Average Error: 0.6 → 0.6
Time: 4.8s
Precision: 64
Internal Precision: 320
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\sqrt{re \cdot re + im \cdot im}\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 0.6

    \[\sqrt{\left(\frac{\left(re \cdot re\right)}{\left(im \cdot im\right)}\right)}\]

  2. Final simplification0.6

    \[\leadsto \sqrt{re \cdot re + im \cdot im}\]

Reproduce

herbie shell --seed 2019091 
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt.p16 (+.p16 (*.p16 re re) (*.p16 im im))))