Error

Derivation

1. Initial program 0.2

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

2. Initial simplification0.2

   \[\leadsto (\left((b \cdot b + \left(a \cdot a\right))_*\right) \cdot \left((b \cdot b + \left(a \cdot a\right))_*\right) + \left((\left(4 \cdot b\right) \cdot b + -1)_*\right))_*\]
3. Using strategy rm

4. Applied add-sqr-sqrt0.2

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

5. Final simplification0.2

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

Runtime

Time bar (total: 9.8s)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(FPCore (a b)
  :name "Bouland and Aaronson, Equation (26)"
  (- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1))