Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
Internal Precision: 128
\[re \cdot im + im \cdot re\]
↓
\[im \cdot \left(re + re\right)\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.0

    \[re \cdot im + im \cdot re\]

  2. Simplified0.0

    \[\leadsto \color{blue}{im \cdot \left(re + re\right)}\]

  3. Final simplification0.0

    \[\leadsto im \cdot \left(re + re\right)\]

Reproduce

herbie shell --seed 2019068 
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))