Error

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-sqr-sqrt0.3

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

5. Applied fma-def0.3

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

7. Applied fma-udef0.3

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

8. Applied associate-+l+0.3

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

9. Simplified0.3

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

11. Applied add-sqr-sqrt0.3

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

12. Applied fma-def0.3

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

13. Final simplification0.3

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

Runtime

Time bar (total: 15.7s)Debug logProfile

herbie shell --seed 2018248 +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))