Error

Try it out

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 expm1-log1p-u3.1

   \[\leadsto \color{blue}{(e^{\log_* (1 + \left(a + \left(\left(b + c\right) + d\right)\right))} - 1)^*} \cdot 2\]
6. Using strategy rm

7. Applied add-cbrt-cube3.2

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

9. Applied associate-+r+3.1

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

10. Final simplification3.1

    \[\leadsto 2 \cdot (e^{\log_* (1 + \sqrt[3]{\left(\left(\left(b + c\right) + a\right) + d\right) \cdot \left(\left(\left(\left(b + c\right) + d\right) + a\right) \cdot \left(\left(\left(b + c\right) + d\right) + a\right)\right)})} - 1)^*\]

Reproduce

herbie shell --seed 2019026 +o rules:numerics
(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))