\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
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: 7.7 s
Input Error: 0.4
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\left(a + \left(b + c\right)\right) + \left(d + e\right)\)
  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
    \[\color{red}{\left(\left(\left(e + d\right) + c\right) + b\right)} + a \leadsto \color{blue}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a\]
    0.3
  4. Using strategy rm
    0.3
  5. Applied expm1-log1p-u to get
    \[\color{red}{\left(\left(e + d\right) + \left(c + b\right)\right)} + a \leadsto \color{blue}{(e^{\log_* (1 + \left(\left(e + d\right) + \left(c + b\right)\right))} - 1)^*} + a\]
    0.8
  6. Applied taylor to get
    \[(e^{\log_* (1 + \left(\left(e + d\right) + \left(c + b\right)\right))} - 1)^* + a \leadsto (e^{\log_* (1 + \left(b + \left(c + \left(d + e\right)\right)\right))} - 1)^* + a\]
    0.8
  7. Taylor expanded around 0 to get
    \[\color{red}{(e^{\log_* (1 + \left(b + \left(c + \left(d + e\right)\right)\right))} - 1)^*} + a \leadsto \color{blue}{(e^{\log_* (1 + \left(b + \left(c + \left(d + e\right)\right)\right))} - 1)^*} + a\]
    0.8
  8. Applied simplify to get
    \[(e^{\log_* (1 + \left(b + \left(c + \left(d + e\right)\right)\right))} - 1)^* + a \leadsto \left(a + \left(b + c\right)\right) + \left(d + e\right)\]
    0.3
  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))