math.abs on complex

Average Error: 31.5 → 17.2

Time: 1.8s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus re

Bits error versus im

Derivation

1. Split input into 3 regimes

2. if re < -3.4475662606183263e130

   1. Initial program 56.9

      \[\]

   2. Taylor expanded around -inf 7.7

      \[\leadsto \]

   3. Simplified 7.7

      \[\leadsto \]

   if -3.4475662606183263e130 < re < 1.8766509938470789e142

   1. Initial program 20.8

      \[\]

   if 1.8766509938470789e142 < re

   1. Initial program 60.5

      \[\]

   2. Taylor expanded around inf 8.5

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

4. Final simplification 17.2

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))