_divideComplex, real part

Average Error: 26.2 → 25.7

Time: 4.6s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus x.re

Bits error versus x.im

Bits error versus y.re

Bits error versus y.im

Derivation

1. Split input into 2 regimes

2. if (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))) < 5.0625460086701354e268

   1. Initial program 14.0

      \[\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 14.0

      \[\leadsto \]

   4. Applied associate-/r* 13.9

      \[\leadsto \]

   if 5.0625460086701354e268 < (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im)))

   1. Initial program 61.9

      \[\]
   2. Using strategy rm

   3. Applied add-sqr-sqrt 61.9

      \[\leadsto \]

   4. Applied associate-/r* 61.9

      \[\leadsto \]

   5. Taylor expanded around -inf 60.2

      \[\leadsto \]

   6. Simplified 60.2

      \[\leadsto \]
3. Recombined 2 regimes into one program.

4. Final simplification 25.7

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x.re x.im y.re y.im)
  :name "_divideComplex, real part"
  :precision binary64
  (/ (+ (* x.re y.re) (* x.im y.im)) (+ (* y.re y.re) (* y.im y.im))))