Average Error: 15.1 → 1.3
Time: 48.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}\]
\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(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}
double f(double K, double m, double n, double M, double l) {
        double r9834773 = K;
        double r9834774 = m;
        double r9834775 = n;
        double r9834776 = r9834774 + r9834775;
        double r9834777 = r9834773 * r9834776;
        double r9834778 = 2.0;
        double r9834779 = r9834777 / r9834778;
        double r9834780 = M;
        double r9834781 = r9834779 - r9834780;
        double r9834782 = cos(r9834781);
        double r9834783 = r9834776 / r9834778;
        double r9834784 = r9834783 - r9834780;
        double r9834785 = pow(r9834784, r9834778);
        double r9834786 = -r9834785;
        double r9834787 = l;
        double r9834788 = r9834774 - r9834775;
        double r9834789 = fabs(r9834788);
        double r9834790 = r9834787 - r9834789;
        double r9834791 = r9834786 - r9834790;
        double r9834792 = exp(r9834791);
        double r9834793 = r9834782 * r9834792;
        return r9834793;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r9834794 = 1.0;
        double r9834795 = l;
        double r9834796 = m;
        double r9834797 = n;
        double r9834798 = r9834796 - r9834797;
        double r9834799 = fabs(r9834798);
        double r9834800 = r9834795 - r9834799;
        double r9834801 = r9834796 + r9834797;
        double r9834802 = 2.0;
        double r9834803 = r9834801 / r9834802;
        double r9834804 = M;
        double r9834805 = r9834803 - r9834804;
        double r9834806 = r9834805 * r9834805;
        double r9834807 = r9834800 + r9834806;
        double r9834808 = exp(r9834807);
        double r9834809 = r9834794 / r9834808;
        return r9834809;
}

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

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019104 
(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)))))))