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Target

Derivation

1. Initial program 3.6

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

2. Initial simplification3.1

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

4. Applied associate-+r+3.1

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

5. Taylor expanded around -inf 2.7

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

7. Applied add-cbrt-cube2.9

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

9. Applied associate-+l+2.7

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

10. Final simplification2.7

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

Runtime

Time bar (total: 20.4s)Debug logProfile

herbie shell --seed 2018295 +o rules:numerics
(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))