\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
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: 13.7 s
Input Error: 0.4
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\left(\left(b + c\right) + \left(a + e\right)\right) + d\)
  1. Started with
    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
    0.4
  2. Using strategy rm
    0.4
  3. Applied add-cbrt-cube to get
    \[\color{red}{\left(\left(\left(e + d\right) + c\right) + b\right) + a} \leadsto \color{blue}{\sqrt[3]{{\left(\left(\left(\left(e + d\right) + c\right) + b\right) + a\right)}^3}}\]
    0.7
  4. Applied taylor to get
    \[\sqrt[3]{{\left(\left(\left(\left(e + d\right) + c\right) + b\right) + a\right)}^3} \leadsto \sqrt[3]{{\left(b + \left(c + \left(d + \left(e + a\right)\right)\right)\right)}^3}\]
    0.7
  5. Taylor expanded around 0 to get
    \[\sqrt[3]{\color{red}{{\left(b + \left(c + \left(d + \left(e + a\right)\right)\right)\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(b + \left(c + \left(d + \left(e + a\right)\right)\right)\right)}^3}}\]
    0.7
  6. Applied simplify to get
    \[\sqrt[3]{{\left(b + \left(c + \left(d + \left(e + a\right)\right)\right)\right)}^3} \leadsto \left(\left(b + c\right) + \left(a + e\right)\right) + d\]
    0.3
  7. 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))