Average Error: 37.8 → 25.2
Time: 2.7s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original37.8
Target25.6
Herbie25.2
\[\]

Derivation

  1. Split input into 3 regimes

  2. if x < -2.02546297141162418e148

    1. Initial program 62.9

      \[\]

    2. Taylor expanded around -inf 15.2

      \[\leadsto \]

    3. Simplified15.2

      \[\leadsto \]

    if -2.02546297141162418e148 < x < 1.1092401306764233e86

    1. Initial program 28.9

      \[\]

    if 1.1092401306764233e86 < x

    1. Initial program 53.6

      \[\]

    2. Taylor expanded around inf 18.2

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

  4. Final simplification25.2

    \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(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))))