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

Average Error: 37.6 → 24.7

Time: 4.2s

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	37.6
Target	25.7
Herbie	24.7

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Derivation

1. Split input into 3 regimes

2. if x < -1.4682484161638135e132

   1. Initial program 60.1

      \[\]

   2. Taylor expanded around -inf 14.8

      \[\leadsto \]

   3. Simplified 14.8

      \[\leadsto \]

   if -1.4682484161638135e132 < x < 3.0752650640767227e117

   1. Initial program 28.6

      \[\]

   2. Taylor expanded around 0 28.6

      \[\leadsto \]

   3. Simplified 28.6

      \[\leadsto \]

   if 3.0752650640767227e117 < x

   1. Initial program 57.0

      \[\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 57.0

      \[\leadsto \]

   4. Applied *-un-lft-identity 57.0

      \[\leadsto \]

   5. Applied times-frac 57.0

      \[\leadsto \]

   6. Applied sqrt-prod 57.0

      \[\leadsto \]

   7. Simplified 57.0

      \[\leadsto \]

   8. Taylor expanded around inf 16.6

      \[\leadsto \]

   9. Simplified 16.6

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

4. Final simplification 24.7

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(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)))