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

↓

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

Error

The X axis uses an exponential scale — Bits error versus `x`

Derivation

Initial program 0.0
\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
Simplified0.0
\[\leadsto \color{blue}{(i \cdot c + \left((a \cdot b + \left((x \cdot y + \left(z \cdot t\right))_*\right))_*\right))_*}\]
Taylor expanded around inf 0.0
\[\leadsto (i \cdot c + \left((a \cdot b + \color{blue}{\left(t \cdot z + x \cdot y\right)})_*\right))_*\]
Simplified0.0
\[\leadsto (i \cdot c + \left((a \cdot b + \color{blue}{\left((t \cdot z + \left(x \cdot y\right))_*\right)})_*\right))_*\]
Final simplification0.0
\[\leadsto (i \cdot c + \left((a \cdot b + \left((t \cdot z + \left(y \cdot x\right))_*\right))_*\right))_*\]

Reproduce

herbie shell --seed 2019088 +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)))