Error

Derivation

1. Initial program 0.2

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

2. Taylor expanded around 0 0.2

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

3. Applied simplify0.2

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

4. Taylor expanded around 0 0.0

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

5. Applied simplify0.0

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

Runtime

Time bar (total: 28.7s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (24)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (+ (* (* a a) (- 1 a)) (* (* b b) (+ 3 a))))) 1))