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

Average Error: 37.8 → 25.6

Time: 5.0s

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	37.8
Target	25.5
Herbie	25.6

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Derivation

1. Split input into 3 regimes

2. if x < -3.04950141066242941e153

   1. Initial program 63.9

      \[\]

   2. Taylor expanded around -inf 15.0

      \[\leadsto \]

   3. Simplified 15.0

      \[\leadsto \]

   if -3.04950141066242941e153 < x < 1.2356342879637884e50

   1. Initial program 28.9

      \[\]

   2. Taylor expanded around 0 28.9

      \[\leadsto \]

   3. Simplified 28.9

      \[\leadsto \]

   if 1.2356342879637884e50 < x

   1. Initial program 48.7

      \[\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 48.7

      \[\leadsto \]

   4. Applied *-un-lft-identity 48.7

      \[\leadsto \]

   5. Applied times-frac 48.7

      \[\leadsto \]

   6. Applied sqrt-prod 48.8

      \[\leadsto \]

   7. Simplified 48.8

      \[\leadsto \]

   8. Taylor expanded around inf 21.9

      \[\leadsto \]

   9. Simplified 21.9

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

4. Final simplification 25.6

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(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)))