math.abs on complex

Average Error: 31.8 → 18.3

Time: 2.9s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus re

Bits error versus im

Derivation

1. Split input into 3 regimes

2. if re < -1.69098607420795857e60

   1. Initial program 44.5

      \[\]

   2. Taylor expanded around -inf 12.0

      \[\leadsto \]

   3. Simplified 12.0

      \[\leadsto \]

   if -1.69098607420795857e60 < re < 4.2484476987621222e82

   1. Initial program 22.6

      \[\]

   if 4.2484476987621222e82 < re

   1. Initial program 48.9

      \[\]

   2. Taylor expanded around inf 11.0

      \[\leadsto \]
3. Recombined 3 regimes into one program.

4. Final simplification 18.3

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))