Average Error: 15.5 → 1.5
Time: 5.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r114198 = K;
        double r114199 = m;
        double r114200 = n;
        double r114201 = r114199 + r114200;
        double r114202 = r114198 * r114201;
        double r114203 = 2.0;
        double r114204 = r114202 / r114203;
        double r114205 = M;
        double r114206 = r114204 - r114205;
        double r114207 = cos(r114206);
        double r114208 = r114201 / r114203;
        double r114209 = r114208 - r114205;
        double r114210 = pow(r114209, r114203);
        double r114211 = -r114210;
        double r114212 = l;
        double r114213 = r114199 - r114200;
        double r114214 = fabs(r114213);
        double r114215 = r114212 - r114214;
        double r114216 = r114211 - r114215;
        double r114217 = exp(r114216);
        double r114218 = r114207 * r114217;
        return r114218;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r114219 = 1.0;
        double r114220 = m;
        double r114221 = n;
        double r114222 = r114220 + r114221;
        double r114223 = 2.0;
        double r114224 = r114222 / r114223;
        double r114225 = M;
        double r114226 = r114224 - r114225;
        double r114227 = pow(r114226, r114223);
        double r114228 = l;
        double r114229 = r114220 - r114221;
        double r114230 = fabs(r114229);
        double r114231 = r114228 - r114230;
        double r114232 = r114227 + r114231;
        double r114233 = exp(r114232);
        double r114234 = r114219 / r114233;
        return r114234;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.5

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

  4. Final simplification1.5

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

Reproduce

herbie shell --seed 2020020 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))