Average Error: 0.4 → 0.4
Time: 8.1m
Precision: 64
Internal Precision: 384
\[\left(\left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + x5\right) + x6\right) + x7\]
↓
\[\left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + \left(x5 + x6\right)\right) + x7\]

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

    \[\leadsto \color{blue}{\left(\left(\left(\left(\left(x0 + x1\right) + x2\right) + x3\right) + x4\right) + \left(x5 + x6\right)\right)} + x7\]

Runtime

Time bar (total: 8.1m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(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))