Average Error: 0.4 → 0.2
Time: 38.0s
Precision: 64
Internal precision: 384
\[\left(\left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5\right) + x6\right) + x7\]
\[\log \left(e^{\left(\left(x7 + x6\right) + \left(x5 + x4\right)\right) + \left(\left(x2 + x1\right) + \left(x0 + x3\right)\right)}\right)\]

Error

Bits error versus x0

Bits error versus x1

Bits error versus x2

Bits error versus x3

Bits error versus x4

Bits error versus x5

Bits error versus x6

Bits error versus x7

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5\right) + x6\right) + x7\]
  2. Using strategy rm
  3. Applied associate-+l+ 0.4

    \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5\right) + \left(x6 + x7\right)}\]
  4. Using strategy rm
  5. Applied add-log-exp 0.4

    \[\leadsto \left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5\right) + \color{blue}{\log \left(e^{x6 + x7}\right)}\]
  6. Applied add-log-exp 0.4

    \[\leadsto \color{blue}{\log \left(e^{\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5}\right)} + \log \left(e^{x6 + x7}\right)\]
  7. Applied sum-log 0.4

    \[\leadsto \color{blue}{\log \left(e^{\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5} \cdot e^{x6 + x7}\right)}\]
  8. Applied simplify 0.2

    \[\leadsto \log \color{blue}{\left(e^{\left(\left(x7 + x6\right) + \left(x5 + x4\right)\right) + \left(\left(x2 + x1\right) + \left(x0 + x3\right)\right)}\right)}\]
  9. Removed slow pow expressions

Runtime

Time bar (total: 38.0s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (x0 x1 x2 x3 x4 x5 x6 x7)
  :name "test02_sum8"
  :pre (and (< 1 x0 2) (< 1 x1 2) (< 1 x2 2) (< 1 x3 2) (< 1 x4 2) (< 1 x5 2) (< 1 x6 2) (< 1 x7 2))
  (+ (+ (+ (+ (+ (+ (+ x0 x1) x2) x3) x4) x5) x6) x7))