FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2

Average Error: 38.3 → 27.0

Time: 3.6s

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	38.3
Target	25.7
Herbie	27.0

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Derivation

1. Split input into 4 regimes

2. if x < -1.04843673512673666e83

   1. Initial program 52.8

      \[\]

   2. Taylor expanded around -inf 19.5

      \[\leadsto \]

   3. Simplified 19.5

      \[\leadsto \]

   if -1.04843673512673666e83 < x < -1.4341076108923288e-274 or 3.02876797301242108e-270 < x < 1.9243525779759927e64

   1. Initial program 29.8

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   if -1.4341076108923288e-274 < x < 3.02876797301242108e-270

   1. Initial program 31.4

      \[\]

   2. Taylor expanded around 0 47.1

      \[\leadsto \]

   if 1.9243525779759927e64 < x

   1. Initial program 50.8

      \[\]

   2. Taylor expanded around inf 20.2

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

4. Final simplification 27.0

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x y z)
  :name "FRP.Yampa.Vector3:vector3Rho from Yampa-0.10.2"
  :precision binary64

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

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