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

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))