Maksimov and Kolovsky, Equation (4)

Average Error: 17.0 → 0.4

Time: 7.3s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus J

Bits error versus l

Bits error versus K

Bits error versus U

Derivation

1. Initial program 17.0

   \[\]

2. Simplified 17.0

   \[\leadsto \]

3. Taylor expanded around 0 0.4

   \[\leadsto \]

4. Simplified 0.4

   \[\leadsto \]
5. Using strategy rm

6. Applied associate-*r* 0.4

   \[\leadsto \]

7. Simplified 0.4

   \[\leadsto \]

8. Final simplification 0.4

   \[\leadsto \]

Reproduce

herbie shell --seed 2020179 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (neg l)))) (cos (/ K 2.0))) U))