sqrt A

Average Error: 30.5 → 0.4

Time: 2.1s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus x

Derivation

1. Split input into 2 regimes

2. if x < 3.741153125096705e-310

   1. Initial program 30.4

      \[\]

   2. Simplified 30.4

      \[\leadsto \]

   3. Taylor expanded around -inf 0.4

      \[\leadsto \]

   4. Simplified 0.4

      \[\leadsto \]
   5. Using strategy rm

   6. Applied add-cube-cbrt 0.4

      \[\leadsto \]

   7. Applied distribute-lft-neg-in 0.4

      \[\leadsto \]

   8. Applied associate-*r* 0.4

      \[\leadsto \]

   9. Simplified 0.4

      \[\leadsto \]

   if 3.741153125096705e-310 < x

   1. Initial program 30.5

      \[\]

   2. Simplified 30.5

      \[\leadsto \]

   3. Taylor expanded around 0 0.4

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

4. Final simplification 0.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (x)
  :name "sqrt A"
  :precision binary64
  (sqrt (+ (* x x) (* x x))))