Average Error: 24.5 → 0.7
Time: 3.0s
Precision: binary64
\[\]
↓
\[\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original24.5
Target0.6
Herbie0.7
\[\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3.06044798588869561e-273

    1. Initial program 24.5

      \[\]

    2. Taylor expanded around -inf 0.6

      \[\leadsto \]

    3. Simplified0.6

      \[\leadsto \]

    if -3.06044798588869561e-273 < y

    1. Initial program 24.6

      \[\]

    2. Taylor expanded around inf 0.8

      \[\leadsto \]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B"
  :precision binary64

  :herbie-target
  (if (< y 2.5816096488251695e-278) (neg (* x y)) (* x (* (sqrt (+ y z)) (sqrt (- y z)))))

  (* x (sqrt (- (* y y) (* z z)))))