\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
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: 🕒
\(\left(\left(a + d\right) + \left(c + b\right)\right) \cdot 2\)
  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 add-cube-cbrt to get
    \[\color{red}{\left(a + \left(b + \left(c + d\right)\right)\right)} \cdot 2 \leadsto \color{blue}{{\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)}^3} \cdot 2\]
    3.8
  4. Applied taylor to get
    \[{\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)}^3 \cdot 2 \leadsto {\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)}^3 \cdot 2\]
    3.8
  5. Taylor expanded around 0 to get
    \[{\left(\sqrt[3]{a + \color{red}{\left(b + \left(c + d\right)\right)}}\right)}^3 \cdot 2 \leadsto {\left(\sqrt[3]{a + \color{blue}{\left(b + \left(c + d\right)\right)}}\right)}^3 \cdot 2\]
    3.8
  6. Applied simplify to get
    \[{\left(\sqrt[3]{a + \left(b + \left(c + d\right)\right)}\right)}^3 \cdot 2 \leadsto \left(\left(a + d\right) + \left(c + b\right)\right) \cdot 2\]
    0
  7. Applied final simplification
  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)))