math.abs on complex

Average Error: 31.0 → 17.6

Time: 1.5s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus re

Bits error versus im

Derivation

1. Split input into 3 regimes

2. if re < -2.3287772795912036e57

   1. Initial program 45.5

      \[\]

   2. Taylor expanded around -inf 12.3

      \[\leadsto \]

   3. Simplified 12.3

      \[\leadsto \]

   if -2.3287772795912036e57 < re < 7.5384845989707597e108

   1. Initial program 21.0

      \[\]

   if 7.5384845989707597e108 < re

   1. Initial program 53.0

      \[\]

   2. Taylor expanded around inf 10.6

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

4. Final simplification 17.6

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))