Maksimov and Kolovsky, Equation (4)

Average Error: 17.3 → 0.4

Time: 8.1s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus J

Bits error versus l

Bits error versus K

Bits error versus U

Derivation

1. Initial program 17.3

   \[\]

2. Taylor expanded around 0 0.4

   \[\leadsto \]

3. Simplified 0.4

   \[\leadsto \]
4. Using strategy rm

5. Applied associate-*l* 0.4

   \[\leadsto \]
6. Using strategy rm

7. Applied pow1 0.4

   \[\leadsto \]

8. Applied pow1 0.4

   \[\leadsto \]

9. Applied pow-prod-down 0.4

   \[\leadsto \]

10. Applied pow1 0.4

    \[\leadsto \]

11. Applied pow-prod-down 0.4

    \[\leadsto \]

12. Simplified 0.4

    \[\leadsto \]

13. Final simplification 0.4

    \[\leadsto \]

Reproduce

herbie shell --seed 2020181 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U))