Linear.Quaternion:$clog from linear-1.19.1.3

Average Error: 21.2 → 0.5

Time: 1.6s

Precision: binary64

Math

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↓

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Error

Bits error versus x

Bits error versus y

Target

Original	21.2
Target	0.4
Herbie	0.5

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Derivation

1. Split input into 3 regimes

2. if x < -8.9999582525827406e135

   1. Initial program 57.1

      \[\]

   2. Taylor expanded around -inf 0.3

      \[\leadsto \]

   3. Simplified 0.3

      \[\leadsto \]

   if -8.9999582525827406e135 < x < 5.73985145420372766e55

   1. Initial program 0.0

      \[\]

   if 5.73985145420372766e55 < x

   1. Initial program 39.5

      \[\]

   2. Taylor expanded around inf 1.7

      \[\leadsto \]

   3. Simplified 1.7

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

4. Final simplification 0.5

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (x y)
  :name "Linear.Quaternion:$clog from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (if (< x -1.5097698010472593e+153) (neg (+ (* 0.5 (/ y x)) x)) (if (< x 5.582399551122541e+57) (sqrt (+ (* x x) y)) (+ (* 0.5 (/ y x)) x)))

  (sqrt (+ (* x x) y)))