Average Error: 0.4 → 0.1
Time: 1.2m
Precision: 64
Internal Precision: 384
\[\left(\left(\left(x0 + x1\right) - x2\right) + \left(\left(x1 + x2\right) - x0\right)\right) + \left(\left(x2 + x0\right) - x1\right)\]
↓
\[\left(x1 + x0\right) - \left(\left(-x1\right) + \left(x1 - x2\right)\right)\]

Error

Bits error versus x0

Bits error versus x1

Bits error versus x2

Derivation

  1. Initial program 0.4

    \[\left(\left(\left(x0 + x1\right) - x2\right) + \left(\left(x1 + x2\right) - x0\right)\right) + \left(\left(x2 + x0\right) - x1\right)\]

  2. Applied simplify0.1

    \[\leadsto \color{blue}{\left(x1 + x0\right) - \left(\left(-x1\right) + \left(x1 - x2\right)\right)}\]

Runtime

Time bar (total: 1.2m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (x0 x1 x2)
  :name "test01_sum3"
  :pre (and (< 1 x0 2) (< 1 x1 2) (< 1 x2 2))
  (+ (+ (- (+ x0 x1) x2) (- (+ x1 x2) x0)) (- (+ x2 x0) x1)))