math.abs on complex

Average Error: 32.2 → 18.1

Time: 1.9s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus re

Bits error versus im

Derivation

1. Split input into 3 regimes

2. if re < -6.7765390925841244e136

   1. Initial program 59.0

      \[\]

   2. Taylor expanded around -inf 8.7

      \[\leadsto \]

   3. Simplified 8.7

      \[\leadsto \]

   if -6.7765390925841244e136 < re < 3.4873064248462076e112

   1. Initial program 22.0

      \[\]

   if 3.4873064248462076e112 < re

   1. Initial program 54.2

      \[\]

   2. Taylor expanded around inf 9.2

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

4. Final simplification 18.1

   \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (re im)
  :name "math.abs on complex"
  :precision binary64
  (sqrt (+ (* re re) (* im im))))