Average Error: 0.0 → 0.0
Time: 50.7s
Precision: 64
Internal Precision: 576
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[x \cdot y + (c \cdot i + \left((a \cdot b + \left(t \cdot z\right))_*\right))_*\]

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. Using strategy rm

  3. Applied associate-+l+0.0

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

  4. Applied simplify0.0

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

  6. Applied associate-+l+0.0

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

  7. Applied simplify0.0

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

Runtime

Time bar (total: 50.7s)Debug logProfile

herbie shell --seed 2018201 +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)))