Average Error: 38.3 → 26.9
Time: 5.6s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original38.3
Target25.7
Herbie26.9
\[\]

Derivation

  1. Split input into 5 regimes

  2. if x < -3.29040423208750134e146

    1. Initial program 62.0

      \[\]

    2. Taylor expanded around -inf 15.2

      \[\leadsto \]

    3. Simplified15.2

      \[\leadsto \]

    if -3.29040423208750134e146 < x < 2.5655741827255853e-127

    1. Initial program 30.5

      \[\]
    2. Using strategy rm

    3. Applied add-cube-cbrt30.5

      \[\leadsto \]

    4. Applied add-sqr-sqrt30.5

      \[\leadsto \]

    5. Applied times-frac30.5

      \[\leadsto \]

    6. Applied sqrt-prod30.6

      \[\leadsto \]

    7. Simplified30.6

      \[\leadsto \]

    8. Simplified30.6

      \[\leadsto \]

    if 2.5655741827255853e-127 < x < 9.27267059557563286e-80

    1. Initial program 28.7

      \[\]
    2. Using strategy rm

    3. Applied add-sqr-sqrt28.9

      \[\leadsto \]

    4. Applied add-sqr-sqrt28.9

      \[\leadsto \]

    5. Applied times-frac28.8

      \[\leadsto \]

    6. Applied sqrt-prod29.0

      \[\leadsto \]

    7. Simplified29.0

      \[\leadsto \]

    8. Simplified29.0

      \[\leadsto \]

    9. Taylor expanded around 0 48.0

      \[\leadsto \]

    if 9.27267059557563286e-80 < x < 1.86734213565976303e76

    1. Initial program 27.8

      \[\]

    if 1.86734213565976303e76 < x

    1. Initial program 52.6

      \[\]

    2. Taylor expanded around inf 20.0

      \[\leadsto \]
  3. Recombined 5 regimes into one program.

  4. Final simplification26.9

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(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)))