Average Error: 37.8 → 24.8
Time: 2.5s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original37.8
Target25.8
Herbie24.8
\[\]

Derivation

  1. Split input into 3 regimes

  2. if x < -2.90586819968306291e135

    1. Initial program 60.5

      \[\]

    2. Taylor expanded around -inf 14.0

      \[\leadsto \]

    3. Simplified14.0

      \[\leadsto \]

    if -2.90586819968306291e135 < x < 1.60624816861743642e135

    1. Initial program 29.0

      \[\]

    if 1.60624816861743642e135 < x

    1. Initial program 60.0

      \[\]

    2. Taylor expanded around inf 14.7

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

  4. Final simplification24.8

    \[\leadsto \]

Reproduce

herbie shell --seed 2020192 
(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))))