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 flip3-+0.3

   \[\leadsto \left(\left(a + d\right) + \color{blue}{\frac{{c}^{3} + {b}^{3}}{c \cdot c + \left(b \cdot b - c \cdot b\right)}}\right) + e\]

5. Applied flip3-+0.3

   \[\leadsto \left(\color{blue}{\frac{{a}^{3} + {d}^{3}}{a \cdot a + \left(d \cdot d - a \cdot d\right)}} + \frac{{c}^{3} + {b}^{3}}{c \cdot c + \left(b \cdot b - c \cdot b\right)}\right) + e\]

6. Applied frac-add0.4

   \[\leadsto \color{blue}{\frac{\left({a}^{3} + {d}^{3}\right) \cdot \left(c \cdot c + \left(b \cdot b - c \cdot b\right)\right) + \left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right) \cdot \left({c}^{3} + {b}^{3}\right)}{\left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right) \cdot \left(c \cdot c + \left(b \cdot b - c \cdot b\right)\right)}} + e\]

7. Simplified0.4

   \[\leadsto \frac{\color{blue}{(\left((\left(d - a\right) \cdot d + \left(a \cdot a\right))_*\right) \cdot \left((\left(b \cdot b\right) \cdot b + \left({c}^{3}\right))_*\right) + \left((b \cdot \left(b - c\right) + \left(c \cdot c\right))_* \cdot (\left(d \cdot d\right) \cdot d + \left({a}^{3}\right))_*\right))_*}}{\left(a \cdot a + \left(d \cdot d - a \cdot d\right)\right) \cdot \left(c \cdot c + \left(b \cdot b - c \cdot b\right)\right)} + e\]

8. Simplified0.3

   \[\leadsto \frac{(\left((\left(d - a\right) \cdot d + \left(a \cdot a\right))_*\right) \cdot \left((\left(b \cdot b\right) \cdot b + \left({c}^{3}\right))_*\right) + \left((b \cdot \left(b - c\right) + \left(c \cdot c\right))_* \cdot (\left(d \cdot d\right) \cdot d + \left({a}^{3}\right))_*\right))_*}{\color{blue}{(b \cdot \left(b - c\right) + \left(c \cdot c\right))_* \cdot (d \cdot \left(d - a\right) + \left(a \cdot a\right))_*}} + e\]

9. Final simplification0.3

   \[\leadsto e + \frac{(\left((\left(d - a\right) \cdot d + \left(a \cdot a\right))_*\right) \cdot \left((\left(b \cdot b\right) \cdot b + \left({c}^{3}\right))_*\right) + \left((b \cdot \left(b - c\right) + \left(c \cdot c\right))_* \cdot (\left(d \cdot d\right) \cdot d + \left({a}^{3}\right))_*\right))_*}{(b \cdot \left(b - c\right) + \left(c \cdot c\right))_* \cdot (d \cdot \left(d - a\right) + \left(a \cdot a\right))_*}\]

Runtime

Time bar (total: 58.6s)Debug logProfile

herbie shell --seed 2018273 +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))