Average Error: 0.0 → 0.0
Time: 3.4s
Precision: 64
Internal Precision: 576
\[re \cdot re - im \cdot im\]
↓
\[\left(im + re\right) \cdot \left(re - im\right)\]

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[re \cdot re - im \cdot im\]
  2. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Runtime

Time bar (total: 3.4s)Debug logProfile

herbie shell --seed 2018217 +o rules:numerics
(FPCore (re im)
  :name "math.square on complex, real part"
  (- (* re re) (* im im)))