Average Error: 38.1 → 25.5
Time: 3.1s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original38.1
Target25.7
Herbie25.5
\[\]

Derivation

  1. Split input into 3 regimes

  2. if x < -7.7048672890511212e131

    1. Initial program 60.2

      \[\]

    2. Taylor expanded around -inf 15.3

      \[\leadsto \]

    3. Simplified15.3

      \[\leadsto \]

    if -7.7048672890511212e131 < x < 8.60598290857993301e143

    1. Initial program 29.1

      \[\]

    if 8.60598290857993301e143 < x

    1. Initial program 62.4

      \[\]

    2. Taylor expanded around inf 16.8

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

  4. Final simplification25.5

    \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(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))))