2-ancestry mixing, positive discriminant

Average Error: 36.3 → 32.0

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 < -2.21602016964167287e-161

   1. Initial program 34.7

      \[\]

   2. Simplified 34.7

      \[\leadsto \]
   3. Using strategy rm

   4. Applied associate-*r/ 34.7

      \[\leadsto \]

   5. Applied cbrt-div 30.7

      \[\leadsto \]

   6. Simplified 30.7

      \[\leadsto \]

   7. Taylor expanded around -inf 30.9

      \[\leadsto \]

   8. Simplified 30.9

      \[\leadsto \]

   if -2.21602016964167287e-161 < g

   1. Initial program 37.7

      \[\]

   2. Simplified 37.7

      \[\leadsto \]
   3. Using strategy rm

   4. Applied associate-*r/ 37.7

      \[\leadsto \]

   5. Applied cbrt-div 34.1

      \[\leadsto \]

   6. Taylor expanded around inf 32.9

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

4. Final simplification 32.0

   \[\leadsto \]

Reproduce

herbie shell --seed 2020180 
(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))))))))