Average Error: 0.2 → 0
Time: 4.7s
Precision: 64
Internal Precision: 320
\[d \cdot 10 + d \cdot 20\]
↓
\[d \cdot \left(20 + 10\right)\]

Error

Bits error versus d

Derivation

  1. Initial program 0.2

    \[\frac{\left(d \cdot \left(real->posit(10)\right)\right)}{\left(d \cdot \left(real->posit(20)\right)\right)}\]

  2. Simplified0

    \[\leadsto \color{blue}{d \cdot \left(\frac{\left(real->posit(20)\right)}{\left(real->posit(10)\right)}\right)}\]

  3. Final simplification0

    \[\leadsto d \cdot \left(20 + 10\right)\]

Reproduce

herbie shell --seed 2019094 +o rules:numerics
(FPCore (d)
  :name "FastMath test1"
  (+.p16 (*.p16 d (real->posit16 10)) (*.p16 d (real->posit16 20))))