Average Error: 0.0 → 0.0
Time: 16.5s
Precision: 64
Internal Precision: 384
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
↓
\[(i \cdot c + \left((a \cdot b + \left((z \cdot t + \left(x \cdot y\right))_*\right))_*\right))_*\]

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

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

  5. Applied associate-+l+0.0

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

  6. Applied simplify0.0

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

  7. Taylor expanded around inf 0.0

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

  8. Applied simplify0.0

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

Runtime

Time bar (total: 16.5s)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' +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)))