Error

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. Applied simplify0.6

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

8. Applied flip-+1.5

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

9. Applied flip-+2.8

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

10. Applied frac-add2.8

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

11. Applied cube-div2.8

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

12. Applied cbrt-div2.9

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

13. Applied simplify0.5

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

14. Applied simplify0.1

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

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed '#(1064300848 3212030778 2049303162 3567222883 2277747821 1384278011)' 
(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))