Error

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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. Using strategy rm

9. Applied log-pow0.0

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

10. Final simplification0.0

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

Runtime

Time bar (total: 9.5s)Debug logProfile

herbie shell --seed 2018354 
(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)))