sqrt B

Average Error: 30.2 → 0.4

Time: 2.2s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < 1.911069691996156e-310

   1. Initial program 29.7

      \[\]

   2. Taylor expanded around -inf 0.5

      \[\leadsto \]

   3. Simplified 0.5

      \[\leadsto \]
   4. Using strategy rm

   5. Applied add-cube-cbrt 0.5

      \[\leadsto \]

   6. Applied distribute-lft-neg-in 0.5

      \[\leadsto \]

   7. Applied associate-*r* 0.4

      \[\leadsto \]

   8. Simplified 0.4

      \[\leadsto \]

   if 1.911069691996156e-310 < x

   1. Initial program 30.7

      \[\]
   2. Using strategy rm

   3. Applied sqrt-prod 0.4

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

4. Final simplification 0.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020190 
(FPCore (x)
  :name "sqrt B"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))