Error

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Target

Derivation

1. Initial program 0.4

   \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]

2. Initial simplification0.2

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

4. Applied add-log-exp0.2

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

5. Applied add-log-exp0.2

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

6. Applied sum-log0.2

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

7. Simplified0.2

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

9. Applied exp-sum0.2

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

10. Applied log-prod0.2

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

11. Applied associate-+l+0.2

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

12. Simplified0.2

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

13. Final simplification0.2

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

Reproduce

herbie shell --seed 2018365 +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: 16.1s)Debug log