Average Error: 14.8 → 1.4
Time: 28.5s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}\]
\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(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}
double f(double K, double m, double n, double M, double l) {
        double r1769864 = K;
        double r1769865 = m;
        double r1769866 = n;
        double r1769867 = r1769865 + r1769866;
        double r1769868 = r1769864 * r1769867;
        double r1769869 = 2.0;
        double r1769870 = r1769868 / r1769869;
        double r1769871 = M;
        double r1769872 = r1769870 - r1769871;
        double r1769873 = cos(r1769872);
        double r1769874 = r1769867 / r1769869;
        double r1769875 = r1769874 - r1769871;
        double r1769876 = pow(r1769875, r1769869);
        double r1769877 = -r1769876;
        double r1769878 = l;
        double r1769879 = r1769865 - r1769866;
        double r1769880 = fabs(r1769879);
        double r1769881 = r1769878 - r1769880;
        double r1769882 = r1769877 - r1769881;
        double r1769883 = exp(r1769882);
        double r1769884 = r1769873 * r1769883;
        return r1769884;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1769885 = 1.0;
        double r1769886 = n;
        double r1769887 = m;
        double r1769888 = r1769886 + r1769887;
        double r1769889 = 2.0;
        double r1769890 = r1769888 / r1769889;
        double r1769891 = M;
        double r1769892 = r1769890 - r1769891;
        double r1769893 = r1769892 * r1769892;
        double r1769894 = l;
        double r1769895 = r1769893 + r1769894;
        double r1769896 = r1769887 - r1769886;
        double r1769897 = fabs(r1769896);
        double r1769898 = r1769895 - r1769897;
        double r1769899 = exp(r1769898);
        double r1769900 = r1769885 / r1769899;
        return r1769900;
}

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 14.8

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

  2. Simplified14.8

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019153 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))