Average Error: 0.0 → 0.0
Time: 4.8s
Precision: 64
Internal precision: 128
\[\left(x \cdot x + y\right) + y\]
⬇
\[{x}^2 + 2 \cdot y\]

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Comparison0.0
Herbie0.0
\[ \left(y + y\right) + {x}^2 \]

Derivation

  1. Initial program 0.0

    \[\left(x \cdot x + y\right) + y\]

  2. Applied taylor 0.0

    \[\leadsto {x}^2 + 2 \cdot y\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{x}^2 + 2 \cdot y}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 4.8s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(712686301 3966648636 2536199626 3685763275 2125097257 3985039682)'
(FPCore (x y)
  :name "Data.Random.Distribution.Normal:normalTail from random-fu-0.2.6.2"

  :target
  (+ (+ y y) (sqr x))

  (+ (+ (* x x) y) y))