Maksimov and Kolovsky, Equation (32)

Average Error: 15.3 → 1.3

Time: 10.1s

Precision: binary64

Math

\[\]

↓

\[\]

Error

Bits error versus K

Bits error versus m

Bits error versus n

Bits error versus M

Bits error versus l

Derivation

1. Initial program 15.3

   \[\]

2. Simplified 15.3

   \[\leadsto \]

3. Taylor expanded around 0 1.3

   \[\leadsto \]

4. Final simplification 1.3

   \[\leadsto \]

Reproduce

herbie shell --seed 2020191 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (neg (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))