Error

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

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In
Out

Enter valid numbers for all inputs

Target

Original	3.6
Target	3.8
Herbie	2.7

\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

Initial program 3.6
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
Initial simplification3.1
\[\leadsto 2 \cdot \left(\left(a + c\right) + \left(b + d\right)\right)\]
Using strategy rm
Applied associate-+l+3.1
\[\leadsto 2 \cdot \color{blue}{\left(a + \left(c + \left(b + d\right)\right)\right)}\]
Using strategy rm
Applied associate-+r+2.7
\[\leadsto 2 \cdot \left(a + \color{blue}{\left(\left(c + b\right) + d\right)}\right)\]
Final simplification2.7
\[\leadsto \left(a + \left(d + \left(b + c\right)\right)\right) \cdot 2\]

Runtime

herbie shell --seed 2018234 +o rules:numerics
(FPCore (a b c d)
  :name "Expression, p6"
  :pre (and (<= -14 a -13) (<= -3 b -2) (<= 3 c 3.5) (<= 12.5 d 13.5))

  :herbie-target
  (+ (* (+ a b) 2) (* (+ c d) 2))

  (* (+ a (+ b (+ c d))) 2))