2-ancestry mixing, positive discriminant

Average Error: 36.0 → 31.8

Time: 8.4s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus g

Bits error versus h

Bits error versus a

Derivation

1. Split input into 2 regimes

2. if g < -4.39214081702909474e-199

   1. Initial program 35.1

      \[\]
   2. Using strategy rm

   3. Applied associate-*l/ 35.1

      \[\leadsto \]

   4. Applied cbrt-div 31.6

      \[\leadsto \]

   5. Simplified 31.6

      \[\leadsto \]

   if -4.39214081702909474e-199 < g

   1. Initial program 36.7

      \[\]
   2. Using strategy rm

   3. Applied associate-*l/ 36.7

      \[\leadsto \]

   4. Applied cbrt-div 33.0

      \[\leadsto \]

   5. Taylor expanded around inf 32.0

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

4. Final simplification 31.8

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (neg g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (neg g) (sqrt (- (* g g) (* h h))))))))