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. Initial simplification0.2

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

4. Applied add-cube-cbrt0.2

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

5. Applied associate-*l*0.2

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

6. Final simplification0.2

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

Runtime

Time bar (total: 23.5s)Debug logProfile

herbie shell --seed 2018290 +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))