Average Error: 0.0 → 0.0
Time: 14.7s
Precision: 64
Internal Precision: 576
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[(x \cdot y + \left((a \cdot b + \left(t \cdot z\right))_*\right))_* + c \cdot i\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Derivation

  1. Initial program 0.0

    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]

  2. Taylor expanded around -inf 0.0

    \[\leadsto \color{blue}{\left(a \cdot b + \left(t \cdot z + x \cdot y\right)\right)} + c \cdot i\]

  3. Simplified0.0

    \[\leadsto \color{blue}{(x \cdot y + \left((a \cdot b + \left(t \cdot z\right))_*\right))_*} + c \cdot i\]

  4. Final simplification0.0

    \[\leadsto (x \cdot y + \left((a \cdot b + \left(t \cdot z\right))_*\right))_* + c \cdot i\]

Runtime

Time bar (total: 14.7s)Debug logProfile

herbie shell --seed 2018248 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))