Error

Target

Derivation

1. Initial program 3.6

   \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
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 associate-+r+2.7

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

9. Applied add-log-exp2.7

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

10. Applied add-log-exp2.7

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

11. Applied sum-log2.6

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

12. Applied add-log-exp2.6

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

13. Applied sum-log2.3

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

14. Simplified2.7

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

15. Final simplification2.7

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

Reproduce

herbie shell --seed 2019091 
(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))