Average Error: 15.2 → 1.3
Time: 21.5s
Precision: binary64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\log \left({\left(e^{\cos \left(\frac{\frac{K \cdot \log \left(\frac{e^{m \cdot m}}{e^{n \cdot n}}\right)}{m - n}}{2} - M\right)}\right)}^{\left(e^{\left|m - n\right| - \left(\ell + {\left(\frac{m + n}{2} - M\right)}^{2}\right)}\right)}\right)\]
\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)}
↓
\log \left({\left(e^{\cos \left(\frac{\frac{K \cdot \log \left(\frac{e^{m \cdot m}}{e^{n \cdot n}}\right)}{m - n}}{2} - M\right)}\right)}^{\left(e^{\left|m - n\right| - \left(\ell + {\left(\frac{m + n}{2} - M\right)}^{2}\right)}\right)}\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
 (log
  (pow
   (exp
    (cos
     (- (/ (/ (* K (log (/ (exp (* m m)) (exp (* n n))))) (- m n)) 2.0) M)))
   (exp (- (fabs (- m n)) (+ l (pow (- (/ (+ m n) 2.0) M) 2.0)))))))
double code(double K, double m, double n, double M, double l) {
	return cos(((K * (m + n)) / 2.0) - M) * exp(-pow((((m + n) / 2.0) - M), 2.0) - (l - fabs(m - n)));
}
↓
double code(double K, double m, double n, double M, double l) {
	return log(pow(exp(cos((((K * log(exp(m * m) / exp(n * n))) / (m - n)) / 2.0) - M)), exp(fabs(m - n) - (l + pow((((m + n) / 2.0) - M), 2.0)))));
}

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 15.2

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

  2. Simplified15.2

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

  4. Applied add-log-exp_binary64_114015.3

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

  5. Simplified1.2

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

  7. Applied flip-+_binary64_10751.2

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

  8. Applied associate-*r/_binary64_10431.2

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

  10. Applied add-log-exp_binary64_11401.3

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

  11. Applied add-log-exp_binary64_11401.3

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

  12. Applied diff-log_binary64_11931.3

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

  13. Final simplification1.3

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

Reproduce

herbie shell --seed 2021075 
(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)))))))