Average Error: 15.4 → 1.4
Time: 5.0s
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 r159791 = K;
        double r159792 = m;
        double r159793 = n;
        double r159794 = r159792 + r159793;
        double r159795 = r159791 * r159794;
        double r159796 = 2.0;
        double r159797 = r159795 / r159796;
        double r159798 = M;
        double r159799 = r159797 - r159798;
        double r159800 = cos(r159799);
        double r159801 = r159794 / r159796;
        double r159802 = r159801 - r159798;
        double r159803 = pow(r159802, r159796);
        double r159804 = -r159803;
        double r159805 = l;
        double r159806 = r159792 - r159793;
        double r159807 = fabs(r159806);
        double r159808 = r159805 - r159807;
        double r159809 = r159804 - r159808;
        double r159810 = exp(r159809);
        double r159811 = r159800 * r159810;
        return r159811;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r159812 = 1.0;
        double r159813 = m;
        double r159814 = n;
        double r159815 = r159813 + r159814;
        double r159816 = 2.0;
        double r159817 = r159815 / r159816;
        double r159818 = M;
        double r159819 = r159817 - r159818;
        double r159820 = pow(r159819, r159816);
        double r159821 = l;
        double r159822 = r159813 - r159814;
        double r159823 = fabs(r159822);
        double r159824 = r159821 - r159823;
        double r159825 = r159820 + r159824;
        double r159826 = exp(r159825);
        double r159827 = r159812 / r159826;
        return r159827;
}

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 15.4

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

  2. Simplified15.4

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020018 
(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)))))))