Average Error: 29.5 → 0.0
Time: 1.1s
Precision: 64
Internal Precision: 320
\[\sqrt{re \cdot re + im \cdot im}\]
↓
\[\sqrt{re^2 + im^2}^*\]

Error

Bits error versus re

Bits error versus im

Derivation

  1. Initial program 29.5

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

  2. Applied simplify0.0

    \[\leadsto \color{blue}{\sqrt{re^2 + im^2}^*}\]

Runtime

Time bar (total: 1.1s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))