Average Error: 0.0 → 0.0
Time: 15.9s
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[z \cdot t + (y \cdot x + \left((i \cdot c + \left(b \cdot a\right))_*\right))_*\]

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. Applied simplify0.0

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

  4. Applied fma-udef0.0

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

  5. Applied associate-+r+0.0

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

  6. Applied simplify0.0

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

  8. Applied fma-udef0.0

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

  9. Applied associate-+l+0.0

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

  10. Applied simplify0.0

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

Runtime

Time bar (total: 15.9s)Debug logProfile

herbie shell --seed '#(1064173506 2580572819 2847706409 4129882574 1125180799 1845288547)' +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)))