\[\left(a + \left(b + \left(c + d\right)\right)\right) \cdot 2\]
Test:
Expression, p6
Bits:
128 bits
Bits error versus a
Bits error versus b
Bits error versus c
Bits error versus d
Time: 19.1 s
Input Error: 4.1
Output Error: 3.5
Log: ⚲
Profile: 🕒
\(\left(\left(\left(a - d\right) \cdot \left(d + a\right) - \left(2 \cdot c\right) \cdot d\right) - \left(\left({b}^2 + {c}^2\right) + \left(d + c\right) \cdot \left(b \cdot 2\right)\right)\right) \cdot \frac{2}{\left(a - b\right) - \left(d + c\right)}\)
  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 add-cube-cbrt to get
    \[\color{red}{\left(a + \left(\left(b + c\right) + d\right)\right)} \cdot 2 \leadsto \color{blue}{{\left(\sqrt[3]{a + \left(\left(b + c\right) + d\right)}\right)}^3} \cdot 2\]
    3.7
  6. Using strategy rm
    3.7
  7. Applied flip-+ to get
    \[{\left(\sqrt[3]{\color{red}{a + \left(\left(b + c\right) + d\right)}}\right)}^3 \cdot 2 \leadsto {\left(\sqrt[3]{\color{blue}{\frac{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}{a - \left(\left(b + c\right) + d\right)}}}\right)}^3 \cdot 2\]
    3.8
  8. Applied cbrt-div to get
    \[{\color{red}{\left(\sqrt[3]{\frac{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}{a - \left(\left(b + c\right) + d\right)}}\right)}}^3 \cdot 2 \leadsto {\color{blue}{\left(\frac{\sqrt[3]{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}}{\sqrt[3]{a - \left(\left(b + c\right) + d\right)}}\right)}}^3 \cdot 2\]
    3.8
  9. Applied cube-div to get
    \[\color{red}{{\left(\frac{\sqrt[3]{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}}{\sqrt[3]{a - \left(\left(b + c\right) + d\right)}}\right)}^3} \cdot 2 \leadsto \color{blue}{\frac{{\left(\sqrt[3]{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}\right)}^3}{{\left(\sqrt[3]{a - \left(\left(b + c\right) + d\right)}\right)}^3}} \cdot 2\]
    3.8
  10. Applied simplify to get
    \[\frac{{\left(\sqrt[3]{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}\right)}^3}{\color{red}{{\left(\sqrt[3]{a - \left(\left(b + c\right) + d\right)}\right)}^3}} \cdot 2 \leadsto \frac{{\left(\sqrt[3]{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}\right)}^3}{\color{blue}{\left(a - b\right) - \left(d + c\right)}} \cdot 2\]
    3.8
  11. Applied taylor to get
    \[\frac{{\left(\sqrt[3]{{a}^2 - {\left(\left(b + c\right) + d\right)}^2}\right)}^3}{\left(a - b\right) - \left(d + c\right)} \cdot 2 \leadsto \frac{{\left(\sqrt[3]{{a}^2 - \left({d}^2 + \left(2 \cdot \left(c \cdot d\right) + \left({c}^2 + \left(2 \cdot \left(b \cdot d\right) + \left(2 \cdot \left(b \cdot c\right) + {b}^2\right)\right)\right)\right)\right)}\right)}^3}{\left(a - b\right) - \left(d + c\right)} \cdot 2\]
    3.7
  12. Taylor expanded around 0 to get
    \[\frac{{\color{red}{\left(\sqrt[3]{{a}^2 - \left({d}^2 + \left(2 \cdot \left(c \cdot d\right) + \left({c}^2 + \left(2 \cdot \left(b \cdot d\right) + \left(2 \cdot \left(b \cdot c\right) + {b}^2\right)\right)\right)\right)\right)}\right)}}^3}{\left(a - b\right) - \left(d + c\right)} \cdot 2 \leadsto \frac{{\color{blue}{\left(\sqrt[3]{{a}^2 - \left({d}^2 + \left(2 \cdot \left(c \cdot d\right) + \left({c}^2 + \left(2 \cdot \left(b \cdot d\right) + \left(2 \cdot \left(b \cdot c\right) + {b}^2\right)\right)\right)\right)\right)}\right)}}^3}{\left(a - b\right) - \left(d + c\right)} \cdot 2\]
    3.7
  13. Applied simplify to get
    \[\frac{{\left(\sqrt[3]{{a}^2 - \left({d}^2 + \left(2 \cdot \left(c \cdot d\right) + \left({c}^2 + \left(2 \cdot \left(b \cdot d\right) + \left(2 \cdot \left(b \cdot c\right) + {b}^2\right)\right)\right)\right)\right)}\right)}^3}{\left(a - b\right) - \left(d + c\right)} \cdot 2 \leadsto 2 \cdot \frac{\left(\left(a + d\right) \cdot \left(a - d\right) - 2 \cdot \left(c \cdot d\right)\right) - \left(\left(c \cdot c + b \cdot b\right) + \left(b \cdot 2\right) \cdot \left(d + c\right)\right)}{\left(a - b\right) - \left(d + c\right)}\]
    3.5
  14. Applied final simplification
  15. Applied simplify to get
    \[\color{red}{2 \cdot \frac{\left(\left(a + d\right) \cdot \left(a - d\right) - 2 \cdot \left(c \cdot d\right)\right) - \left(\left(c \cdot c + b \cdot b\right) + \left(b \cdot 2\right) \cdot \left(d + c\right)\right)}{\left(a - b\right) - \left(d + c\right)}} \leadsto \color{blue}{\left(\left(\left(a - d\right) \cdot \left(d + a\right) - \left(2 \cdot c\right) \cdot d\right) - \left(\left({b}^2 + {c}^2\right) + \left(d + c\right) \cdot \left(b \cdot 2\right)\right)\right) \cdot \frac{2}{\left(a - b\right) - \left(d + c\right)}}\]
    3.5
  16. 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)))