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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 associate-+r+2.8

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

5. Applied add-cbrt-cube2.9

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

7. Applied flip-+3.1

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

8. Applied flip-+3.2

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

9. Applied flip-+3.3

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

10. Applied frac-times3.3

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

11. Applied frac-times3.3

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

12. Applied cbrt-div3.3

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

13. Simplified0.5

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

15. Applied pow30.5

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

16. Applied rem-cbrt-cube0.3

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

17. Final simplification0.3

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

Runtime

Time bar (total: 2.8m)Debug logProfile

herbie shell --seed 2018214 
(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))