Error

The X axis uses an exponential scale — Bits error versus `a`

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Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

Initial program 0.0
\[a \cdot \left(\left(b + c\right) + d\right)\]
Initial simplification0.0
\[\leadsto \left(\left(b + c\right) + d\right) \cdot a\]
Taylor expanded around -inf 0.0
\[\leadsto \color{blue}{a \cdot d + \left(a \cdot b + a \cdot c\right)}\]
Simplified0.0
\[\leadsto \color{blue}{a \cdot \left(b + \left(d + c\right)\right)}\]
Using strategy rm
Applied distribute-lft-in0.0
\[\leadsto \color{blue}{a \cdot b + a \cdot \left(d + c\right)}\]
Using strategy rm
Applied distribute-rgt-in0.0
\[\leadsto a \cdot b + \color{blue}{\left(d \cdot a + c \cdot a\right)}\]
Final simplification0.0
\[\leadsto \left(c \cdot a + d \cdot a\right) + a \cdot b\]

Runtime

herbie shell --seed 2018296 
(FPCore (a b c d)
  :name "Expression, p14"
  :pre (and (<= 56789 a 98765) (<= 0 b 1) (<= 0 c 0.0016773) (<= 0 d 0.0016773))

  :herbie-target
  (+ (* a b) (* a (+ c d)))

  (* a (+ (+ b c) d)))