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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 flip-+0.5

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

4. Taylor expanded around 0 0.5

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

5. Applied simplify0.3

   \[\leadsto \color{blue}{\frac{c + \left(d + e\right)}{1} + \left(a + b\right)}\]
6. Using strategy rm

7. Applied add-log-exp0.3

   \[\leadsto \frac{c + \left(d + e\right)}{1} + \color{blue}{\log \left(e^{a + b}\right)}\]

8. Applied add-log-exp0.3

   \[\leadsto \color{blue}{\log \left(e^{\frac{c + \left(d + e\right)}{1}}\right)} + \log \left(e^{a + b}\right)\]

9. Applied sum-log0.3

   \[\leadsto \color{blue}{\log \left(e^{\frac{c + \left(d + e\right)}{1}} \cdot e^{a + b}\right)}\]

10. Applied simplify0.3

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018193 
(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))