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Target

Derivation

1. Initial program 3.7

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

3. Applied add-cbrt-cube3.7

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

4. Applied simplify0.6

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

6. Applied *-un-lft-identity0.6

   \[\leadsto \sqrt[3]{{\color{blue}{\left(1 \cdot \left(\left(c + b\right) + \left(d + a\right)\right)\right)}}^{3}} \cdot 2\]

7. Applied unpow-prod-down0.6

   \[\leadsto \sqrt[3]{\color{blue}{{1}^{3} \cdot {\left(\left(c + b\right) + \left(d + a\right)\right)}^{3}}} \cdot 2\]

8. Applied cbrt-prod0.6

   \[\leadsto \color{blue}{\left(\sqrt[3]{{1}^{3}} \cdot \sqrt[3]{{\left(\left(c + b\right) + \left(d + a\right)\right)}^{3}}\right)} \cdot 2\]

9. Applied simplify0.6

   \[\leadsto \left(\color{blue}{\sqrt[3]{1}} \cdot \sqrt[3]{{\left(\left(c + b\right) + \left(d + a\right)\right)}^{3}}\right) \cdot 2\]

10. Applied simplify0

    \[\leadsto \left(\sqrt[3]{1} \cdot \color{blue}{\left(\left(c + b\right) + \left(a + d\right)\right)}\right) \cdot 2\]

Runtime

Time bar (total: 32.6s)Debug logProfile

herbie shell --seed 2020178 +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))