math.log/1 on complex, real part

Average Error: 31.3 → 16.9

Time: 1.6s

Precision: binary64

Math

\[\]

↓

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Error

Bits error versus re

Bits error versus im

Derivation

1. Split input into 3 regimes

2. if re < -3.3662080223699987e135

   1. Initial program 58.9

      \[\]

   2. Taylor expanded around -inf 7.1

      \[\leadsto \]

   3. Simplified 7.1

      \[\leadsto \]

   if -3.3662080223699987e135 < re < 1.28420524529039342e121

   1. Initial program 20.8

      \[\]

   if 1.28420524529039342e121 < re

   1. Initial program 54.7

      \[\]

   2. Taylor expanded around inf 7.9

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

4. Final simplification 16.9

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))