\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
Test:
Expression, p6
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 14.5 s
Input Error: 4.1
Output Error: 3.4
Log: ⚲
Profile: 🕒
\(\left(a + \left(\log_* (1 + (e^{\frac{{b}^2 - {c}^2}{b - c}} - 1)^*) + d\right)\right) \cdot 2\)
  1. Started with
    \[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
    4.1
  2. Using strategy rm
    4.1
  3. Applied associate-+r+ to get
    \[\left(a + \color{red}{\left(b + \left(c + d\right)\right)}\right) \cdot 2 \leadsto \left(a + \color{blue}{\left(\left(b + c\right) + d\right)}\right) \cdot 2\]
    3.7
  4. Using strategy rm
    3.7
  5. Applied log1p-expm1-u to get
    \[\left(a + \left(\color{red}{\left(b + c\right)} + d\right)\right) \cdot 2 \leadsto \left(a + \left(\color{blue}{\log_* (1 + (e^{b + c} - 1)^*)} + d\right)\right) \cdot 2\]
    3.4
  6. Using strategy rm
    3.4
  7. Applied flip-+ to get
    \[\left(a + \left(\log_* (1 + (e^{\color{red}{b + c}} - 1)^*) + d\right)\right) \cdot 2 \leadsto \left(a + \left(\log_* (1 + (e^{\color{blue}{\frac{{b}^2 - {c}^2}{b - c}}} - 1)^*) + d\right)\right) \cdot 2\]
    3.4
  8. 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)))