Average Error: 30.0 → 0.0
Time: 2.0s
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 30.0

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

  2. Applied simplify0.0

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

Runtime

Time bar (total: 2.0s)Debug logProfile

herbie shell --seed '#(1071215679 2002590028 935158157 1944352234 2656991306 2955288481)' +o rules:numerics
(FPCore (re im)
  :name "math.abs on complex"
  (sqrt (+ (* re re) (* im im))))