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 log1p-expm1-u2.8

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

7. Applied add-cbrt-cube2.9

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

9. Applied associate-+r+2.7

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

10. Final simplification2.7

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

Reproduce

herbie shell --seed 2019094 +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))