Average Error: 37.9 → 25.2
Time: 3.1s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original37.9
Target25.4
Herbie25.2
\[\]

Derivation

  1. Split input into 3 regimes

  2. if x < -1.024325663364325e116

    1. Initial program 57.1

      \[\]

    2. Taylor expanded around -inf 16.2

      \[\leadsto \]

    3. Simplified16.2

      \[\leadsto \]

    if -1.024325663364325e116 < x < 4.68887343008616523e139

    1. Initial program 29.0

      \[\]

    if 4.68887343008616523e139 < x

    1. Initial program 61.5

      \[\]

    2. Taylor expanded around inf 15.8

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

  4. Final simplification25.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(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))))