\[x \cdot \left(x \cdot x\right) + x \cdot x\]
Test:
Expression 3, p15
Bits:
128 bits
Bits error versus x
Time: 5.5 s
Input Error: 0.1
Output Error: 0.1
Log: ⚲
Profile: 🕒
\({x}^2 + {x}^{3}\)
  1. Started with
    \[x \cdot \left(x \cdot x\right) + x \cdot x\]
    0.1
  2. Applied simplify to get
    \[\color{red}{x \cdot \left(x \cdot x\right) + x \cdot x} \leadsto \color{blue}{{x}^2 \cdot \left(1 + x\right)}\]
    0.1
  3. Applied taylor to get
    \[{x}^2 \cdot \left(1 + x\right) \leadsto {x}^2 + {x}^{3}\]
    0.1
  4. Taylor expanded around 0 to get
    \[\color{red}{{x}^2 + {x}^{3}} \leadsto \color{blue}{{x}^2 + {x}^{3}}\]
    0.1

Original test:


(lambda ((x default))
  #:name "Expression 3, p15"
  (+ (* x (* x x)) (* x x))
  #:target
  (* (* (+ 1.0 x) x) x))