Average Error: 0.0 → 0.0
Time: 6.7s
Precision: 64
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]

Error

Bits error versus a

Bits error versus b

Target

Original0.0
Target0.0
Herbie0.0
\[\left(\left(b \cdot a + b \cdot b\right) + b \cdot a\right) + a \cdot a\]

Derivation

  1. Initial program 0.0

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

  3. Applied distribute-rgt-in0.0

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

  4. Final simplification0.0

    \[\leadsto a \cdot \left(b + a\right) + \left(b + a\right) \cdot b\]

Reproduce

herbie shell --seed 2019100 
(FPCore (a b)
  :name "Expression 4, p15"
  :pre (and (<= 5 a 10) (<= 0 b 0.001))

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

  (* (+ a b) (+ a b)))