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 add-sqr-sqrt0.6

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

4. Applied fma-def0.5

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

6. Applied associate-+l+0.5

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

7. Simplified0.3

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

9. Applied add-log-exp0.3

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

10. Applied add-log-exp0.3

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

11. Applied sum-log0.3

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

12. Simplified0.3

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

13. Final simplification0.3

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

Reproduce

herbie shell --seed 2019008 +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: 11.9s)Debug log