\[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
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: 8.2 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\((i * c + \left((b * a + \left((y * x + \left(t \cdot z\right))_*\right))_*\right))_*\)
  1. Started with
    \[\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i\]
    0.1
  2. Applied simplify to get
    \[\color{red}{\left(\left(x \cdot y + z \cdot t\right) + a \cdot b\right) + c \cdot i} \leadsto \color{blue}{(i * c + \left(a \cdot b\right))_* + (y * x + \left(t \cdot z\right))_*}\]
    0.1
  3. Using strategy rm
    0.1
  4. Applied fma-udef to get
    \[\color{red}{(i * c + \left(a \cdot b\right))_*} + (y * x + \left(t \cdot z\right))_* \leadsto \color{blue}{\left(i \cdot c + a \cdot b\right)} + (y * x + \left(t \cdot z\right))_*\]
    0.1
  5. Applied associate-+l+ to get
    \[\color{red}{\left(i \cdot c + a \cdot b\right) + (y * x + \left(t \cdot z\right))_*} \leadsto \color{blue}{i \cdot c + \left(a \cdot b + (y * x + \left(t \cdot z\right))_*\right)}\]
    0.1
  6. Applied simplify to get
    \[i \cdot c + \color{red}{\left(a \cdot b + (y * x + \left(t \cdot z\right))_*\right)} \leadsto i \cdot c + \color{blue}{(b * a + \left((y * x + \left(z \cdot t\right))_*\right))_*}\]
    0.1
  7. Applied taylor to get
    \[i \cdot c + (b * a + \left((y * x + \left(z \cdot t\right))_*\right))_* \leadsto i \cdot c + (b * a + \left((y * x + \left(t \cdot z\right))_*\right))_*\]
    0.1
  8. Taylor expanded around 0 to get
    \[i \cdot c + \color{red}{(b * a + \left((y * x + \left(t \cdot z\right))_*\right))_*} \leadsto i \cdot c + \color{blue}{(b * a + \left((y * x + \left(t \cdot z\right))_*\right))_*}\]
    0.1
  9. Applied simplify to get
    \[i \cdot c + (b * a + \left((y * x + \left(t \cdot z\right))_*\right))_* \leadsto (i * c + \left((b * a + \left((y * x + \left(t \cdot z\right))_*\right))_*\right))_*\]
    0.1
  10. Applied final simplification

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)))