\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
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: 11.0 s
Input Error: 0.4
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\log_* (1 + (e^{\frac{\left(c + e\right) + \left(b + d\right)}{1}} - 1)^*) + a\)
  1. Started with
    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
    0.4
  2. Using strategy rm
    0.4
  3. Applied flip-+ to get
    \[\color{red}{\left(\left(\left(e + d\right) + c\right) + b\right)} + a \leadsto \color{blue}{\frac{{\left(\left(e + d\right) + c\right)}^2 - {b}^2}{\left(\left(e + d\right) + c\right) - b}} + a\]
    0.5
  4. Using strategy rm
    0.5
  5. Applied log1p-expm1-u to get
    \[\color{red}{\frac{{\left(\left(e + d\right) + c\right)}^2 - {b}^2}{\left(\left(e + d\right) + c\right) - b}} + a \leadsto \color{blue}{\log_* (1 + (e^{\frac{{\left(\left(e + d\right) + c\right)}^2 - {b}^2}{\left(\left(e + d\right) + c\right) - b}} - 1)^*)} + a\]
    0.5
  6. Applied simplify to get
    \[\log_* (1 + \color{red}{(e^{\frac{{\left(\left(e + d\right) + c\right)}^2 - {b}^2}{\left(\left(e + d\right) + c\right) - b}} - 1)^*}) + a \leadsto \log_* (1 + \color{blue}{(e^{\frac{\left(c + e\right) + \left(b + d\right)}{1}} - 1)^*}) + a\]
    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))