\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
Test:
Linear.V4:$cdot from linear-1.19.1.3
Bits:
128 bits
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
Time: 9.5 s
Input Error: 0.0
Output Error: 0.0
Log: ⚲
Profile: 🕒
\((z * t + \left((y * x + \left((i * c + \left(b \cdot a\right))_*\right))_*\right))_*\)
  1. Started with
    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
    0.0
  2. Applied simplify to get
    \[\color{red}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i} \leadsto \color{blue}{(i * c + \left(a \cdot b\right))_* + (y * x + \left(t \cdot z\right))_*}\]
    0.0
  3. Using strategy rm
    0.0
  4. Applied fma-udef to get
    \[(i * c + \left(a \cdot b\right))_* + \color{red}{(y * x + \left(t \cdot z\right))_*} \leadsto (i * c + \left(a \cdot b\right))_* + \color{blue}{\left(y \cdot x + t \cdot z\right)}\]
    0.0
  5. Applied associate-+r+ to get
    \[\color{red}{(i * c + \left(a \cdot b\right))_* + \left(y \cdot x + t \cdot z\right)} \leadsto \color{blue}{\left((i * c + \left(a \cdot b\right))_* + y \cdot x\right) + t \cdot z}\]
    0.0
  6. Applied simplify to get
    \[\color{red}{\left((i * c + \left(a \cdot b\right))_* + y \cdot x\right)} + t \cdot z \leadsto \color{blue}{(y * x + \left((i * c + \left(a \cdot b\right))_*\right))_*} + t \cdot z\]
    0.0
  7. Applied taylor to get
    \[(y * x + \left((i * c + \left(a \cdot b\right))_*\right))_* + t \cdot z \leadsto (y * x + \left((i * c + \left(b \cdot a\right))_*\right))_* + t \cdot z\]
    0.0
  8. Taylor expanded around 0 to get
    \[\color{red}{(y * x + \left((i * c + \left(b \cdot a\right))_*\right))_*} + t \cdot z \leadsto \color{blue}{(y * x + \left((i * c + \left(b \cdot a\right))_*\right))_*} + t \cdot z\]
    0.0
  9. Applied simplify to get
    \[\color{red}{(y * x + \left((i * c + \left(b \cdot a\right))_*\right))_* + t \cdot z} \leadsto \color{blue}{(z * t + \left((y * x + \left((i * c + \left(b \cdot a\right))_*\right))_*\right))_*}\]
    0.0
  10. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default) (b default) (c default) (i default))
  #:name "Linear.V4:$cdot from linear-1.19.1.3"
  (+ (+ (+ (* x y) (* z t)) (* a b)) (* c i)))