Error

Target

Derivation

1. Initial program 0.0

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

2. Initial simplification0.0

   \[\leadsto (a \cdot \left(b + d\right) + \left(a \cdot c\right))_*\]
3. Using strategy rm

4. Applied add-sqr-sqrt0.5

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

6. Applied pow10.5

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

7. Applied pow10.5

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

8. Applied pow-prod-down0.5

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

9. Simplified0.0

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

10. Final simplification0.0

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

Runtime

Time bar (total: 10.7s)Debug logProfile

herbie shell --seed 2018277 +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)))