Error

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

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Target

Original	3.7
Target	3.9
Herbie	0

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

Derivation

Initial program 3.7
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
Using strategy rm
Applied associate-+r+2.8
\[\leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
Using strategy rm
Applied add-cbrt-cube2.9
\[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(\left(b + c\right) + d\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)\right) \cdot \left(a + \left(\left(b + c\right) + d\right)\right)}} \cdot 2\]
Applied simplify0.6
\[\leadsto \sqrt[3]{\color{blue}{{\left(\left(b + c\right) + \left(a + d\right)\right)}^{3}}} \cdot 2\]
Using strategy rm
Applied rem-cbrt-cube0
\[\leadsto \color{blue}{\left(\left(b + c\right) + \left(a + d\right)\right)} \cdot 2\]

Runtime

herbie shell --seed 2019053 +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))