Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1

Average Error: 38.2 → 26.7

Time: 3.4s

Precision: binary64

Math

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↓

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Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	38.2
Target	26.2
Herbie	26.7

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Derivation

1. Split input into 4 regimes

2. if x < -1.95445500961015716e112

   1. Initial program 55.6

      \[\]

   2. Taylor expanded around -inf 17.7

      \[\leadsto \]

   3. Simplified 17.7

      \[\leadsto \]

   if -1.95445500961015716e112 < x < -6.7336058996915783e-215 or -1.81250657436522472e-266 < x < 3.2526274382715766e104

   1. Initial program 29.7

      \[\]

   2. Taylor expanded around 0 29.8

      \[\leadsto \]

   3. Simplified 29.8

      \[\leadsto \]

   if -6.7336058996915783e-215 < x < -1.81250657436522472e-266

   1. Initial program 34.0

      \[\]
   2. Using strategy rm

   3. Applied sqrt-div 34.1

      \[\leadsto \]

   4. Simplified 34.1

      \[\leadsto \]

   5. Taylor expanded around 0 47.1

      \[\leadsto \]

   if 3.2526274382715766e104 < x

   1. Initial program 55.2

      \[\]
   2. Using strategy rm

   3. Applied sqrt-div 55.2

      \[\leadsto \]

   4. Simplified 55.2

      \[\leadsto \]

   5. Taylor expanded around inf 18.5

      \[\leadsto \]
3. Recombined 4 regimes into one program.

4. Final simplification 26.7

   \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(FPCore (x y z)
  :name "Data.Array.Repa.Algorithms.Pixel:doubleRmsOfRGB8 from repa-algorithms-3.4.0.1"
  :precision binary64

  :herbie-target
  (if (< z -6.396479394109776e+136) (/ (neg z) (sqrt 3.0)) (if (< z 7.320293694404182e+117) (/ (sqrt (+ (+ (* z z) (* x x)) (* y y))) (sqrt 3.0)) (* (sqrt 0.3333333333333333) z)))

  (sqrt (/ (+ (+ (* x x) (* y y)) (* z z)) 3.0)))