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Derivation

1. Initial program 0.2

   \[\left({\left(a \cdot a + b \cdot b\right)}^{2} + 4 \cdot \left(\left(a \cdot a\right) \cdot \left(1 + a\right) + \left(b \cdot b\right) \cdot \left(1 - 3 \cdot a\right)\right)\right) - 1\]

2. Initial simplification0.2

   \[\leadsto \left(\left(4 \cdot a\right) \cdot \left(a + a \cdot a\right) + \left(a \cdot a + b \cdot b\right) \cdot \left(a \cdot a + b \cdot b\right)\right) + \left(\left(4 \cdot \left(b \cdot b\right)\right) \cdot \left(a \cdot -3 + 1\right) - 1\right)\]

3. Taylor expanded around -inf 0.0

   \[\leadsto \left(\left(4 \cdot a\right) \cdot \left(a + a \cdot a\right) + \color{blue}{\left({b}^{4} + \left({a}^{4} + 2 \cdot \left({a}^{2} \cdot {b}^{2}\right)\right)\right)}\right) + \left(\left(4 \cdot \left(b \cdot b\right)\right) \cdot \left(a \cdot -3 + 1\right) - 1\right)\]

4. Final simplification0.0

   \[\leadsto \left(\left(-3 \cdot a + 1\right) \cdot \left(4 \cdot \left(b \cdot b\right)\right) - 1\right) + \left(\left(\left(2 \cdot \left({a}^{2} \cdot {b}^{2}\right) + {a}^{4}\right) + {b}^{4}\right) + \left(a + a \cdot a\right) \cdot \left(4 \cdot a\right)\right)\]

Runtime

Time bar (total: 40.2s)Debug logProfile

herbie shell --seed 2018274 
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (25)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (+ 1 a)) (* (* b b) (- 1 (* 3 a)))))) 1))