Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
Internal Precision: 576
\[re \cdot im + im \cdot re\]
↓
\[\left(re + re\right) \cdot im\]

Error

Bits error versus re

Bits error versus im

Try it out

  1. Inputs

  2. Original Output:

    Herbie Output:

Derivation

  1. Initial program 0.0

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

  2. Applied simplify0.0

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

Runtime

Time bar (total: 1.4s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, imaginary part"
  (+ (* re im) (* im re)))