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. Using strategy rm

7. Applied associate-+r+2.7

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

9. Applied flip-+3.0

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

10. Applied flip3-+3.0

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

11. Applied frac-times3.0

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

12. Applied associate-*l/3.0

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

13. Applied cbrt-div3.0

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

14. Simplified2.8

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

15. Final simplification2.8

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

Reproduce

herbie shell --seed 2019050 
(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))