\[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
Test:
Rosa's Benchmark
Bits:
128 bits
Bits error versus x
Time: 5.7 s
Input Error: 0.4
Output Error: 0.2
Log: ⚲
Profile: 🕒
\(\left(0.954929658551372 - {x}^2 \cdot 0.12900613773279798\right) \cdot x\)
  1. Started with
    \[0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)\]
    0.4
  2. Applied simplify to get
    \[\color{red}{0.954929658551372 \cdot x - 0.12900613773279798 \cdot \left(\left(x \cdot x\right) \cdot x\right)} \leadsto \color{blue}{x \cdot 0.954929658551372 - 0.12900613773279798 \cdot {x}^3}\]
    0.4
  3. Using strategy rm
    0.4
  4. Applied cube-mult to get
    \[x \cdot 0.954929658551372 - 0.12900613773279798 \cdot \color{red}{{x}^3} \leadsto x \cdot 0.954929658551372 - 0.12900613773279798 \cdot \color{blue}{\left(x \cdot \left(x \cdot x\right)\right)}\]
    0.4
  5. Applied associate-*r* to get
    \[x \cdot 0.954929658551372 - \color{red}{0.12900613773279798 \cdot \left(x \cdot \left(x \cdot x\right)\right)} \leadsto x \cdot 0.954929658551372 - \color{blue}{\left(0.12900613773279798 \cdot x\right) \cdot \left(x \cdot x\right)}\]
    0.2
  6. Using strategy rm
    0.2
  7. Applied associate-*r* to get
    \[x \cdot 0.954929658551372 - \color{red}{\left(0.12900613773279798 \cdot x\right) \cdot \left(x \cdot x\right)} \leadsto x \cdot 0.954929658551372 - \color{blue}{\left(\left(0.12900613773279798 \cdot x\right) \cdot x\right) \cdot x}\]
    0.2
  8. Using strategy rm
    0.2
  9. Applied add-sqr-sqrt to get
    \[x \cdot 0.954929658551372 - \color{red}{\left(\left(0.12900613773279798 \cdot x\right) \cdot x\right)} \cdot x \leadsto x \cdot 0.954929658551372 - \color{blue}{{\left(\sqrt{\left(0.12900613773279798 \cdot x\right) \cdot x}\right)}^2} \cdot x\]
    0.3
  10. Applied taylor to get
    \[x \cdot 0.954929658551372 - {\left(\sqrt{\left(0.12900613773279798 \cdot x\right) \cdot x}\right)}^2 \cdot x \leadsto x \cdot 0.954929658551372 - {\left(x \cdot \sqrt{0.12900613773279798}\right)}^2 \cdot x\]
    0.2
  11. Taylor expanded around 0 to get
    \[x \cdot 0.954929658551372 - {\color{red}{\left(x \cdot \sqrt{0.12900613773279798}\right)}}^2 \cdot x \leadsto x \cdot 0.954929658551372 - {\color{blue}{\left(x \cdot \sqrt{0.12900613773279798}\right)}}^2 \cdot x\]
    0.2
  12. Applied simplify to get
    \[x \cdot 0.954929658551372 - {\left(x \cdot \sqrt{0.12900613773279798}\right)}^2 \cdot x \leadsto \left(0.954929658551372 - {x}^2 \cdot 0.12900613773279798\right) \cdot x\]
    0.2
  13. Applied final simplification

Original test:


(lambda ((x default))
  #:name "Rosa's Benchmark"
  (- (* 0.954929658551372 x) (* 0.12900613773279798 (* (* x x) x))))