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

↓

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

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

	Baseline	Herbie	Oracle	Span	%
Regimes	0.0	0.0	0.0	0.0	0%

herbie shell --seed 2018339 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))