Average Error: 0.0 → 0.0
Time: 1.9m
Precision: 64
Internal Precision: 576
\[\left(a + b\right) \cdot \left(a + b\right)\]
↓
\[(\left((a \cdot 2 + b)_*\right) \cdot b + \left(a \cdot a\right))_*\]

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. Taylor expanded around 0 0.0

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

  3. Applied simplify0.0

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed 2018207 +o rules:numerics
(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)))