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Target

Derivation

1. Initial program 3.7

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]

2. Initial simplification3.1

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

4. Applied associate-+l+3.1

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

6. Applied associate-+r+2.8

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

8. Applied add-cbrt-cube2.9

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

10. Applied associate-+r+2.8

    \[\leadsto 2 \cdot \sqrt[3]{\left(\left(a + \left(\left(c + b\right) + d\right)\right) \cdot \left(a + \left(\left(c + b\right) + d\right)\right)\right) \cdot \color{blue}{\left(\left(a + \left(c + b\right)\right) + d\right)}}\]

11. Final simplification2.8

    \[\leadsto \sqrt[3]{\left(\left(a + \left(d + \left(b + c\right)\right)\right) \cdot \left(a + \left(d + \left(b + c\right)\right)\right)\right) \cdot \left(d + \left(a + \left(b + c\right)\right)\right)} \cdot 2\]

Runtime

Time bar (total: 19.6s)Debug logProfile

herbie shell --seed 2018354 
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))