Average Error: 0.4 → 0.2
Time: 10.7s
Precision: 64
Internal precision: 384
\[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
⬇
\[\log \left(e^{\left(e + c\right) + \left(a + \left(b + d\right)\right)}\right)\]

Error

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Target

Original0.4
Comparison0.2
Herbie0.2
\[ \left(d + \left(c + \left(a + b\right)\right)\right) + e \]

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(e + d\right) + c\right) + b\right) + a\]
  2. Using strategy rm

  3. Applied associate-+l+ 0.3

    \[\leadsto \color{blue}{\left(\left(e + d\right) + c\right) + \left(b + a\right)}\]
  4. Using strategy rm

  5. Applied add-log-exp 0.3

    \[\leadsto \left(\left(e + d\right) + c\right) + \color{blue}{\log \left(e^{b + a}\right)}\]

  6. Applied add-log-exp 0.3

    \[\leadsto \color{blue}{\log \left(e^{\left(e + d\right) + c}\right)} + \log \left(e^{b + a}\right)\]

  7. Applied sum-log 0.3

    \[\leadsto \color{blue}{\log \left(e^{\left(e + d\right) + c} \cdot e^{b + a}\right)}\]

  8. Applied simplify 0.2

    \[\leadsto \log \color{blue}{\left(e^{\left(e + c\right) + \left(a + \left(b + d\right)\right)}\right)}\]
  9. Removed slow pow expressions

Runtime

Time bar (total: 10.7s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(FPCore (a b c d e)
  :name "Expression 1, p15"
  :pre (<= 1 a 2 b 4 c 8 d 16 e 32)

  :target
  (+ (+ d (+ c (+ a b))) e)

  (+ (+ (+ (+ e d) c) b) a))