Error

Derivation

1. Initial program 0.2

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

3. Applied add-cube-cbrt0.5

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

4. Taylor expanded around 0 0.5

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

5. Applied simplify0.2

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

6. Taylor expanded around 0 0.0

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' 
(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))