\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
Test:
Expression, p6
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 6.8 s
Input Error: 3.6
Output Error: 0
Log: ⚲
Profile: 🕒
\(\left(\left(d + a\right) + \left(b + c\right)\right) \cdot 2\)
  1. Started with
    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
    3.6
  2. Using strategy rm
    3.6
  3. Applied associate-+r+ to get
    \[\left(a + \color{red}{\left(b + \left(c + d\right)\right)}\right) \cdot 2 \leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
    2.7
  4. Using strategy rm
    2.7
  5. Applied log1p-expm1-u to get
    \[\color{red}{\left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2 \leadsto \color{blue}{\log_* (1 + (e^{a + \left(\left(b + c\right) + d\right)} - 1)^*)} \cdot 2\]
    2.7
  6. Applied taylor to get
    \[\log_* (1 + (e^{a + \left(\left(b + c\right) + d\right)} - 1)^*) \cdot 2 \leadsto \log_* (1 + (e^{b + \left(c + \left(d + a\right)\right)} - 1)^*) \cdot 2\]
    0.1
  7. Taylor expanded around 0 to get
    \[\log_* (1 + \color{red}{(e^{b + \left(c + \left(d + a\right)\right)} - 1)^*}) \cdot 2 \leadsto \log_* (1 + \color{blue}{(e^{b + \left(c + \left(d + a\right)\right)} - 1)^*}) \cdot 2\]
    0.1
  8. Applied simplify to get
    \[\color{red}{\log_* (1 + (e^{b + \left(c + \left(d + a\right)\right)} - 1)^*) \cdot 2} \leadsto \color{blue}{\left(\left(d + a\right) + \left(b + c\right)\right) \cdot 2}\]
    0
  9. Removed slow pow expressions

Original test:


(lambda ((a (uniform -14 -13)) (b (uniform -3 -2)) (c (uniform 3 3.5)) (d (uniform 12.5 13.5)))
  #:name "Expression, p6"
  (* (+ a (+ b (+ c d))) 2)
  #:target
  (+ (* (+ a b) 2) (* (+ c d) 2)))