\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
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: 6.2 s
Input Error: 0.4
Output Error: 0.2
Log: ⚲
Profile: 🕒
\(\left(\left(a + b\right) + \left(c + d\right)\right) + e\)
  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
    \[\left(\color{red}{\left(\left(e + d\right) + c\right)} + b\right) + a \leadsto \left(\color{blue}{\left(e + \left(d + c\right)\right)} + b\right) + a\]
    0.4
  4. Using strategy rm
    0.4
  5. Applied add-sqr-sqrt to get
    \[\left(\color{red}{\left(e + \left(d + c\right)\right)} + b\right) + a \leadsto \left(\color{blue}{{\left(\sqrt{e + \left(d + c\right)}\right)}^2} + b\right) + a\]
    0.6
  6. Applied taylor to get
    \[\left({\left(\sqrt{e + \left(d + c\right)}\right)}^2 + b\right) + a \leadsto \left({\left(\sqrt{c + \left(d + e\right)}\right)}^2 + b\right) + a\]
    0.6
  7. Taylor expanded around 0 to get
    \[\left({\left(\sqrt{\color{red}{c + \left(d + e\right)}}\right)}^2 + b\right) + a \leadsto \left({\left(\sqrt{\color{blue}{c + \left(d + e\right)}}\right)}^2 + b\right) + a\]
    0.6
  8. Applied simplify to get
    \[\left({\left(\sqrt{c + \left(d + e\right)}\right)}^2 + b\right) + a \leadsto \left(\left(a + b\right) + \left(c + d\right)\right) + e\]
    0.2
  9. Applied final simplification

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))