Error

Target

Derivation

1. Initial program 0.0

   \[a \cdot \left(\left(b + c\right) + d\right)\]
2. Using strategy rm

3. Applied add-sqr-sqrt0.5

   \[\leadsto \color{blue}{\sqrt{a \cdot \left(\left(b + c\right) + d\right)} \cdot \sqrt{a \cdot \left(\left(b + c\right) + d\right)}}\]
4. Using strategy rm

5. Applied pow10.5

   \[\leadsto \sqrt{a \cdot \left(\left(b + c\right) + d\right)} \cdot \color{blue}{{\left(\sqrt{a \cdot \left(\left(b + c\right) + d\right)}\right)}^{1}}\]

6. Applied pow10.5

   \[\leadsto \color{blue}{{\left(\sqrt{a \cdot \left(\left(b + c\right) + d\right)}\right)}^{1}} \cdot {\left(\sqrt{a \cdot \left(\left(b + c\right) + d\right)}\right)}^{1}\]

7. Applied pow-prod-down0.5

   \[\leadsto \color{blue}{{\left(\sqrt{a \cdot \left(\left(b + c\right) + d\right)} \cdot \sqrt{a \cdot \left(\left(b + c\right) + d\right)}\right)}^{1}}\]

8. Simplified0.0

   \[\leadsto {\color{blue}{\left((\left(c + d\right) \cdot a + \left(a \cdot b\right))_*\right)}}^{1}\]

9. Final simplification0.0

   \[\leadsto (\left(d + c\right) \cdot a + \left(a \cdot b\right))_*\]

Runtime

Time bar (total: 18.5s)Debug logProfile

herbie shell --seed 2018234 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

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

  (* a (+ (+ b c) d)))