\[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
Test:
FastMath repmul
Bits:
128 bits
Bits error versus d1
Time: 1.3 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\({d1}^{4}\)
  1. Started with
    \[\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1\]
    0.1
  2. Applied simplify to get
    \[\color{red}{\left(\left(d1 \cdot d1\right) \cdot d1\right) \cdot d1} \leadsto \color{blue}{{d1}^2 \cdot {d1}^2}\]
    0.2
  3. Applied taylor to get
    \[{d1}^2 \cdot {d1}^2 \leadsto {d1}^{4}\]
    0.1
  4. Taylor expanded around 0 to get
    \[\color{red}{{d1}^{4}} \leadsto \color{blue}{{d1}^{4}}\]
    0.1

Original test:


(lambda ((d1 default))
  #:name "FastMath repmul"
  (* (* (* d1 d1) d1) d1)
  #:target
  (pow d1 4))