Error

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Target

Derivation

1. Initial program 0.4

   \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
2. Using strategy rm

3. Applied associate-+l+0.3

   \[\leadsto \color{blue}{\left(\left(e + d\right) + c\right) + \left(b + a\right)}\]

4. Taylor expanded around 0 0.3

   \[\leadsto \color{blue}{\left(e + \left(c + d\right)\right)} + \left(b + a\right)\]
5. Using strategy rm

6. Applied add-log-exp0.3

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

7. Applied add-log-exp0.3

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

8. Applied sum-log0.3

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

9. Simplified0.2

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

10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019005 +o rules:numerics
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :herbie-target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))

Details

Time bar (total: 12.6s)Debug log