\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
Test:
Expression 1, p15
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Bits error versus e
Time: 14.6 s
Input Error: 0.4
Output Error: 0.2
Log: ⚲
Profile: 🕒
\(\log \left(e^{d + b}\right) + \left(e + \left(c + a\right)\right)\)
  1. Started with
    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
    0.4
  2. Using strategy rm
    0.4
  3. Applied associate-+l+ to get
    \[\color{red}{\left(\left(\left(e + d\right) + c\right) + b\right)} + a \leadsto \color{blue}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a\]
    0.4
  4. Using strategy rm
    0.4
  5. Applied add-log-exp to get
    \[\left(\left(e + d\right) + \color{red}{\left(c + b\right)}\right) + a \leadsto \left(\left(e + d\right) + \color{blue}{\log \left(e^{c + b}\right)}\right) + a\]
    0.4
  6. Applied add-log-exp to get
    \[\left(\color{red}{\left(e + d\right)} + \log \left(e^{c + b}\right)\right) + a \leadsto \left(\color{blue}{\log \left(e^{e + d}\right)} + \log \left(e^{c + b}\right)\right) + a\]
    0.4
  7. Applied sum-log to get
    \[\color{red}{\left(\log \left(e^{e + d}\right) + \log \left(e^{c + b}\right)\right)} + a \leadsto \color{blue}{\log \left(e^{e + d} \cdot e^{c + b}\right)} + a\]
    0.4
  8. Applied simplify to get
    \[\log \color{red}{\left(e^{e + d} \cdot e^{c + b}\right)} + a \leadsto \log \color{blue}{\left(e^{\left(d + b\right) + \left(c + e\right)}\right)} + a\]
    0.3
  9. Using strategy rm
    0.3
  10. Applied exp-sum to get
    \[\log \color{red}{\left(e^{\left(d + b\right) + \left(c + e\right)}\right)} + a \leadsto \log \color{blue}{\left(e^{d + b} \cdot e^{c + e}\right)} + a\]
    0.3
  11. Applied log-prod to get
    \[\color{red}{\log \left(e^{d + b} \cdot e^{c + e}\right)} + a \leadsto \color{blue}{\left(\log \left(e^{d + b}\right) + \log \left(e^{c + e}\right)\right)} + a\]
    0.3
  12. Applied associate-+l+ to get
    \[\color{red}{\left(\log \left(e^{d + b}\right) + \log \left(e^{c + e}\right)\right) + a} \leadsto \color{blue}{\log \left(e^{d + b}\right) + \left(\log \left(e^{c + e}\right) + a\right)}\]
    0.3
  13. Applied simplify to get
    \[\log \left(e^{d + b}\right) + \color{red}{\left(\log \left(e^{c + e}\right) + a\right)} \leadsto \log \left(e^{d + b}\right) + \color{blue}{\left(e + \left(c + a\right)\right)}\]
    0.2

Original test:


(lambda ((a (uniform 1 2)) (b (uniform 2 4)) (c (uniform 4 8)) (d (uniform 8 16)) (e (uniform 16 32)))
  #:name "Expression 1, p15"
  (+ (+ (+ (+ e d) c) b) a)
  #:target
  (+ (+ d (+ c (+ a b))) e))