4 \cdot \left(b \cdot b\right) - 1\right)\]

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Derivation

Initial program 0.2
\[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(b \cdot b\right)\right) - 1\]
Initial simplification0.2
\[\leadsto \left(\left(b \cdot b\right) \cdot 4 - 1\right) + \left(b \cdot b + a \cdot a\right) \cdot \left(b \cdot b + a \cdot a\right)\]
Taylor expanded around 0 0.0
\[\leadsto \left(\left(b \cdot b\right) \cdot 4 - 1\right) + \color{blue}{\left(2 \cdot \left({b}^{2} \cdot {a}^{2}\right) + \left({a}^{4} + {b}^{4}\right)\right)}\]
Final simplification0.0
\[\leadsto \left(\left({a}^{2} \cdot {b}^{2}\right) \cdot 2 + \left({b}^{4} + {a}^{4}\right)\right) + \left(4 \cdot \left(b \cdot b\right) - 1\right)\]

herbie shell --seed 2018215 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))