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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-cube3.8

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

5. Applied pow13.8

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

6. Applied pow13.8

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

7. Applied pow13.8

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

8. Applied pow-prod-down3.8

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

9. Applied pow-prod-down3.8

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

10. Simplified0.6

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

12. Applied unpow30.6

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

13. Final simplification0.6

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018249 
(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))