Average Error: 15.1 → 1.3
Time: 7.3s
Precision: binary64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}\]
\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
↓
e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}
(FPCore (K m n M l)
 :precision binary64
 (*
  (cos (- (/ (* K (+ m n)) 2.0) M))
  (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))
↓
(FPCore (K m n M l)
 :precision binary64
 (exp (- (fabs (- m n)) (+ (pow (- (/ (+ m n) 2.0) M) 2.0) l))))
double code(double K, double m, double n, double M, double l) {
	return ((double) (((double) cos(((double) ((((double) (K * ((double) (m + n)))) / 2.0) - M)))) * ((double) exp(((double) (((double) -(((double) pow(((double) ((((double) (m + n)) / 2.0) - M)), 2.0)))) - ((double) (l - ((double) fabs(((double) (m - n))))))))))));
}
↓
double code(double K, double m, double n, double M, double l) {
	return ((double) exp(((double) (((double) fabs(((double) (m - n)))) - ((double) (((double) pow(((double) ((((double) (m + n)) / 2.0) - M)), 2.0)) + l))))));
}

Error

Bits error versus K

Bits error versus m

Bits error versus n

Bits error versus M

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

    \[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

  2. Simplified15.1

    \[\leadsto \color{blue}{\cos \left(K \cdot \frac{m + n}{2} - M\right) \cdot e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}}\]

  3. Taylor expanded around 0 1.3

    \[\leadsto \color{blue}{1} \cdot e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}\]

  4. Final simplification1.3

    \[\leadsto e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}\]

Reproduce

herbie shell --seed 2020198 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))