Error

Try it out

Target

Derivation

1. Initial program 0.0

   \[\left(a + b\right) \cdot \left(a + b\right)\]

2. Taylor expanded around -inf 0.0

   \[\leadsto \color{blue}{{a}^{2} + \left({b}^{2} + 2 \cdot \left(a \cdot b\right)\right)}\]
3. Using strategy rm

4. Applied add-log-exp0.0

   \[\leadsto {a}^{2} + \left({b}^{2} + \color{blue}{\log \left(e^{2 \cdot \left(a \cdot b\right)}\right)}\right)\]

5. Applied add-log-exp0.0

   \[\leadsto {a}^{2} + \left(\color{blue}{\log \left(e^{{b}^{2}}\right)} + \log \left(e^{2 \cdot \left(a \cdot b\right)}\right)\right)\]

6. Applied sum-log0.0

   \[\leadsto {a}^{2} + \color{blue}{\log \left(e^{{b}^{2}} \cdot e^{2 \cdot \left(a \cdot b\right)}\right)}\]

7. Simplified0.0

   \[\leadsto {a}^{2} + \log \color{blue}{\left({\left(e^{b}\right)}^{\left(\left(a + a\right) + b\right)}\right)}\]

8. Taylor expanded around 0 0.0

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

9. Simplified0.0

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

10. Final simplification0.0

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

Runtime

Time bar (total: 18.4s)Debug logProfile

herbie shell --seed 2018296 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

  :herbie-target
  (+ (+ (+ (* b a) (* b b)) (* b a)) (* a a))

  (* (+ a b) (+ a b)))