Average Error: 3.6 → 0
Time: 11.3s
Precision: 64
Internal Precision: 384
\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
↓
\[\left(\left(a + d\right) + \left(b + c\right)\right) \cdot 2\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Target

Original3.6
Target3.8
Herbie0
\[\left(a + b\right) \cdot 2 + \left(c + d\right) \cdot 2\]

Derivation

  1. Initial program 3.6

    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
  2. Using strategy rm

  3. Applied add-cbrt-cube3.7

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(a + \left(b + \left(c + d\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)\right) \cdot \left(a + \left(b + \left(c + d\right)\right)\right)}} \cdot 2\]

  4. Applied simplify0.6

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\left(a + d\right) + \left(b + c\right)\right)}^{3}}} \cdot 2\]
  5. Using strategy rm

  6. Applied rem-cbrt-cube0

    \[\leadsto \color{blue}{\left(\left(a + d\right) + \left(b + c\right)\right)} \cdot 2\]

Runtime

Time bar (total: 11.3s)Debug logProfile

herbie shell --seed '#(1064397287 3527694221 3797617954 1138343853 2854031332 1153838279)' +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))